Aditi, Devika, Lorraine Basudeb

Anna Bérénice

Crem

Gabin

Clément

Ons, May, Guigui Nico Guillaume

Anne Guillaume

Isa Dawa

Anna Geb

Sarah Kereoz

Avant toutes choses je tiens à remercier Benoît Tarroux d'avoir accepté de diriger cette thèse, pour sa disponibilité, son soutien et ses conseils qui ont été nombreux et importants. C'est avec beaucoup de reconnaissance et de fierté que je termine ma thèse sous sa direction. J'adresse ´egalement mes remerciements aux membres du jury : Catherine Baumont et Yannick L'Horty qui ont accepté la tâche fastidieuse qu'est de rapporter une thèse. Merci également à Isabelle Lebon et Fabien Moizeau d'avoir accepte ´ de rejoindre ce jury. Je remercie aussi Yvon Rocaboy et les membres du CREM pour les nombreuses discussions qui ont pu m'aider à avancer dans mon travail. Beaucoup de personnes seraient à citer, mais je remercie tout particulièrement Isabelle Vialle, pour ses précieuses relectures et Fabien Moizeau pour ses conseils

Introduction Générale

Les questions d'identité et d'intégration sont au coeur du débat public en France. De nombreuses polémiques ont vu le jour concernant les phénomènes identitaires qui peuvent conduire à la séparation des individus et entraîner des situations de ségrégation. Il n'est donc pas étonnant que les chercheurs en sciences sociales, et notamment les économistes, s'emparent de ces questions. Cette thèse porte sur l'étude des phénomènes de ségrégation urbaine, c'est à dire l'isolement à la fois social et spatial des groupes d'individus au sein des villes. L'objet de cette thèse est à l'intersection de l'étude de la ségrégation urbaine et de la prise en compte de l'identité dans la compréhension des phénomènes et interactions économiques.

1 Etat des lieux de la ségrégation en France Du latin segregare qui signifie écarter du troupeau le terme de ségrégation implique l'idée d'une mise à l'écart d'un ou plusieurs individus. Dans le langage courant actuel la ségrégation décrit une "organisation de l'espace en zones à forte homogénéité sociale interne et à fortes disparités sociales entre elles" [START_REF] Castells | La question urbaine[END_REF]). La ségrégation peut être institutionnalisée ou le résultat de multiples décisions individuelles. Cette division peut se réaliser sur la base de la catégorie sociale, du revenu ou de l'origine (c'est par exemple le cas des migrants). Analyser les phénomènes de ségrégation nécessite d'identifier les groupes sociaux sur lesquels le processus de division s'appuie. Cette question a été étudiée par les sciences sociales. De nombreux travaux se sont attachés a étudier les causes, les conséquences et à mesurer l'ampleur du phénomène de ségrégation. Par exemple, les travaux des sociologues de l'école de sociologie de Chicago, datant du début du XXème siècle, se sont centrées sur les questions de ségrégation ethnique, à savoir la division des populations afro-américaines et blanches dans les grandes villes américaines.

Le phénomène de ségrégation n'est pas un fait nouveau, au contraire, depuis que les villes existent la différentiation socio-spatiale de leurs quartiers semble bien être la norme, comme le souligne la citation de Platon en préambule de cette thèse. Les exemples les 1 Introduction Générale plus connus de ségrégation sont le cas de l'apartheid mise en place en Afrique du sud à partir de 1948 ou bien encore de la ségrégation raciale aux Etats Unis faisant suite à la guerre de sécession. En France, l'exemple de phénomène de ségrégation le plus criant est celui des banlieues où se concentrent les difficultés économiques et sociales. Si la ségrégation a parfois été institutionnalisée, elle résulte aujourd'hui le plus souvent de l'interaction de choix individuels. [START_REF] Préteceille | La ségrégation sociale a-t-elle augmenté ?[END_REF] qui étudie la ségrégation selon les classes sociales montre que les classes sociales les plus privilégiées sont plus ségrégées que les classes sociales populaires. L'existence, réelle ou supposée, d'externalités de voisinage conduit les individus à développer des stratégies de localisation et à choisir soigneusement leur lieu de résidence. L'éducation peut être un moteur des stratégies d'évitement.

En effet, les parents recherchent pour leurs enfants l'environnement social et éducatif le plus favorable à leur éducation et leur développement : on recherche les "meilleures" écoles ou celles qui ont la meilleure réputation, de même que des quartiers les plus calmes ou peuplés de familles favorisées. L'enfant pourra alors profiter d'un effet de pair ou d'entrainement positif (complémentarité stratégique en termes économiques). Les catégories sociales favorisées fuient alors les catégories sociales moyennes, elles-mêmes fuyant les familles les plus défavorisées. Ceci a bien été renseigné par la littérature économique. Dans son ouvrage le ghetto français , [START_REF] Maurin | Le ghetto français[END_REF] étudie les phénomènes de ségrégation résidentielle en France. Il montre que les phénomènes de ségrégation ne se limitent pas aux banlieues enclavées mais au contraire correspondent à un phénomène qui touche toutes les classes sociales par des mécanismes de recherche de l'entre-soi, notamment il met en lumière l'existence de ghettos riches où les classes plus aisées de la société se regroupent. Par ailleurs, [START_REF] Benabou | Workings of a city : location, education, and production[END_REF] montre que les externalités locales d'éducation, à travers les effets de pairs, poussent les travailleurs qualifiés à ne pas résider à côté de travailleurs non qualifiés. Ces stratégies d'évitement sont renforcées par l'existence de la carte scolaire qui affecte les élèves dans une école selon leur lieu de domiciliation (Fack loi impose en outre aux communes importantes de disposer d'au moins 20% de logements sociaux. La mise en place de ces politiques publique implique de disposer d'outils de mesure du phénomène de ségrégation afin d'en caractériser l'ampleur et l'évolution.

En France cependant ces études restent rares, elles sont notamment marquées par le biais américain et s'intéressent à la mesure de la ségrégation catégorielle. Certaines études se sont par exemple intéressées à la ségrégation ethnique des immigrés en France [START_REF] Verdugo | Public housing and residential segregation of immigrants in france[END_REF], [START_REF] Safi | La dimension spatiale de l'intégration : évolution de la ségrégation des populations immigrées en france entre 1968 et[END_REF], Pan Ké Shon (2010)), elles montrent que les populations immigrées faisant le plus l'objet d'une ségrégation importante sont les maghrébins, les africains subsahariens, les turcs et les asiatiques. Elles montrent également que sur une période longue D'autre part, les phénomènes de ségrégation sont liés à l'existence de groupes sociaux.

S'intéressant à l'identité sociale, [START_REF] Tajfel | An integrative theory of intergroup conflict[END_REF] développent le paradigme du groupe minimal selon lequel les individus privilégient les membres de leurs groupes, même si ces groupes sont artificiellement créés. Ces auteurs avait mené une étude auprès d'adolescents où des groupes avaient été créés sur la base de critères arbitraires. Le principal résultat est que les sujets discriminaient positivement les membres de leurs groupes.

Le fait que les individus discriminent selon les groupes sociaux peut avoir d'importantes répercussions économiques et sociales, non seulement sur le plan individuel mais également à l'échelle des quartiers d'une ville. C'est pourquoi les questions d'identité représentent une question majeure de politiques publiques. Dans une étude menée dans la ville de Zurich, [START_REF] Falk | Discrimination and in-group favoritism in a citywide trust experiment[END_REF] ont montré qu'ils existaient des phénomènes de discrimination selon le quartier de résidence des individus. Au sein de cette ville, les participants montraient des niveaux de confiance plus faibles envers les individus résidant dans des quartiers plus ségrégés. Ce résultat implique des conséquences importantes en termes de politiques publiques, notamment les individus peuvent être discriminés dans l'accès à l'emploi simplement parce qu'ils habitent des quartiers différents dans la ville.

De plus, cette absence de confiance menace les intéractions socio-économiques et peut contribuer à accélérer les processus de ségrégation dans la ville.

Dans le chapitre 3 nous nous intéressons à ces questions et nous étudions les effets de la ségrégation urbaine sur les préférences des individus, notamment sur le degré de confiance aux autres. Ce chapitre vise à étudier les liens existants entre l'environnement social des individus, notamment leur quartier de résidence, et leur degré de coopération et de confiance aux autres. Nous avons menée une étude expérimentale dans plusieurs collèges rennais en proposant à des collégiens de troisième de participer à des jeux de confiance. Nous nous intéressons à des collégiens afin de réduire les problèmes d'endogénéité possibles dans la mesure où les adolescents ne choisissent pas leur lieu de résidence, celui-ci ne dépend donc pas de leurs préférences individuelles. Ces expériences visent à répondre aux questions suivantes : -Comment le contexte social, et notamment le degré de mixité sociale, agit sur le niveau de confiance des individus ? -Le degré de confiance en l'autre est-il influencé par l'identité de son partenaire (en outre, si celui-ci vient du même collège que lui ou non)

Introduction

Sociologists as well as economists have focused more attention in recent years on important effects of segregation, arguing that this residential space crystallizes interactions that influence individual preferences, skills, children's attitude or the choice of school (see, for instance, [START_REF] Cutler | Are ghettos good or bad ?[END_REF], [START_REF] Cutler | When are ghettos bad ? lessons from immigrant segregation in the united states[END_REF], [START_REF] Echenique | Is school segregation good or bad ?[END_REF], [START_REF] Goux | Close neighbours matter : Neighbourhood effects on early performance at school*[END_REF]).

The literature dealing with measures of segregation developed many indicators in order to undertake analyses of categorical segregation, that is, the distribution of people across categories (see for instance [START_REF] Duncan | A methodological analysis of segregation indexes[END_REF], [START_REF] Massey | The dimensions of residential segregation[END_REF], [START_REF] Reardon | Measures of spatial segregation[END_REF],R. M. [START_REF] Hutchens | Segregation curves, lorenz curves, and inequality in the distribution of people across occupations[END_REF],R. [START_REF] Hutchens | Numerical measures of segregation : desirable properties and their implications[END_REF],R. [START_REF] Hutchens | One measure of segregation*[END_REF] or [START_REF] Chakravarty | A generalized index of employment segregation[END_REF]). The occupational segregation of men and women and the residential segregation of white and black population in cities are the most popular examples of categorial segregation.

Chapitre 1 : Income segregation in large French cities Surprisingly, residential segregation by income have not been extensively studied by the literature (notable exceptions are [START_REF] Hardman | Neighbors' income distribution : economic segregation and mixing in us urban neighborhoods[END_REF], [START_REF] Jargowsky | Take the money and run : economic segregation in us metropolitan areas[END_REF], [START_REF] Ioannides | Neighborhood wealth distributions[END_REF], [START_REF] Hardman | Neighbors' income distribution : economic segregation and mixing in us urban neighborhoods[END_REF], [START_REF] Davidoff | Income sorting : Measurement and decomposition[END_REF] or [START_REF] Watson | Inequality and the measurement of residential segregation by income in american neighborhoods[END_REF]).

By residential segregation by income, we mean the way by which individuals who can be described by their income are broken down among local areas of a city. [START_REF] Jargowsky | Take the money and run : economic segregation in us metropolitan areas[END_REF] proposed a measure of economic segregation, defined as pure. This measure, which Jargowsky referred to, is the Neighbourhood Sorting Index (NSI), simply defined as the square root of the ratio of the variance of neighbourhoods' mean incomes over the overall variance. Defining the information theory of segregation, [START_REF] Jargowsky | A measure of spatial segregation : The generalized neighborhood sorting index[END_REF], stated that all measures of inequality and all measures of segregation are united within a broader and single framework. This framework helps them to define new measures of segregation and to implement well known measures to continuous variables.

Furthermore, they derive several properties that should be satisfied by the common measures of inequality and segregation. The inequality ratio property states that there exists a segregation measure for any inequality index, which is based on the ratio of the income inequality measured at the group level and the overall income inequality. The pure measure property states that a measure of segregation must satisfy the inequality ratio property to be valid. The one-to-one relationship between inequality and segregation measures suggests that "a measure of inequality that can be applied to either binary or continuous variables generates a measure of segregation that can be applied to either binary or continuous variables."

The aim of this chapter is to examine theoretically and empirically the family of segre- Neighbourhood Sorting Index (NSI) as defined by [START_REF] Jargowsky | Take the money and run : economic segregation in us metropolitan areas[END_REF], and a segregation index based on the Gini index, namely the Gini Segregation Index (GSI). We perform this analysis using households' income and their distribution within the residential space from several scales : IRIS and Grand Quartier. The main result is that residential segregation by income has decreased over the period considered. Furthermore, we show that the economic segregation in French cities is scale dependent and is not related with income inequality as measured by Gini coefficient. This performed empirical investigation proves that these measures are very appealing for applied analysis : it does not demand prohibitive dataset and it can draw a picture that is somewhat different from the one depicted by inequality measures.

gation
The remainder of the chapter is structured as follows. The next section is devoted to the notion of residential segregation by income. The following section defines formally the family of segregation measures and in particular the NSI as well as the GSI, and explores the properties satisfied by this family of segregation measures The use of these two measures as part of the measurement of the segregation of large French cities is undertaken in section 4. The final part concludes.

Measuring residential segregation by income

We consider cities where each individual is endowed with income and is located in a given area. A city is populated by n individuals from some finite set N = {1, ..., i, ..., n}.

Let's assume also that this city is made up of m geographical areas (or, more generally, of m subgroups) and populated by n j individuals, and define M the finite set of areas of the city, M = {1, ...j, ..., m}. This city can be defined by two elements : (1) a distribution of income among the population and (2) a partition of the population between the m Chapitre 1 : Income segregation in large French cities geographical areas of the city. Assuming that incomes are drawn from an interval D of R, the overall income distribution of the population can be described by a vector :

Y = (y 1 , ..., y i , ..., y n )
where y i is the income of the individual i. The breakdown of individuals into a set of areas is described by a partition P of the population within a set of m mutually exclusive and exhaustive subsets (areas). We use P to represent the set of all possible partitions, P = N 1 , ..., N m , where N j is the set of individuals living in area j. The income distribution within area j ∈ M is given by the vector Y j = y j 1 , ..., y j i , ..., y j n j where y j i is the income of individual i living in area j. A city can be thus depicted by a pair (P, Y ) ∈ P × D n .

By simplicity, we can described the overall income distribution of the population as :

Y = (Y 1 , ..., Y m ) = y 1 1 , .., y 1 n 1 , y 2 1 , ..., y m n m
Let µ denote the mean income of the city and µ j the mean income of the area j.

The index studied in this chapter is based on the decomposition of an inequality index between within-group and between-group components. [START_REF] Jargowsky | The information theory of segregation : Uniting segregation and inequality in a common framework[END_REF] argue that there exists a segregation measure for any inequality index and this measure is based on the ratio of the income inequality measured at the group level and the overall income inequality (the inequality ratio property). For an inequality index I :

D n → R,
a segregation index, denoted by S I : P × D n → R, can be thus defined by :

S I (P, Y ) = I(Y µ ) I(Y ) (1.1)
where Y µ is the hypothetical income distribution such that each individual receives the mean income of his area, that is, Y µ = (µ 1 1 n 1 , ..., µ m 1 n m ) where 1 n j is the vector of dimension n j × 1 where each element is equal to 1. We may require that the inequality index we select respects some desirable properties : symmetry, replication invariance (i.e., Dalton population principle) and Pigou-Dalton principle of progressive transfers.

Subgroup decomposability property 1 is not necessary for segregation index to respect some desirable properties. However the property of the inequality index is useful if we want that S I (P, Y ) values belong to the interval [0, 1].

Proposition 1.1 (Normalisation). :

i. If the distribution of mean incomes Y µ is of the form Y µ = (c1 n 1 , ..., c1 n m ) where c is a scalar, then S I (P, Y ) = 0.

1. Subgroup decomposability imposes that the inequality index can be written as follows :

I(Y ) = j f I(Y j ) + I(Yµ).
ii. Assume that I is additively decomposable by subgroups. If the distribution of mean incomes Y µ is such that y p i = µ p for all i ∈ N p and µ p = µ q for p = q ∈ M , then S I (P, Y ) = 1.

Segregation under movements

The starting point of our analysis is the evaluation of segregation when the only change is movement(s) of individual(s) among areas given that there is no change in the income distribution. In other words how can we reduce segregation (or improve social mixing) only by movements of individuals within the city ? Consider the following examples. (1, 2, 3; 8, 9, 10).

Example 1. Consider the following income distribution

: Y = (Y 1 , Y 2 ) =
The richest individual of area 2 moves to area 1 ; the new situation is then : (1, 2, 3, 10; 8, 9). Our intuition is that Y is less segregated than Y .

Y = ( Y 1 , Y 2 ) =
Example 2. Consider now that the richest individual of area 2 moves to area 1 while one individual changes also his location. The new situation is then : (1, 2, 10; 3, 8, 9). According to our intuition such movements reduce segregation. means of movement of one individual if there exists an area q such that :

Y = ( Y 1 , Y 2 ) =
(a) N p = N p / {k} (b) N q = N q ∪ {k} (c) Y = Y for all = p, q
We might rewrite conditions (a) and (b) of the previous definition in terms of areas' income distributions. These conditions are equivalent, respectively, to :

(a') Y p = y p 1 , ..., y p k-1 , y p k+1 , ..., y p n p (b') Y q = y q 1 , ..., y q n q , y p k
The following proposition describes the link between unilateral movement and change in segregation as measured by our family of indices :

Proposition 1.3 (Segregation under unilateral movement). :

Let (P, Y ) and ( P , Y ) two cities such that ( P , Y ) is obtained from (P, Y ) by a movement of individual k from area p to q. Assuming that I respects the Pigou-Dalton principle of progressive transfer, the following cases can be considered :

i. If y p k > µ p > µ q or µ q > µ p > y p k , then : S I (P, Y ) > S I ( P , Y ). ii. If y p k > µ q > µ p or µ p > µ q > y p k , then : S I (P, Y ) < S I ( P , Y ). (See appendix for the proof ).

The intuition behind this proposition is quite obvious. Any emigration of an individual who is richer than the mean incomes of his initial area and of his new one reduces the gap between mean incomes. Inequality between areas is then lower. We can see by the same token that any emigration of a poor individual from a poor to a rich area reduces also between-areas inequality.

Another transformation is the switch of two individuals, which consists in two simultaneous movements of a rich and a poor individuals.

(a) N p = N p /{k} ∪ {h} (b) N q = N q /{h} ∪ {k}
This transformation can also be interpreted as an exchange of income between two individuals who are located in two different areas and can thus be expressed in terms of areas' income distributions. The two conditions of the definition 1.4 might be substituted by the following conditions :

(a') y p k = y q h (b') y q h = y p k (c') y j i = y j i for j = p, q and i = k, h (d') y j i = y j i for all j = p, q and i = 1, ..., n j

The following proposition describes how a switch affects our segregation measure.

Proposition 1.5 (Segregation under switch). :

Let (P, Y ) and ( P , Y ) two cities such that ( P , Y ) is obtained from (P, Y ) by a switch of two individuals k and h between areas p and q. Assuming that I respects the Pigou-Dalton principle of progressive transfer, the following cases can be considered :

i. If y p k < y q h and µ p < µ q , then : S I (P, Y ) > S I ( P , Y ). ii. If y p k < y q h and µ p > µ q , then : S I (P, Y ) < S I ( P , Y ).

iii. In other cases, such a switch has no clear implication.

(See appendix for the proof ).

A switch of two individuals will decrease our segregation measure if the richest individual is originally located in the richest area and the poorest one in the poorest area. This bilateral movement results in a transfer of mean income from the richest to the poorest area. Since our measure of segregation is based on an inequality index respecting the principle of progressive transfer, I(Y µ ) will decrease and segregation measure S I will also decrease. The same type of reasoning can apply when the richest individual is originally located in the poorest area and the poorest one in the richest area.

Segregation under income transfers

We consider now the impact of a transformation of the income distribution on the NSI given that the partition of the population between areas remains the same. In the measurement of income inequality, an elementary transformation is the Pigou-Dalton principle of transfer which states that a transfer of income from a rich individual to a poorer one reduces inequality.

Example 3. Consider the following income distribution : 10, 15, 21 ; 17, 25, 30).

Y = (Y 1 , Y 2 ) = (
Transferring income between two individuals in the richest area modifies the income distribution as follows : (10, 15, 21 ; 22, 25, 25). While inequality decreases, the richest area becomes more homogeneous in terms of income and the overlapping of areas' income distributions disappears. Indeed, the richest individual of the poorest area is now poorer than the poorest individual of the richest area. Our intuition is that Y is less segregated than Y .

Example 4. Weigh up now the case of a regressive transfer in the richest area that leads to the following modified income distribution : (10, 15, 21 ; 12, 30, 30). The final situation could be evaluated as better in terms of segregation since the social mixing has been increased and the overlapping of the distribution is higher.

A progressive transfer may then be not so relevant in the assessment of economic segregation of a city all the more so as such transfer occurs within the same area. We study the case of an income transfer between two individuals located in the same area, namely a within-area income transfer. Chapitre 1 : Income segregation in large French cities (a) y p h = y p h + δ and y p k = y p k -δ (b) y j i = y j i for j = p and i = k, h and y j i = y j i for all j = p and i ∈ N j

The question we study now is to ascertain conditions for which a transfer reduces or worsens segregation. A progressive transfer reduces discrepancy of income in a given area and in the overall city but inequality between mean incomes is not affected by such an income transfer. We resume in the following proposition the main implications of a within-area income transfer when the initial level of segregation is not zero. This proposition says that increasing overall inequality among individuals reduces segregation if increasing overall inequality does not lead to increase inequality among areas mean incomes. That illustrates the conflict, which may exist between segregation by income and income inequality. Another interpretation is that segregation is evaluated in relation to overall inequality. More precisely, segregation is inequality among areas once overall inequality is neutralized. From a "pure" perspective, segregation is a problem of allocation of individuals among areas given the income distribution. Such an approach is however unable to compare cities with different levels of inequality (as measured by an appropriate index). To illustrate this point, consider the following cities : Y = (1, 2, 3; 3, 4, 5) and Y = (2, 2, 2; 3, 4, 5). It is not possible to derive Y from Y by any movement of individual(s) between the two areas ; the difference between Y and Y lies in different income distributions.

Finally it is worth noting that the value of segregation measure S I remains the same if the city is initially perfectly mixed (S I = 0). If all individuals have the same income (i.e., I(Y ) = 0 and thus I(Y µ ) = 0), it is obvious that we are not able to perform progressive income transfer and a regressive transfer leaves unchanged I(Y µ ). If all areas have the same mean income (i.e., I(Y µ ) = 0), there is no segregation as measured by S I and, then, internal transfer leaves segregation unchanged. Consider the following city : (1, 1, 10; 4, 4, 4) for which S I = 0 since I(Y µ ) = 0. If we transfer income from the rich individual to one of the two poor ones in the first area, the S I value does not increase since the inequality between areas remains the same. The same observation can be made when we consider a transfer from a poor to the rich in the first area. It means that the change in the S I value following a within-area transfer depend on the gap between the mean incomes. We may undoubtedly consider this type of dis-continuity as a theoretical weakness of our segregation measure (1.1). However from empirical perspective, it may not be so problematic since the probability of S I = 0 is certainly very low.

Sensitivity to areas definition

The previous properties presented above assume spatial partition as given : it may be purely arbitrary or conversely based on geographical or urban meaningful characteristics. We now study how segregation index (1.1) is sensitive to the spatial partition of a given urban area. To illustrate the problem, let consider the following example.

Example 5 Consider the following income distribution : (1, 2, 3 ; 5, 6, 7 ; 8, 9, 10).

Y = (Y 1 , Y 2 , Y 3 ) =
Consider that the first and third areas merge : (1, 2, 3, 8, 9, 10 ; 5, 6, 7).

Y = ( Y 1 , Y 2 ) =
It is intuitive to say that there is more social mixing or less segregation in Y than in Y since poor people mix with rich people in the new first area.

Jargowsky pointed out that the NSI does not capture the important physical dimensions of segregation. With the next property, we investigate the variability of the NSI with respect to the definition of area unit. Aggregation of areas consists in merging two areas into a unique area. Definition 1.8. Areas aggregation.

Let (P, Y ) and ( P , Y ) two cities such that ( P , Y ) is obtained from (P, Y ) by means of an aggregation of areas p and q if for P = N 1 , ..., N p , ..., N q , ..., N m and P = N 1 , ..., N m-1 :

(a) N j = N j ∀j < q, j = p and

N j = N j-1 ∀j > q (b) N p ∪ N q = N p
The next proposition considers sensitivity of our segregation measure to aggregation of areas : If merged areas have the same mean income, there is no change in segregation according to the S I . However, if one merges two areas with different mean incomes, the aggregation increases income heterogeneity within areas and decreases the variability in mean incomes. (See appendix for the proof ).

In other words, this property states that the S I does not decrease when the number of areas increases ; because the inequality between mean incomes can not decrease. 2 As [START_REF] Shorrocks | Spatial decomposition of inequality[END_REF] have showed, the expected value of between-component of any inequality measure increases with the number of areas.

Even though the S I fails to account for spatial patterning of areas 3 , this property might help to give a picture of spatial segregation. Indeed, it is sensitive to the definition of the boundaries of areas and assumes that each individual lives near all individuals of his area and far from individuals located in another area (even across the street from one another). Consider two sets of areas' boundaries, P and P , such that P is obtained from P by a finite set of adjacent areas aggregation. In other words, we consider two partitions of individuals among areas, P = N 1 , ..., N m and P = N 1 , ..., N , such that N j is the union of two or more adjacent (sub)areas N k (with k ∈ {1, ..., m}) for all j ∈ {1, ..., }. If the segregation index takes the same value whatever the partition P and P , it means that areas are adjacent to similar areas (in terms of mean income).

On the contrary, the larger difference between the two values taken by the segregation index is, the more areas are heterogeneous. This reasoning holds comparing two cities.

Consider two cities with the same value of S I for the finest areas division. If the value of S I differs according to a different partition, then a city has more homogeneous grouping of sub-areas and is thus more spatially segregated.

Economic segregation in French urban areas

The residential segregation has been discussed among the social scientists and in the public debate for more than twenty years. By studying changes in social class and income composition of the close neighbourhoods, [START_REF] Maurin | Le ghetto français[END_REF] shows that income segregation has been stable over the period from 1991 to 2002. [START_REF] Préteceille | La ségrégation sociale a-t-elle augmenté ?[END_REF] studies the geographical breakdown of social classes in Paris urban area by using the dissimilarity index.

The author shows that the most privileged social classes are more segregated than the 2. One might be interested in considering the case of area division rather than areas aggregation. Obviously, if the division is such that the two new areas have the same mean income, segregation remains the same ; because variability in mean incomes is the same before and after the division. But segregation becomes worse if the division of the area allows a sorting of individuals with respect to income.

3. In particular, the checkerboard problem and the modifiable areal unit problem are ignored by such indices. See for example [START_REF] White | The measurement of spatial segregation[END_REF], [START_REF] Reardon | Measures of spatial segregation[END_REF] and [START_REF] Jargowsky | A measure of spatial segregation : The generalized neighborhood sorting index[END_REF]. popular categories. White-collar workers 4 and executive employees 5 tend to be less segregated in 1999 than in 1990. Contrarily, segregation has increased between 1990 and 1999 for the blue-collar workers. Recently, some papers investigate the segregation of immigrants or ethnic segregation (see for instance [START_REF] Verdugo | Public housing and residential segregation of immigrants in france[END_REF][START_REF] Safi | La dimension spatiale de l'intégration : évolution de la ségrégation des populations immigrées en france entre 1968 et[END_REF] or Pan Ké Shon ( 2010)). Our study complement these empirical investigations by studying how income segregation has changed in French urban areas during the 2000s. Some segregation measures have been used in several papers in order to understand the segregation in the US cities (for instance, [START_REF] Jargowsky | Take the money and run : economic segregation in us metropolitan areas[END_REF], [START_REF] Jargowsky | A measure of spatial segregation : The generalized neighborhood sorting index[END_REF], [START_REF] Yang | Suburban development and economic segregation in the 1990s[END_REF] or [START_REF] Wheeler | Neighborhood income inequality[END_REF]). Recently, using the census tract level family income data, [START_REF] Watson | Inequality and the measurement of residential segregation by income in american neighborhoods[END_REF] shows that income segregation has increased between 1970 and 2000 in 216 US urban areas. 6 Moreover, inequality is found to be positively correlated with the NSI.

Database description

We use the Revenus Fiscaux Localisés database, provided by INSEE. 7 This database provides, over a 8 year period (2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008) and for each area unit, the mean and the median income, the Gini Inequality coefficient, the quartiles and the deciles. The area unit considered by INSEE is the IRIS, 8 defined as an area comprising between 1800 and 5000 inhabitants : IRIS are uniform in their habitat type and their borders are based on the large cuts in the urban area, such as main roads, railways, rivers, etc. This spatial unit is close to the principle of Tract in the USA. Note that an important characteristic of this database is that INSEE is using exhaustive files providing by the Direction Générale des Impôts rather than a sample of inhabitants.

The definition of income adopted for our study is the taxable income, which is established from two different files of the income statement and property tax. INSEE estimates the taxable income for several geographical levels. The taxable household is an ordinary household formed by the combination of taxable families listed in the same dwelling.

The taxable income is the amount of resources reported by taxpayers on the income statement, before any reduction (which is not equivalent to the concept of disposable income). Therefore this income variable accounts for wages, unemployment benefices, pensions, capital income and non salaries revenue.

4. Employés and professions intermédiaires. 5. Cadres and professions libérales. 6. The author uses the census tract as the definition of a local area. As such an area is composed by roughly 4,000 people, her results could be compared with ours.

7. Institut National de la Satistique et des Etudes Economiques 8. IRIS : Ilots Regroupés pour l'Information Statistique.

Chapitre 1 : Income segregation in large French cities

The income is expressed in Consumption Unit, which accounts for the size and the structure of household into consideration. Indeed, differences in household structure between areas are sometimes such that the fact of using income per consumption unit offers a different picture of levels and differences in relation to the reasoning per household or per person. This equivalence scale is commonly used by INSEE and Eurostat to study income expressed as equivalent adult. For a given household, the first adult counts for one consumption unit, while the remaining persons count for 0.5 consumption unit if they are more than 14 years old, and children (less than 14 years old) count for 0.3 consumption unit.

We calculated the NSI and the GSI for 7 years (2001, 2002, 2004, 2005, 2006, 2007 and 2008) for the 30 largest urban areas 9 and computed it for different geographical levels, testing different scales of spatial areas. We first computed both indices for the IRIS level, then for the Grand Quartier level, which are less fine partitions of the urban areas. More precisely, a Grand Quartier is defined as a grouping of several adjoining IRIS inside a city. The size is variable but respects some population norms. A city with 20 000 inhabitants is generally divided into less than 3 Grand Quartier and few cities with less than 10 000 inhabitants are identified as a unique Grand Quartier.

Table 1.1 presents some general information related to our database, including, for each city, the population expressed in consumption unit, the number of IRIS and Grand Quartier, the absolute variation of the number of IRIS and Grand Quartier, and the variation of the population over the period considered (2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008). The last column presents the share of population accounted for, dropping the population belonging to IRIS for which at least one piece of information of the Revenus Fiscaux Localisés database is not available.

Results

In this section we present our empirical results, which exhibit a slightly decrease in segregation over the considered period. We first compare both segregation indices (GSI and NSI) and show that, though correlated, they imply different rankings of the cities over the period. Furthermore, we perform the inter-city comparison based on their ranking and their values and we discuss the nature of the relationship between income segregation and income inequality.

9. We use the concept of unité urbaine which is defined by INSEE as a set of districts for which at least 2,000 people is living in a continuous developed area. Comparison between GSI and NSI. For the 30 cities, table 1. Pearson correlation coefficient at IRIS level is high (0.78) and highly significant (see table 1.4). This correlation is even stronger at the Grand Quartier scale, where the Pearson coefficient correlation is equal to 0.8962 (see table 1.5). However, these indices draw different pictures when we make an inter-city comparison over time.

Inter-city comparisons. Here we compare the cities throughout the period according to both indices. Figures 1.4 and 1.3 give respectively the values taken by both indices and the ranking of the 30 cities over the period. 10 These figures highlight some differences in the segregation pattern of the cities drawn by both indices. For all the cities, the GSI appears to be higher and more stable over time than the NSI. As me mentioned before, both indices are highly correlated but we observe quite important differences in 10. As an ordinal measure, the NSI and GSI are particularly useful to classify and rank urban areas. But it cannot quantify the segregation and indicate whether segregation represents an amount x or y.

Gini coefficients

Coefficient of variation Gini Segregation NSI Gini Inequality GSI 1.0000 NSI 0.8962 1.0000 Gini Inequality 0.5241 0.3439 1.0000 the rankings for some cities. For instance, Paris is the most segregated city according to the Gini Segregation, while regarding the NSI Paris is in the middle of the ranking. 11. Of course such a cutting-up is arbitrary. To check robustness of our results, alternatives were implemented but the qualitative result was not affected.

12. North and Bassin Parisien : Paris, Le Havre, Orléans, Reims, Rouen, Tours, Amiens, Lille and Dunkerque. West : Angers, Bayonne, Bordeaux,Limoges, Caen, Le Mans,Brest, Nantes and Rennes. East : Dijon, Grenoble, Lyon, Mulhouse, Saint-Etienne, Clermont-Ferrand and Strasbourg. Mediterranean region : Marseille, Montpellier, Nice, Toulon and Toulouse.

13. However, the lower mean NSI value and the higher standard-deviation can be explained by the fact that Bayonne belongs to this region. If we exclude Bayonne from this region, we would find a mean IRIS -based NSI value of 0.28 and a standard-deviation of 0.023 ; a mean Grand Quartier -based NSI value of 0.21 and a standard-deviation of 0.047. holds when we study these correlations based on the Grand Quartier. However, given that there are several observations per each city, it is likely that this estimate of the correlation does not make any sense and does not assess properly the link between inequality and segregation. Consequently, we use a simple tobit model with random effects in order to estimate the link between the NSI's rank and the (inequality) Gini's rank and the link between the Gini Segregation's rank and the Coefficient of Variation's rank. 16 Table 1.7 summarizes our results 17 . It appears that the rank with respect to the Inequality Index does not influence the rank with respect to the segregation Index .

Interestingly, thanks to a similar tobit model with random effects, we find that the value of NSI is negatively correlated with the value of Gini Inequality coefficient.That is to say, the more a city is equal, the more segregated the city is. However this correlation is significantly positive between the GSI and the Coefficient of Variation (though low, +0.02) The econometric results are summarized in table 1.7.

14. As GSI and the Gini Inequality coefficient are intrinsically correlated we focus on the correlation between GSI and the Coefficient of Variation, similarly, we study the correlation between the NSI and and the Gini Inequality coefficient 15. Readers interested in properties verified by inequality measures could refer to Chakravarty (1999) or Cowell (2000) 16. The purpose of these simple econometric estimates is not to give a complete overall explanation of the segregation rankings and measures but to give an idea of the correlation between inequality and segregation. 17. Three-stars means that the coefficient is significantly different to zero at 99% ; two-stars means that the coefficient is significantly different to zero at 95% ; W is the Chi-2 Wald statistic of test ; ρ is the percent contribution to the total variance of the panel-level variance component. Indeed, since NSI and Gini Inequality coefficients do not draw the same picture, using NSI provides an interesting and useful information : the more unequal cities are not the more segregated cities. According to the latter result, segregation tends to decrease with an increase in inequality. How can we explain this result ? Even if Gini Inequality coefficient and NSI are not mechanically linked, segregation as measured by NSI is not independent of inequality. Indeed, NSI could be interpreted as the ratio between the Coefficient of Variation between local areas and the Coefficient of Variation for the overall city. Considering that Gini inequality coefficient and coefficient of variation are positively correlated,18 an increase in income inequality as observed during 2000s (see table 1.2) does logically lead to a decrease in NSI, ceteris paribus.

Conclusion

The goal of this chapter is to lay out a set of properties satisfied by a family of measures of residential segregation by income. The approach studied in this chapter is as follows : once selecting a measure of income inequality which respects some basic properties (such as the Pigou-Dalton principle), a segregation measure is the ratio between does not depend on whether areas are labelled or whether individuals within areas are named. The most serious drawback of the NSI, as pointed out by [START_REF] Jargowsky | Take the money and run : economic segregation in us metropolitan areas[END_REF], is that it is sensitive to the modifiable areal unit problem and to the physical location of are unit vis-vis one another.

This chapter concludes with an illustration as part of the measurement of the residential segregation by income in the 30 largest French cities. As pointed out in the previous sections, the NSI and the GSI are very appealing for applied analysis. On the first hand, the necessary dataset for their implementation is not prohibitive. On the other hand, these indices can provide some interesting information and usefully complement inequality measures. In the case of the 30 of the largest French cities, we show that, though correlated, the NSI and the GSI draw different rankings of the cities over time.

Futhermore, they draw a ranking of cities that is different (and not correlated) from the one according to Gini Inequality index.

Basic properties

Proposition 1.10 (Symmetry). :

Symmetry within area. Let (P, Y ) and (P, Y ) two cities such that Y j = D j Y j (j ∈ M ) with D j an individual permutation matrix and Y q = Y q for all q = j. Hence S I (P, Y ) = S I ( P , Y ). QED.

Proofs of propositions

Proof of proposition 1.1 (Normalisation)

The proof of this proposition is straightforward.

If

y j i = µ j for all j ∈ M , then V (Y j ) = 0 for all j ∈ M and V w = j∈M n j n V (Y j ) = 0. Obviously, V (Y ) = V b (Y )
and N SI = 1 if µ j = µ j for two at least areas j and j such that j = j ∈ M .

If µ j = µ j for all j and j such that j = j ∈ M , V b (Y ) = 0. Then N SI = 0.

Proof

I(Y µ ) > I( Y µ ).
We can then write the distribution of mean incomes :

Y µ = (µ 1 , ..., µ 1 n 1 times , µ 2 , ..., µ 2 , µ 2 n 2 times ) Y µ = ( µ 1 , ..., µ 1 , µ 1 (n 1 +1)times , µ 2 , ..., µ 2 (n 2 -1)times )
where

µ 1 = n 1 n 1 + 1 µ 1 + γ n 1 + 1 and µ 2 = n 2 n 2 -1 µ 2 - γ n 2 -1
This unilateral movement can be interpreted as a set of Pigou-Dalton rank-preserving progressive transfers of income between an individual originally located in area 2 and another one originally located in area 1 given that each individual is supposed to have the mean income of her area. That is, Y µ can be obtained from Y µ by a finite set of rank-preserving progressive transfers :

1. Each individual i ∈ N 1 N 1 receives from each individual i ∈ N 2 N 2 a transfer
of income for an amount of :

δ a = 1 n 2 -1 (γ -µ 2 ) n 1 > 0
Such a transfer of income is progressive. There are n 1 (n 2 -1) transfers of this type.

Each individual

i ∈ N 1 N 1 receives from individual i ∈ N 2 N 1 a transfer of
income for an amount of :

δ b = µ 2 -n 1 n 1 +1 µ 1 -γ n 1 +1 n 1 > 0
Such a transfer of income is progressive. There are n 1 transfers of this type.

Hence the new distribution of mean incomes is :

Y µ = (µ 1 + δ a + δ b , ..., µ 1 + δ a + δ b n 1 times , µ 2 -n 1 δ b , µ 2 - n 1 δ a n 2 -1 , ..., µ 2 - n 1 δ a n 2 -1 (n 2 -1)times )
As I is supposed to respect the Pigou-Dalton principle of progressive transfer,

I(Y µ ) > I( Y µ ).
The proof is similar for the other parts of the proposition.

Switch

Proof of part i. of Proposition 1.5.

By simplicity, we consider a city with two local areas such that µ 1 < µ 2 . Assume a switch of two individuals i (originally in area 1) and j (originally in area 2) such that y 2 j > y 1 i . Once again as overall income distribution remains unchanged, S I (P, Y ) > S I ( P , Y ) if

and only if I(Y µ ) > I( Y µ ).
Then, new mean incomes are :

µ 1 = µ 1 + γ n 1 and µ 2 = µ 2 - γ n 2 with γ = y 2 j -y 1 i > 0.
Hence the distributions of mean incomes are :

Y µ = (µ 1 , ..., µ 1 n 1 times , µ 2 , ..., µ 2 n 2 times ) Y µ = ( µ 1 , ..., µ 1 n 1 -1 times , µ 2 , µ 2 -, ..., µ 2 n 2 -1 times , µ 1 ) Y µ = (µ 1 + γ n 1 , ..., µ 1 + γ n 1 n 1 times , µ 2 - γ n 2 , ..., µ 2 - γ n 2 n 2 times )
Assuming that I respects symmetry, we can obviously see that a switch implies a series of mean income transfers between individuals located in different areas. Each individual transfer has an amount of γ n 1 n 2 and such a transfer is progressive. As I is supposed to respect the Pigou-Dalton principle of progressive transfer,

I(Y µ ) > I( Y µ ).
The proof is similar for the other parts of the proposition. The proof is similar for the other parts of the proposition. 5.2.5 Proof of proposition 1.9 (Sensitivity to areas aggregation)

Let (P, Y ) and ( P , Y ) two cities. By definition, ( P , Y ) is obtained from (P, Y ) by means of an aggregation of areas p and q, i.e., P = N 1 , ..., N p , ..., N q , ..., N m and P = N 1 , ..., N m-1 . Then, we can write :

-N j = N j , ∀j < q, j = p and

N j = N j-1 , ∀j > q -N p ∪ N q = N p -n p + n q = n p -µ = µ Then, n p µ p + n q µ q = n p µ p ⇔ ( µ p ) 2 = [δµ p + (1 -δ)µ q ] 2 (1.2) with δ = n p n p and (1 -δ) = n q n p
Hence,

S(P, Y ) ≥ S( P , Y ) ⇔ m j=1 n j (µ j -µ) 2 ≥ m-1 j=1 n j ( µ j -µ) 2 ⇔ n p (µ p ) 2 + n q (µ q ) 2 = n p ( µ p ) 2 (1.3) From (1.2) and (1.3), it follows that -S(P, Y ) ≥ S( P , Y ) ⇔ δ(µ p ) 2 + (1 -δ)(µ q ) 2 ≥ [δµ p + (1 -δ)µ q ] 2 -⇔ (µ q -µ p ) 2 ≥ 0 Chapitre 2
National Identity and Immigrants' Assimilation in

France

Determination and changes of immigrants' identity resulting from intercultural contacts impact their socio-economic integration. To precisely assess individuals' identity, we propose a continuous index which aims to overcome interpretation troubles faced by usual measures of ethnic identity. Then, we investigate the determinants of immigrants' ethnic identity in France. We compare our composite and continuous index exhibiting individuals' assimilation with a usual measure of ethnic identity -the national identity ("I feel French" dummy). We underline the importance of some sociodemographic characteristics in ethnic identity formation and detail immigrants' assimilation in France.

We are thus able to show that cultural assimilation and national identity do not always coincide. It seems that the further the origin (in cultural terms), the higher the national identity, but the lower the assimilation. We also present evidence of second generations' identity convergence to natives' one, either in terms of national identity (almost total commitment) or assimilation.

Introduction

Under the impact of immigration, modern societies become culturally plural [START_REF] Berry | Immigration, acculturation, and adaptation[END_REF]). People of many cultural backgrounds have to live together and immigrants' assimilation is thus a crucial issue. Two models of integration can be pointed out. The multiculturalism model adopted by Anglo-Saxon countries is based on the coexistence of various cultures. On the other hand, the assimilation model adopted in France compels 38 Chapter 2 : National Identity and Immigrants' Assimilation in France that immigrants perfectly and uniquely integrate the culture of the host country (see [START_REF] Bloemraad | Unity in diversity ? bridging models of multiculturalism and immigrant integration[END_REF]).

Ethnic identity of immigrants is an expression of their integration. This issue has been traditionally addressed by socioiogists [START_REF] Berry | Immigration, acculturation, and adaptation[END_REF]) and political scientists [START_REF] Abdelal | Measuring identity : A guide for social scientists[END_REF]). Economists have recently paid attention to immigrants' identity since it is likely to impact individuals' behaviors and decisions [START_REF] Akerlof | Economics and identity[END_REF]) and therefore to induce consequences on their socioeconomic integration (see for empirical Nevertheless, this measurement of ethnic identity suffers from a number of drawbacks.

The first one is that the surveyed individual has to place herself regarding the native's identity -for instance, through questions like "do you feel french (or "British", or "German", etc.)" That can only be answered by a simple yes or no. This discrete measure of identity loses the fact that the immigrants' identity may be more or less close to the natives' one. For instance, valuable information would similarly be lost by assessing individuals' incomes as "rich" or "poor" rather than a continuous distribution.

A second drawback raised by [START_REF] Lee | Between social theory and social science practice : Toward a new approach to the survey measurement of "race[END_REF] underlines the subjective interpretation that each respondent may give to the reference category ("as French", "as british", "as German", etc.). Indeed, this latter may not be equally salient and valid across individuals and contexts. Similarly, [START_REF] Citrin | Balancing national and ethnic identities the psychology ofe pluribus unum. Measuring identity : A guide for social scientists[END_REF] point out that while answering to a "Do you feel French ?" question like, it is not clear whether the respondent considers the "civic" or "ethnic" (say, "cultural") conception of a nation ? In other words, some may consider themselves as civically French (i.e. in a legal point of view) with, however, multiple ethnic identities (in a cultural point of view). National identity questions cannot report these.

A third one is given by [START_REF] Abdelal | Measuring identity : A guide for social scientists[END_REF]. It emphasizes the fact that it may be stigmatizing to answer that you do not feel like the natives, particularly when the pollster is a native.

This chapter makes four contributions.

First, we provide a new measure of ethnic idendity that circumvents drawbacks of existing measures. Its key feature is that it is based on characteristics that individuals choose to define themselves. Precisely, we use the TeO survey conducted by INED and INSEE in 2008 which is aimed to inform about the life conditions of immigrants and their descendants in France. To assess enhnic identity, we uee the following question "Which of the following features define yourself the most ?" Individuals can choose at most 4 features among the following 14 items : "my age/generation", "my gender", "my job occupation", "my educational attainment", "my neighborhood or my town", "my health", "my citizenship", "my origins", "my skin color", "my religion", "my hobbies", "my political opinion", "my region of origin" and "my family situation". We conduct a Multiple Correspondence Analysis (MCA) on these 14 items and we interestingly observe that the first dimension discriminates characteristics chosen by immigrants from those chosen by native respondents. This crucial dimension represents the ethnic or cultural part of respondents' identity. Note that we do not ask for this imnigrants-versus-natives opposition. No information regarding immigration position is included in the MCA. We ex-post observe such an opposition and conclude that the ethnic dimension of identity is the most important.

Following this result, we are thus able to build a weighted composite index of these 14 items where the weights are the correlation coefficients between each item and the first dimension. By construction, this index has to capture respondents' ethnic identity.

The bigger the index, the closer the self-definition from the "typical" native one. The construction of the composite index follows the methodology provided by [START_REF] Filmer | Estimating wealth effects without expenditure data-or tears : An application to educational enrollments in states of india*[END_REF] in a rather different context.

Our index therefore circumvents the difficulties faced by the standard measure of ethnic identity. It is continuous and allows obtaining a measure of the cultural distance beeween immigrants and natives. Furthermore, it overcomes the salience and validity troubles since respondents do not situate themselves regarding a given category but choose characterictics that ex-post locate them in an ethnic idenyity axis, thanks to the MCA procedure. By doing so, it also follows Sen (2007)'s call for multiple identities consideration, rather than a one-dimensional position. Finally, in a face-to-face interview, respondents are likely to feel less under pressure by defining themselves through multiple characteristics than regarding the dominant group belonging (natives).

Second, considering that the presence and importance of identity questions largely differ among surveys and countries, the assimilation index is not a ready-made tool for further studies. However, its methodology is exportable and interesting results are extracted from MCA. in particular, we find on the one hand that immigrants and, to a lesser extent, descendants of immigrants are likely to define themselves with attributes related to their ethnic group (origins, nationality, religion, skin color). On the other hand, natives choose more individualistic items (job, level of education, hobbies). At the risk of paraphrasing [START_REF] Durkheim | De la division du travail social[END_REF], the ethnic part of immigrants' identity could be seen as a mechanical identity, because self-definition is made by homogeneity with other ethnic group members. On the contrary, natives' one would be as organic identity, since it highlights individuals' socio-economic interdependence with others members (for more details about mechanical versus organic integration in France see in SCHNAPPER ( 2007)).

Third, we try to clarify the interpretations that can be done thanks to ethnic identity in terms of socioeconomic integration. Among the existing measures in the empirical literature, national identity is by far the most used. We discuss and qualify conclusions implied by this use by running regressions on national identity and on the assimilation index in parallel. The comparison of the results for both measures enables us to deepen the understanding of national identity and, in particular, to explore its meaning and performance regarding assimilation. This leads us to challenge some conclusions of the economic literature. In particular, [START_REF] Manning | Culture clash or culture club ? national identity in britain*[END_REF] investigate national identity determinants ih Great-Britain and find that "the process of assimilation is faster for those from poorer and less democratic countries". With our data we have a similar conclusion with national identity. However, this conclusion is completely reversed when we use our assimilation index. Then, our contributnon is simple, national identity quite imperfectly assesses the convergence of immigrants' ethnic identity toward natives' one.

Furthermore, it seems that when assimilation of an immigrant is high, the claim for national identity remains less necessary.

Finally, we give a detailed description of the determinants of ethnic identity. Notably, as found in tne literature [START_REF] Manning | Culture clash or culture club ? national identity in britain*[END_REF], [START_REF] Battu | Oppositional identities and employment for ethnic minorities : Evidence from england*[END_REF], [START_REF] Casey | Immigrants' identity, economic outcomes and the transmission of identity across generations[END_REF]), time since arrival is crucial. Thus we show that, compared with first generations, second generations claim more often national identity (93.12%, against 63.33%) and assimilate better. Nevertheless, the assimilation index of second generations is much lower than natives' and some determinants as discrimination or religiosity that do no impact first generations are activated for second's.

The following section presents the literature. Section 3 describes more precisely the identity features and assimilation index achievement after a brief presentation of the survey.

We also present the potential measures of identity. In section 4, we introduce the exogenous variables and corresponding descriptive statistics. Ethnic identity's determinants for the whole French population (thanks to representative weights) are presented in Section 5. Section 6 focuses on a comparison of first and second generations of migrants and presents related determinants. Section 7 concludes.

Literature review

This chapter focuses on the measurement of ethnic identity with the aim of improving the understanding of immigrants' integration. It thus belongs to two strands of literature, economics of immigration and economics of identity.

The literature in economics about identity is recent. [START_REF] Akerlof | Economics and identity[END_REF], Austen- 2010)). None of these studies investigate the case of France which is interesting in two ways. First, France has a specific model of integration which promotes cultural conformity of people (natives and immigrants) toward the "French Republican ideal".

Second, for two centuries, France has experienced a relatively high rate of immigration1 .

Furthermore, the issue of identity measurement is crucial but poorly documented by the liberature. This concern is at the core of this chapter.

Besides national identity, a few other empirical works have focused on the measurement of ethnic identity [START_REF] Constant | Measuring ethnic identity and its impact on economic behaviour[END_REF] In 2011, [START_REF] Bisin | Ethnic identity and labour market outcomes of immigrants in europe[END_REF] focus on ethnic identities of immigrants in Europe. Thanks to factor analysis, they construct a composite index with three variables that are attachment to religion, attachment to traditions and customs, language spoken at home. They present determinants of identity as origins, age, educational level, gender and years since arrival. Then, they analyze the influence of ethnic identity on educational and economic outcomes. However, their index is based on only three variables. The quality and amount of information given by the TeO survey as well as the use of Multiple Correspondence Analysis are assets of our index.

Our work provides new information about immigrant's identity in France. Furthermore, we confront usual measures to a new one which exhibits immigrants' assimilation based on individuals' self image. Thus, compared with previous studies, we can show that national identity and assimilation of immigrants, although tied, are not equivalent.

3 Data, sample and measures of ethnic identity The survey can be divided into 3 main themes : domestic and social environment (classical but numerous socio-demographics), access to social life resources (employment, educational, housing outcomes), different dimensions of origins, and cultural belongings (parents' origin, senses of belonging, discriminations, etc.). One of its main appeals is that it includes an entire part about "person's self image".

The assimilation index

Each one or the existing measures has its limits : interpretation dilemmas with national identity, endogeneity issues in identity formation explanation with the ethnosizer, lack of information and improper statistical method with the composite index of [START_REF] Bisin | Ethnic identity and labour market outcomes of immigrants in europe[END_REF]. Here, we propose a methodology aiming to circumvent drawbacks of these measures.

Construction

Tajfel (1974) explains that individuals identify themselves by features that both translate their belonging to a specific group and distinguish them from other groups. The

TeO survey offers a large set of variables regarding respondents' identity. One question is particutarly interesting in the questionnaire, "Which of the following features would you choose to define yourself ? Please choose at most 4 of them". Then, 14 features are proposed : "my age/generation", "my gender", "my job occupation", "my education", "my neighborhood or town", "my health", "my nationality", "my origins", "my skin color3 ", "my religion", "my hobbies", "my political opinion", "my region of origin" and "my family situation". We call these previous features identity attributes in the sense that they are chosen by respondents to define themselves. In other words, these attributes are 14 endogenous variables corresponding to 14 specific dimensions of a person's identity. The challenge is to find a proper way to summarize this heterogeneous information about individuals' identity in a unique measure.

In a totally different context, [START_REF] Filmer | Estimating wealth effects without expenditure data-or tears : An application to educational enrollments in states of india*[END_REF] create a weighted index of Indian individuals' material possessions (washing machine, clock, etc.) in order to approach long-run wealth. They run a Principal Component Analysis with all individuals possessions as exogenous and assume that the first dimension exhibit respondents' wealth, i.e.

their long-run wealth index. Therefore, weights equal correlation coefficients between each possession variable and the first dimension. [START_REF] Bisin | Ethnic identity and labour market outcomes of immigrants in europe[END_REF] follow this approach with a limited amount of information.

Chapter 2 : National Identity and Immigrants' Assimilation in France However, PCA in [START_REF] Filmer | Estimating wealth effects without expenditure data-or tears : An application to educational enrollments in states of india*[END_REF] and factor analysis in [START_REF] Bisin | Ethnic identity and labour market outcomes of immigrants in europe[END_REF] are not suitable procedures when exogenous attributes are discrete. That is why we prefer another multivariate procedure, the Multiple Correspondence Analyses (MCA).

MCA helps us to uncover and summarize the ethnic part of individuals' identity that is common to the 14 identity attributes. Indeed, this statistical procedure aims to classify different variables (here the identity attributes) among several axes, the dimensions, such that the first dimension accounts for as much of the variability in the data as possible and, in turn, each succeeding dimension has to get the highest variance as possible under the constraint that it is uncorrelated with the preceding one. Therefore, each dimension is a weighted linear combination of all the variables entering in the statistical procedure where weights are the corresponding MCA's correlation coefficients.

Obviously, MCA is a blind procedure and interpretation of each dimension that it produces is left to researchers. Here is an important assumption stipulating that the first dimension (i.e. the one that captures the highest possible part of the common information) exhibits ethnic identity. Running the MCA -without postulating on what should be immigrants' or natives' characteristics (these information about individuals' origins are not used neither needed to run the MCA) -we obtain the satisfaction of this assumption since immigrants are retrospectively located on negative and natives on positive values of the first dimension. This dimension can be extracted as an indicator thanks to correlation coefficients, this indicator being henceforth our assimilation index.

The index will then have the following form for respondent j :

I 1j = w 11 .X 1j + w 12 .X 2j + . . . + w 1Z .X Zj
with I 1j being the index (equal to the first dimension) for individual j, w 1Z the correlation coefficient between the zth identity attribute and the first component (that is weights) and the value for the zh attribute. Its minimum is -12.25 and its maximum 7.89 with a mode around 0.41 and a standard deviation equal to 3.47. The higher it is, the closer (resp. the further) the respondent self-image or identity from the natives' typical one (resp. immigrant's). We interpret moves of the index as improvement or worsening of individual's assimilation since it corresponds to Berry's typology and is positively correlated with the assimilation state of the ethnosizer 4 .

4. Thanks to our data, we were able to build the ethnosizer developed by Constant et al. We then observed that assimilation was the state of acculturation which was the most correlated with our index. In the interest of clarity of the chapter, we do not develop the construction of our ethnosizer hereafter. However, further details and results about our "TeO-based" ethnosizer and its relations with our index are available upon request. identity attributes which increase the assimilation index when chosen : hobbies, job occupation, political view and generation being the four most representative. Conversely, there are 5 attributes that decrease the index with particularly high coefficients for religion, skin color, nationality and origins. By construction, the assimilation index does not represent the entire individual identity but only the ethnic dimension of it.

Weights for assimilation index

We insist or the fact that these attributes are not dummies which would indicate whether the respondent is a male or a femaie, is graduated or not, has a religion or not and so forth, but dummies which take 1 if she believes that these attributes actually define herself, 0 otherwise. To say it even simpler, every respondent has a family position but everyone does not select it to define herself.

Index performances

Reader used to multivariate analysis knows that the percentage of inertia is crucial to determine the importance of each dimension. Here, the percentage of total inertia explained by the first dimension may seem too low (10.53%). However, M. [START_REF] Greenacre | From correspondence analysis to multiple and joint correspondence analysis[END_REF] points out that, with MCA, it would be "futile to expect a good approximation of a matrix of zero and ones in a two dimensional map of points". He advises to find other ways to assess the quality of the dimensions and notably to look at the correctness of predictions. To do so, we run 14 probit regressions with each of the fourteen identity items as endogenous and the assimilation index as the unique regressor. We then The assimilation index alone predicts almost 70% of no (zero) and 62% of yes (ones).

These relatively high percentages suggest that the first dimension (the index) succeed in summarizing the information that is common to all identity attributes.

As main works in this literature, we use national identity ("I feel French" dummy).

Nevertheless, most papers directly regard national identity as an expression of ethnic identity and even more abusively of immigrants' assimilation.

Our assimilation index, with its combination of multiple attributes, has the advantage to not directiy ask people about which group they belong (which is more or less implicitly what national identity and the ethnosizer 5 do) but about which personal characteristics they identify and then to locate them on an endogenous ethnic identity dimension. By doing so, it deepens individuals' identity investigation and enlightens national identity.

4 Treatment and descriptive evidence 5. The appendix provides a comparison of the assimilation index and our TeO-based calculation of the ethnosizer.

Treatment

In this section and the following, we only focus on national identity and the assimilation index. We look at their determinants thanks to probit -for national identity -and OLS regressions -for the ipdex. Endogeneity is obviously a main concern, insofar as we do not clearly distinguish how far identity explains individual behaviors from how far individual positions influence identity. That is the reason why we focus, as far as possible, on impact of exogenous demographic characteristics as :

For each group, -Age ; -Gender ; -Education, 1 if higher than certificate of general education ("brevet des colleges"), 0 We are aware of the risk of endogeneity or some of the previous variables (education, discrimination, for instance) and we try to minimize it as far as possible. However, we cannot completely avoid it and interpretations must be cautious.

The survey provides representative weights that will be used in every treatment of our study. It also proposes a huge amount of other possible variables and we chose the most relevamt ones after trying a lot of them. Context variables (as unemployment rate in the neighborhood, average level of education, etc.) could be used but, surprisingly, none of them has a significant impact on either national identity or assimilation index and, more importantly, they would increase endogeneity issues.

Framing effect issue

A well-known issue raised by this type of question is the framing effect. Indeed, while answering a multiple answers question, respondents are likely to choose the first ones.

Anticipating this, the fourteen items were written in two different orders (A or B).

They were then randomly proposed to respondents. 50.08% of respondents answered a A-order questionnaire, 49.98% answered a B-order questionnaire. Not surprisingly, the comparison of answers among the two series shows that a framing effect occurs.

However, in this work, our first interest is not to find the characteristics that people choose to define themselves but if there are differences in these choices between groups.

The two series being randomly determined, the difference betwetn each group choice (native, immigrants, and descendants of immigrants) is not impacted. However, the framing effect also influences MCA coefficients. In order, to address this issue, a dummy corresponding to the items' order proposed to each respondent is integrated in the following regressions.

Descriptive statistics

TeO survey allows differentiation of respondents as regard to their personal migratory history (that is their parents' or their own origin). In particutar, it is possible to know whether an individual belongs to the French natives group (that we define as respondents with no migratory history for less than two generations), the first generation group (immigrants) or the second generation group (descendants of immigrants). Here we present some descriptive statistics for each of these groups and for the whole sample. Interpretations for the assimilation index are more diffictlt and regressions results will be much more interesting. Concerning relations between national identity and the assimilation index, we observe a positive correlation between both measures 6 . By construction of the sample, second generations are much younger than natives and even more than first generations (see the appendix for detailed figures). Such a gap in age is likely to induce differences of identity. This will be controlled as far as possible and notably by using representative weights and performing distinct regressions for first and second generations. The highest differences can be observed in religions. While almost none of the natives' parents are Muslims (less than 1%), this religion was followed by parents of 43% of immigrants and more than 25% of descendants. On the contrary, Christian and atheistic represents almost the totality of natives' parents, against less than a half of immigrants' parents and around two thirds of descendants' parents.

European and Arabic languages are the most spoken foreign languages in France (see appendix ). We distinguish Sahelian languages from other African languages following 6. In order to observe the relation between both measures, we run a simple OLS regression with the assimilation index as endogenous and national identity as regressor, estimate = 1.744***.

Weighted shares of origins

Origin

Determinants of ethnic identity : whole sample

Our aim is to investigate the importance of each determinant and wonder to what extent national identity is an informative measure of ethnic identity thanks to its comparison with the assimilation index. Table 2.5 presents the results of a weighted probit on rational identity and a weighted OLS regressions on the assimilation index on socioeconomic regressors for the French representative population.

The first remark is that, for this sample, determinants' impacts are quite similar (in terms of signs and significance) for both measures. Though, the assimilation index seems to depend on more numerous determinants than national identity. This is particularly visible for languages 7 . Generally speaking, French taken as control, the use of a foreign language by parents leads to increase respondents' distance from native identity (either assessed by national identity or by the assimilation index). However, one can remark 7. We consider the first language used by both parents to speak with the respondent during her childhood. When the language spoken by mother and father was different (and different from French) we picked the language spoken by the father. Though subjective, this choice does not affect the analyses since this situation represents only 1.6% of our immigrants' sample (first and second generations). some specificity. European languages only affect national identity. Arab only affects assimilation. We are going to focus deeper on languages in the next section since they can be seen as an assimilation effort of parents for second generanions and an asset in terms of human capital for both second and first generations.

Not surprisingly, French origin taken as the reference, respondents' origins have globally negative effects on commitment toward natives' identity. However, situations differ among ethnic groups regarding the selected measure of ethnic identity. While some origins only affect national identity (Northern America, Northern Europe), others exclusively impact the assimilation index (South America, Asia, Sahelian and other Africa). This is an important result of our study, immigrants from culturally close origins (roughly speaking, developed countries) less commit toward national identity but have higher score in the assimilation index. The reverse conclusion holds for culturally far origins.

As expected mixed origin (exactly one parent who is born French) increases both national identity claim and assimilation. Furthermore, it leads to the highest variation among all regressors for national identity and the second highest one for the assimilation index.

Age has significant effects or both measures of ethnic identity but these are surprisingly negative. This can be explainhd by the fact that first generations, who are the farthest from natives' identity, are elder than other groups (natives and second generations).

There is no impact of gender. Education may be a source of endogeneity since the causality way with ethnic identity is unclear. Many previous researches use the time of education which does not solve this issue. Thus, we created a dummy with the certificate of general education (CGE) -Brevet des colleges -which is the first national diploma that all French pupils have to pass (around 14 or 15 years old, compulsory). Respondents who have a higher diploma are assigned 1 and 0 otherwise. we thus minimize time before diploma and then the potential reverse impact of identity on educational choice. Interestingly, national identity does not depend on diploma whereas the impact of this latter on assimilation index is the highest.

Discrimination feeling is obviously subjective and may imply endogeneity troubles. One must thus be cautious. Yet, it seems that skin color 8 based discrimination does not impact national identity, contrary to origin discrimination. Regarding assimilation index, the coefficient associated with origin discrimination is lower (and less significant) than the skin color's one. In any case, the sign is negative and discrigination increases the distance from natives' identity 9 .

During the survey, respondents had to give their own estimation about the proportion of immigrants in their living area. Although there is no way to control for over-or underestimation, this variable is of first interest and could be seen as a perceived segregation indicator. Estimates are significant and suggest the likelier conservation of ethnnc identity in segregated areas.

A strong identification with home national identity implies a lower commitment toward identity of natives. This was expectable for the assimilation index since assimilation is a process that does not theoretically accept the conservation of ethnic identities. In a sense, this goes against the hypothesis of multiple identities claiming tham ethnic identities are not substitutes but complements.

Pursuant to previous findings, a positive impact of years since arrival can be exhibited [START_REF] Manning | Culture clash or culture club ? national identity in britain*[END_REF] ; [START_REF] Casey | Immigrants' identity, economic outcomes and the transmission of identity across generations[END_REF] ; [START_REF] Battu | Oppositional identities and employment for ethnic minorities : Evidence from england*[END_REF]) on national identity. However, it does not impact the assimilation index (it does in the next section when we focus on first generations in particular).

Finally, we are able to look at parents' religions and the importance of religion during respondent's childhood. National identity is not significantly driven by parents' religion and the only significant impact on the assimilation index comes from the practice of Islam by the mother. However, robustness of this result is weak since it does not hold in 8. Surprisingly we did not find significant crossed effect of African origin and skin color discrimination. 9. Endogeneity could appear if people with strong ethnic identity react stronger to potential discrimination than those close to natives' identity and thus declare it more often to the pollster.

Comparison of Identities between First and Second Generations

National If we now focus on languages spoken by parents during childhood, these differently impact first and second generations. Four groups of languages (European, African, Asian, and Turkish) have a negative impact on first generations' national identity but no one influences the assmilation index. On the opposite, a few second generations' childhood languages impact their assimilation scores (Arab, African and Turkish) whereas only

European languages lead to a decrease of their national identity.

Age has different roles on national identity. Considering the first generations (resp. second generations), the elder they are, the lower (resp. the higher) their national identity.

Though, it does not drive the assimilation index neither for immigrants nor descendants of immigrants.

French citizenship 10 and its acquisition type give expectable and positive results regarding national identity. However, it seems to have no influence on the assimilation index.

French citizenship acquisition by reintegration claim 11 for second generations even has a surprising negative estimate on assimilation.

Gender only affects first generations and males are closer from natives' identity.

A surprising result concerns respondents' diploma. This latter only significantly plays a role in first generations assimilation index formation. This result may come from our restrictive choice of considering only the first national grade that French pupils have to pass as a proxi of respondents' education. By doing so, we aim to reduce the endogeneity bias.

Parents' religion does not drive ethnic identities. However, its importance in respondent's childhood is highly significant for each generation and negatively related to each identity measure.

Finally, many determinants have expectable and similar coefficients. A mixed origin and a well-educated mother are assets to commit toward natives' identity, while living in a segregated area (immigrants in neighborhood), a strong identification with home country (I feel [home country]), and a discrimination experience are not.

Years since arrival for immigrants have a quite high impact on national identity since the average migrant that spent 20 years on the French territory would face a 19% increase of her probability to feel French. Not surprisingly, ethnic identities commitment is a time-costly process. Nevertheless, time since arrival -even though significant -plays a much less important role on assimilation index compared with other determinant.

10. One could wonder why a second generation respondent can be foreigner as regard to the French "jus solis" for citizenship. The reason is that a second generation individual, when she attains legal majority, is given the opportunity to choose to keep either home and host nationalities (usual choice) or only one (scarcer case).

11. This procedure refers to people who have had their French citizenship lost and want it back.

Key differences between national identity and assimilation

In section 5, signs and significances generally coincide among ethnic identity measures. This is not the case if we focus on first and second generations only. Many determinants impact one but not the other. Some even have opposite signs.

On the one hand, some determinants affect national identity but not the assimilation index. This is the case of age, origin related discrimination, acquired French citizenship and European languages spoken by parents. On the other hand, skin color related discrimination, mother diploma and the control for the framing effect are significant determinants of assimilation but not of national identity.

More strikingly, origins of respondents significantly lead to different signs of coefficients.

To consider only one measure in order to give conclusions on ethnic identity formation is thus likely to imply partially wrong understandings. To highlight this risk, let us focus on origins of first generations. The reference origin, other (i.e. than North and Sahel)

Africa, is the same for all models. However, while almost all groups of origins are less likely to claim national identity than the control, they assimilate more French typical self-definition (assimilation index). In particular, western European immigrants have a probability to claim national identity almost 30% lower than Sub-Saharan African ones. This was not expected but consistent with Manning and Roy (2010) findings.

Using only British national identity (answer to "What do you consider your national identity to be ?"), they indeed conclude that immigrants from poorer and less democratic countries assimilate better. Yet, if we consider origins' estimates for the assimilation index, Western Europe coefficient of first generations is the highest positive one, that is to say that western European immigrants assimilate better than Sub-Saharan. Our conclusion is thus opposite to [START_REF] Manning | Culture clash or culture club ? national identity in britain*[END_REF] since, here, assimilation of poorer and less democratic countries' natives appears to be lower.

We do not see these remarks as evidence for the failure of one measure or the other, but as the justification of their combination in such a study. They do not measure exactly the same process but, taken separately, they are not sufficient to give proper information on identity formation and, further, on the influence of ethnic identity on socioeconomic outcomes. Their combination can even be helpfull to understand their working. For instance, we believe that if assimilation of an immignant is high, the claim for national identity is made less necessary to belong to the society. The national identity claim can be seen less as a proxy for French identity than a way to fulfill an already existing assimilation gap.

Conclusion

Ethnic identity has become a key element in studies focusing on immigration. Issues and changes resulting from intercultural contacts are indeed a major concern. This chapter aims to investigate the lack of interest given to ethnic identity measurement in previous studies and to use these understandings to tell more about immigrants' assimilation in France.

In order to complement usual measures, we build an assimilation index that takes into account the distance to the host culture while having identified its cultural characteristics through a statistical method, without making prior assumptions on these characteristics.

We thus assess and investigate ethnic identity through two different channels : a dummy for national identity and a continuous variable for assimilation. We claim that this measure brings new information about migrants' assimilation in France, and is more suitable for an analysis of the effects of assimilation on migrants' economics outcomes as it captures an actual distance in identity.

The MCA analysis enables to clearly distinguish different sets of variables that distinguish immigrants' from French natives' self-image. According to this analysis, 5 typical immigrant features increase the distance with the French identity when chosen that are religion, origins, skin color and nationality. On the opposite, the three most representative variables for the natives are hobbies, job and generation.

What this chapter shows is that both measures, national identity and assimilation index, bring different and complementary information about migrants' identity. However, national identity cannot be substituted to assimilation measures since it does not sufficiently and finely approach ethnic identity. We know that it can even lead to wrong interpretations. Indeed, individuals possibly identify themselves like French natives do but reject the national identity, whereas others who do not assimilate French stereotypes claim the national identity. This is even more striking when considering origins of immigrants.

National identity captures an assimilation will or wish, the assimilation index captures, as far as possible, realized assimilatian.

Our results qualify Manning & Roy (2010)'s conclusion since we find that assimilation of immigiants from poorest countries is lower, even though they are more likely to "feel

French". This justifies the plea of political science for combination of measurements [START_REF] Sylvan | Trade-offs in measuring identities : A comparison of five approached[END_REF], [START_REF] Abdelal | Measuring identity : A guide for social scientists[END_REF]) and, notably, for continuous variables [START_REF] Lee | Between social theory and social science practice : Toward a new approach to the survey measurement of "race[END_REF]).

Chapter 2 :National Identity and Immigrants' Assimilation in France 61 Thus, we claim that finer measures like the assimilation index would be more suitable to analyze the impact of ethnic identity (as a distance to natives' identity) on socioeconomic outcomes.

Identity theory is particularly suitable for the investigation of the French model of assimilation. Indeed, immigrants in France are expected to economically and socially integrate but they also had to assimilate French values and culture which mainly differs from multiculturalism. Our results -notably regarding time since arrival and the comparison of assimilation levels between first and second generations -suggest that assimilation is a long process and that determinants of ethnic identity formation cannot be well understood by using national identity as a unique proxy.

As regard to our results about ethnic identity's determinants, some facts can be exhibited. As said before, immigration structure has changed in six decades, thus today's and yesterday's immigrants should not be directly compared. However, inertia of origins decreases for second generations' assimilation. Descendants' national identity rate is very close from natives and their assimilation index is much higher than first generations' one.

Appendix

A.1. Descriptive statistics We design an experiment to study the effect of teenagers' social environment on their trust : in particular, our aim is to test the relation between social mixing and trust behavior. To study this question, we used an extra-laboratory experiment based on a trust game. Subjects are teenagers of two secondary schools located in Rennes (France). These secondary schools are both located in different neighborhoods within a city, contrasting in their degree of social mixing. Thanks to a within-subjects design, it is possible to study whether teenagers condition their trust choice on the school belonging of their partner and how school identity affects their trust and trustworthiness.

Introduction

Without trust, economic and social relations are hindered if not impossible. Indeed, many relations rely on implicit contracts where trust is therefore a key element. In many real world examples, trust appear to be essential to create or maintain a relationship.

An often quoted example is for instance when taking a taxi abroad where only a certain degree of trust between the taxi driver and the user enables this transaction. Moreover, trust is part of social capital held by an individual and might have consequences on economic outcomes, indeed, low levels of trust are associated with poorer economic performance [START_REF] Knack | Does social capital have an economic payoff ? a crosscountry investigation[END_REF] ; [START_REF] Zak | Trust and growth[END_REF]). A growing litterature has focused on the effects of social capital, this is therefore not surprising that economists have investigated the topic and accumulated a large body of evidence on the economic consequences of trust.

In this chapter we are interested in investigating the potential links existing between trust and segregation. On one hand, as a pillar of economic and social life, trust enables to facilitate and maintain relationships between individuals. On the contrary, the absence of trust and trustworthiness can lead to enforce segregated environment, where individuals from different groups or with different characteristics do not interact. Therefore, segregation could be a consequence of the absence of trust. One cause of segregation has been discussed by [START_REF] Schelling | Dynamic models of segregation[END_REF] who showed that even a small preference for one's neighbors to be of the same color could lead to complete segregation.

On the other hand, segregated environment may impact the degree of trust and trustworthiness of individuals. This aspect lead us to focus on segregation and social environment as determinants of trust. Actually, little is known about trust determinants and whether people experience different degree of trust and trustworthiness regarding their socio-economic background. We investigate the potential relations between trust and the social environment of teenagers. We focus on teenagers as they do not choose their residential location which avoids some endogeneity issues where trust could condition the localisation choice of individuals. Indeed, in the case of adults, social preferences, and among them trust, may impact the residential location choice. Furthermore, we are interested in the following questions : can we observe in-group favoritism in trust, and if so, do people from different socioeconomic groups discriminate similarly ?

We address these questions with the help of a field experiment conducted among 100 teenagers in two middle schools in Rennes, France. The experimental game is a variant of the so-called trust or investment game. In this sequential two-player game first movers (players A) send a transfer to second movers (players B), which is tripled by the experimenters. Second movers then decide how much to return. The amounts sent and returned inform us about the levels of trust and trustworthiness, respectively. Studying trust discrimination requires a social environment that defines distinct groups. In our study these groups are defined by two secondary schools located in two different neighborhoods in Rennes. These neighborhoods are different in terms of socio-economic segregation, indeed, one of the secondary school is located in a highly segregated area while the other one is located in a mixed neighborhood.

Our results can be summarized as follows. First we find that players A shows relatively high levels of trust and transfer around 60% of their initial endowment to players B.

We find that players A in the segregated school significantly trust less than participants in the mixed school. We do not find evidence for in-group favoritism for players A however we find that players B in the segregated school tend to be less egalitarian and discriminate in both ways, whether they favor a participant from their own school or from another school.

The remainder of the chapter is organized as follows. The first part provides a litterature review on measuring trust and trust determinants. The second part provides the design of the experiment and gives some background information. Section 3 discusses the results and section 4 concludes.

2 Litterature review

Measuring trust

In this chapter we retain the generally used definition of trust introduced by [START_REF] Coleman | Foundations of social theory[END_REF] according to whom "an individual trusts if he or she voluntary places resources at the disposal of another party without any legal commitment from the latter, but with the expectation that the act of trust will pay off". In order to measure trust economists have developed various tools. Traditionally, the measurement of trust relies on attitudinal questions. Previous research are based on a question in the General Social Survey (GSS) which is the following :"Generally speaking, would you say that most people can be trusted or that you can't be too careful in dealing with people". The latest ranking based on the question in the GSS reveals that 74.2% of people in Norway mostly trust others while they are 3.8% in Trinidad and Tobago. In France they are 18.8% while the average is 26.1%. In studies based on this type of question [START_REF] Arrow | Gifts and exchanges[END_REF][START_REF] Fukuyama | Trust : the social virtues and the creation of prosperity[END_REF] conclude that the level of trust in a society strongly predicts its economic success.

Similarly, [START_REF] Knack | Does social capital have an economic payoff ? a crosscountry investigation[END_REF] show that an increase of one standard deviation in country-level trust predicts an increase in economic growth of more than one-half of a standard deviation. According to [START_REF] Knack | Does social capital have an economic payoff ? a crosscountry investigation[END_REF] "if you take a broad enough definition of trust, then it would explain basically all the difference between the per schools capita income of the United States and Somalia". In their survey [START_REF] Algan | Trust, growth and well-being : New evidence and policy implications[END_REF] highlight the dynamics of trust and document the role of climate, weight of history and income on degree of trust. The latest OECD report (OCDE ( 2008)) highlights that richer countries trust more, indeed the share of people expressing high levels of trust is positively correlated to the median equivalised household income. Moreover, trust is higher when income inequality is lower, there exists a negative correlation between levels of trust and Gini coefficient.

However [START_REF] Glaeser | Do institutions cause growth ?[END_REF] Decisions from the second mover constitute a measure of trustworthiness as it measures the degree of reciprocity of this player. Many versions of this game exist has it has been replicated frequently and is a popular choice among trust researchers. Several authors have analysed the relationship between survey-answer and decisions in the trust game and found mixed results. In their study, [START_REF] Glaeser | Measuring trust[END_REF] found that questions about trusting attitudes do not predict trusting behavior but appear to predict trustworthiness while [START_REF] Fehr | A nationwide laboratory examining trust and trustworthiness by integrating behavioural experiments into representative surveys[END_REF] find the opposite. [START_REF] Holm | Tropic trust versus nordic trust : Experimental evidence from tanzania and sweden*[END_REF] find a positive correlation between survey-answers and behavior in trust game in Sweden but not in Tanzania. These results are difficult to compare as the experiments are quite different in these studies.

Chapter 3 :Segregation and Trust : An experiment in French secondary schools 69

Trust determinants

Among trust researchers some have focused on trust determinants and little is known about what can influences trust. Using data from U.S. localities, [START_REF] Alesina | Participation in heterogeneous communities (Rapport technique[END_REF] estimate that the strongest factors that reduce trust are a recent history of traumatic experiences, belonging to a discriminated group (an ethnic minority or to a lesser extent being a woman), being economically unsuccessful in terms of income and education and living in a racially mixed community and/or in one with a high degree of income disparity.

The trust game introduced by [START_REF] Berg | Trust, reciprocity, and social history[END_REF] has been conducted many times in many countries to test the determinants of trust. Here we focus on studies that have test the effect of social distance on trust. Using an inter-country design where students are paired whether with someone from their university or with someone from another university few studies have shown little or no evidence for social distance effect [START_REF] Netzer | Intercultural trust. an experiment in austria and japan[END_REF] ; [START_REF] Willinger | A comparison of trust and reciprocity between france and germany : experimental investigation based on the investment game[END_REF]) in the sense that the country of residence of their partner does not affect trust behavior of the senders and the recipients. Similarly [START_REF] Fershtman | Discrimination in a segmented society : An experimental approach[END_REF] have implemented a trust game with students from two distinct ethnic groups in Israel : Ashkenazic Jews and Eastern Jews. In this version of the game students are paired whether with someone from their own ethnic group or with someone from a distinct ethnic group. They find an ethnicity effect rather than a social distance effect where Ashkenazic players receive on average a higher amount. Few other studies have focused on the effect of the belonging to a common group on experimental trust [START_REF] Karlan | Using experimental economics to measure social capital and predict financial decisions[END_REF] ; [START_REF] Etang | Does trust extend beyond the village ? experimental trust and social distance in cameroon[END_REF] ; [START_REF] Cadsby | Trust, reciprocity and social distance in china : an experimental investigation[END_REF]) where this belonging to a group can be associated with social distance effect. The weakness in these studies is that group membership could be a treatment effect (joining the group leads people to trust each other) or a selection effect (people who trust each other join the group). To overtake this caveat [START_REF] Buchan | Let's get personal : An international examination of the influence of communication, culture and social distance on other regarding preferences[END_REF] artificially create random groups, this method follows the Minimal Group Paradigm (MGP) approach commonly used in psychology [START_REF] Tajfel | Experiments in intergroup discrimination[END_REF]) which suggests that subjects are more likely to trust people from their own group even if the groups are artificially created. In their study [START_REF] Buchan | Let's get personal : An international examination of the influence of communication, culture and social distance on other regarding preferences[END_REF] set up an experiment where students from different countries can be match only with a player from their own country after having spent few minutes chatting with their potential partner. When playing the trust game, subjects are told if they are playing with someone from their discussion group (in-group matching) or from a different group (out-group).

The effect of this artificially social distance varies across countries, americans send (and return) more money to in-group members while chinese students send more to out-group members. A handful of studies have proposed to measure trust through a trust game in a field experiment, [START_REF] Harbaugh | Risk attitudes of children and adults : Choices over small and large probability gains and losses[END_REF] conducted a field experiment in classroom in Chapter 3 : Segregation and Trust : An experiment in French secondary schools order to evaluate trust and trustworthiness across age and examine its development over time. They propose a version of the [START_REF] Berg | Trust, reciprocity, and social history[END_REF] trust game for children of different age where individuals received an initial endowment of 4 tokens. [START_REF] Falk | Discrimination and in-group favoritism in a citywide trust experiment[END_REF] proposed a city-wide experiment in Zurich in order to examine in-group favoritism and evaluate the determinants of trust. They allow senders to base their trusting decision on the neighborhood residency of the receiver. Similarly, [START_REF] Etang | Does trust extend beyond the village ? experimental trust and social distance in cameroon[END_REF] realize a field experiment in Cameroon where they allow the sender to base his decision on the village belonging of the receiver. Both studies highlight in-group favoritism and show that the localization of the receiver matters while choosing the amount sent. Comparably to these studies in our experiment the senders can discriminate regarding the school belonging of their partner.

Design and Background Information

In this section we give detailed information regarding the city and the secondary schools where the experiment was settled. We then describe the experiment.

Background information

The experiment took place in two secondary schools located in two different areas in Rennes, France. Collège Emile Zola (school M thereafter) is located in the city center while the collège des Hautes Ourmes (school S) is located in the south of the city, in a poorer area. Both secondary schools are located in neighborhoods contrasting in their degree of social mixing. School M is located in neighborhood 1 (see figure 3.1), while school S is located in a more segregated area (neighborhood 11 on the map 3.1 ) S is actually located in a urban renewal zone (Zone Urbaine Sensible) characterized as a priority zone for urban public policy. Futhermore, school S is classified as a priority education zone (Zone d'Education Prioritaire) defined as a zone with higher public dotations and higher autonomy in order to face socio-economic difficulties.

We also present statistics about socio-economic context of each neighborhood. Table 3.1 provides the population, the mean and median incomes, inequality indices and a segregation index for each neigborhoods. Concerning segregation index, we use the NSI as introduced by [START_REF] Jargowsky | Take the money and run : economic segregation in us metropolitan areas[END_REF]. As used in chapter 1, the NSI is defined as the square root of the ratio of the income variance between IRIS composing a neighborhood over the income variance within the neighborhood. The NSI belongs to the interval [0,1],

where 1 states for a complete degree of segregation. School S is located in the more segregated area in the city, in this neighorhood the median income is two times lower to the median income of the neighborhood where school M is located. Moreover, the 3.3 gives detail information on the areas (IRIS ) where both schools are located precisely. The median income and the population are calculated in the area where the school are located. The Iris considered is thus the heart of the school area, the other adjacent Iris are ignored. Here again, the area where school S is located is characterized by strong inequalities (the interdecile ratio is equal to 14 while it is equal to 8 in the area where school M is located) and by a median income two times lower than in the area where school M is located.

Moreover, schools themselves experience different degree of social mixing. Table 3.2 gives some information regarding their social mixity. School M is located in Rennes' city center, in this school, 14% of pupils are considered disadvantaged [START_REF] Merle | Carte scolaire et ségrégation sociale des établissements. une analyse monographique des collèges rennais[END_REF] while they are 48% in school S.

In a post-experiment questionnaire we asked teenagers their neighborhood residency (see below for more information about this post-experiment questionnaire). Figure 3.2 shows repartition of teenagers in the different neighborhoods. We can see that neighbordhood residency is more diversed in school M where teenagers live in various neighborhoods, only 23% live in the city center while 63% of teenagers from school S live in neighborhood 11 where S is located (see also column "same neighborhood" in table 3

Experimental procedure

To investigate the determinants of trust and trustworthiness we use a variant of the trust game introduced by [START_REF] Berg | Trust, reciprocity, and social history[END_REF]. The general structure of the trust game is as follows. There are two players, player A and player B, and each of them has an initial endowment, equal to 4 experimental units in our experiment. In a first stage, player A can send between 0 and 4 units to player B. More precisely, she has to choose an integer between 0 and 4, i.e., 0, 1, 2, 3 or 4 points. This transfer is tripled by the experimenter and sent to the player B. In a second stage, the player B can send back between 0 and In order to to elicit the willingness to reciprocate of player B, we used once again the strategy method. Then player B has to decide a back transfer for each of the 4 possible transfer amount that the player A can choose [START_REF]The school name and location were not specified[END_REF][START_REF]jouera le rôle du joueur B[END_REF][START_REF]Ta décision et la sienne détermineront la valeur de ton bon d'achat ainsi que la valeur du sien. Chaque point gagné te rapporte 60 centimes d'euros supplémentaires. Par exemple, si le jeu te permet de gagner 5 points, tu gagnes un bon d'achat d'une valeur de 13 euros : 10 euros + 5 points x 60 centimes[END_REF]4). They had thus two decisions sheets to fill in : "Suppose player A is from your school, how many points would you like to send him back if he sends you 1 point .... 2 points ... 3 points ... 4 points" respectively if player A is from another school.

Using the strategy method has several advantages. First it enables us to collect more data on individuals decisions. It also enables us to study the tendency of teenagers to favor someone from their own group. Introduced by [START_REF] Selten | Die strategiemethode zur erforschung des eingeschränkt rationalen verhaltens im rahmen eines oligopolexperimentes[END_REF] this strategy method has been widely discussed. Besides, one can wonder if this method is not biased as it could drive people to behave more equally in order to not show discriminatory behaviors.

Brandts & Charness (2011) compare the strategy method and the direct answers method in a meta analysis. Based on 29 experiments both methods give similar results : no difference exist in 16 over the 29 experiments, significant differences are seen in four experiments and mixed results are found in the 9th other experiments. Most authors insist on the fact that the strategy method is particularly effective in the case of "simple" games. According to [START_REF] Fong | Guilt driven reciprocity in a psychological signaling game[END_REF] or [START_REF] Solnick | Cash and alternate methods of accounting in an experimental game[END_REF] there is no difference between both methods in the trust game. However, [START_REF] Casari | The strategy method lowers measured trustworthy behavior[END_REF] compare these two methods in a simplified version of the investment game and find no difference for players A but players B tend to return a lesser amount in the strategy method. Finally, here we are interesting in comparing the decisions taken by the participants for a given method.

Our subjects are teenagers in 10th grade in two secondary schools in Rennes. This is important in order to study the determinants of trust and trustworthiness as our subject pool experiment more variance in their socio-economic background than the typical students sample in laboratory. The experiment was conducted in classrooms with pen and papers. In total 100 teenagers took part in the experiment (49 first movers and 51 second movers). The experiment was set up as follows : The instructions of the game and 2 different envelopes containing the two different sheets were disposed on the tables before the experiment. The envelopes were randomly disposed in two different order, first playing with a teenager from their school and then with a teenager from a different school and conversaly. The instructions were read out loud and we asked for understanding questions. Then participants could ask for questions individually answered. Participants opened the first envelope and filled in the first sheet. Then they sealed the envelope and filled in the second sheet. Decisions were thus taken sequencially with no possibility of changing the answers. The envelopes were collected and participants filled in the additional questionnaire. This questionnaire asked about personal attributes like gender, age, parents' occupation. In addition we elicited information about residential background of students which included questions about neighborhood' residency,duration of residency in the neighborhood, friends' residency. Participants then randomly selected whether they would play with someone from their school or another school by selecting at random a piece of paper. After the experiment we randomly formed pairs for the payments. After a month participants received their payments in the form of gifts vouchers in a sealed enveloppe with information regarding the school belonging of their partner and the amount received. One experimental unit equals 60 cents, the average payoff is 13.88 euros. The calendar of the session is summarized in figure 3.7

Results

In this section we detail our results. We first provide general results and then investigate whether we can observe in-group favoritism or discrimination.

General results

Players A We first study the results for players A. Our results can be summarized in the following way.

Result 1. Regarding players A -On average first movers reveal a relatively high willingness to trust and invest about 60 percent of their endowment.

-Players A from the non segregated school (M) trust more than players from the segregated school (S). Indeed, the amount of the transfer is significantly smaller for players A from school S, regardless the school belonging of player B.

-Players A exhibit same levels of trust whichever the school belonging of player B.

Figure 3.5 shows the distribution of transfers from first movers in both schools. Table 3.4 indicates the percentage of endowment transferred by players A in both schools.

Result 1 is consistent with previous results in the litterature where the average transfer is around 60%. Table 3.4 indicates the mean percent of endowment sent by first movers when playing with a player from their school (within-school transfer) and when playing with a player from another school (between-school transfer). A do not seem (on average) to discriminate regarding the school belonging of player B.

3.5 seems however indicating that players A from school S trust more a player B from a different school rather than from the same school. Wilcoxon rank test enable us to conclude that on average there is no discrimination regarding the school belonging of player B : p = 0.7041 for the whole sample, p = 0.3173 for players from school M and p = 0.8217 for players from school S.

Within-school Between-school

Result 2. Regarding players B :

-There is no significant difference between players from the non segregated school (M) and from the segregated school (S) ; -Similarly, the school belonging of player A does not influence the rate of back transfer from player B. Finally, it seems that on average there is not a different behavior between players B from school M and from school S. In contrast, the repartition of retun rates seems to be more concentrated for players from school M (around 1/3 and 2/3) than for players from school S. However Wilcoxon statistical test indicate that there is no significant difference between the two samples : p = 0, 9623 when player A belongs to the same school and p = 0, 3168 when he is in a different school.

Expected and actual returns

While filling the different sheets, players A had to make predictions about the willingness to reciprocate of players B indicating the number of points they think player B will return. On average players A make good predictions as the expected and actual returns are not significantly different. Table 3.6 gives the average percentage of expected and actual returns of player B.

Chapter 3 : Segregation and Trust : An experiment in French secondary schools Among the players from school M, they adopt an egalitarian behavior in average in 2.04 cases among 4. The number of discriminatory decisions against the other group or the own group is 1. Wilcoxon' rank test indicate that there exist significant differences between the number of egalitarian decisions and discriminatory decisions : respectively p = 0, 0466 (equality versus intra-group favoritism) and p = 0, 0766 (equality versus inter-group favoritism). In contrast there is no significant difference between the two types of discriminatory decisions (p = 0, 6314, Wilcoxon test). Decisions made by players from school S tend to be distributed uniformly between the three different behaviors.

According to Wilcoxon rank sum test, there is no significant difference : p = 0, 4375 (equality versus intra-group favoritism), p = 0, 7956 (equality versus inter-group favoritism) and p = 0, 7882 (intra-group versus inter-group favoritism).

As each player had two decisions sheets we can analyze whether they discriminate or not regarding the school belonging of their potential partner.

In-group

In-group Equality favoritism discrimination School M 23,00% 25,00% 52,00% School S 37,00% 35,00% 28,00%

Table 3.9: Favoritism according to the payment decisions Table 3.10 indicates the percentage of in-group favoritism, discrimination or egalitarianism of players B according to the potential transfer of player A (1,2, 3 or 4 points).When a player A potentially send 1 point, 18.52% of players B from school S favor their own group while they are 25% in school M to send more to a partner from their own school.

Some decisions are significantly different depending on the school belonging of player B, we observe significantly more in-group favoritism of players B from the segregated school (S) when the potential transfer from player A is 3 (we run a Student test where t=0.03).

Indeed 44.44% of players B from the segregated school do send a higher back transfer to a partner from their own school while they are 16.67% in school M to favor their own group.Similarly players B from school S are significantly less egalitarian (t=0.007) when players A have potentially sent 3 points. 18.52% of players B from school S choose to send the same amount to a player A from his school or from another school having sent 3 points, while they are 54.17% in school M.

concluding remarks

In this chapter we study the relations between social environment and trust. We conduct an extra-laboratory experiment with 100 teenagers in two secondary schools located Chapter 3 :Segregation and Trust : An experiment in French secondary schools 83 in two different neighborhoods in Rennes. We find that players A are characterized by high levels of trust, they send around 60% of their endowment to players B. This result is consistent with previous studies. Players A from the segregated school appear significantly trust-less and send lesser amounts than the participants from the mixed school. Thus the social environment seems to have an effect on trust behavior. Players A from both school do not discriminate and their transfers are not significantly different according to the school belonging of their partner. We find that players A make good predictions about the back transfer from players B as the expected and actual returns are not significantly different.

We then study the existence of in-group favoritism and find no evidence for players A, however we find that players B from the segregated school discriminate more. This discrimination goes in both ways as players B tend to favor equally in-group partners as out-groups partners and appear significantly less equalitarian. In-group favoritism or discrimination can have important economic and social consequences as many socioeconomic relations involve some element of trust. At the level of neighborhoods in a city trust discrimination may feed segregation and lead to the spatial separation of groups within the city.

Questionnaire collégien

N° d'anonymat : ________ Instructions : Dans ce questionnaire on te pose des questions sur toi, ta famille, tes ami(e)s, ce que tu aimes faire.

Ce n'est pas un test, il n'y a pas de bonne ou mauvaise réponse. Tes réponses seront anonymes, ton nom et ton prénom ne seront pas communiqués. Prends le temps de répondre à chaque question et d'indiquer ce que tu ressens vraiment, en cas de doute tu peux nous demander de l'aide.

--------------------------------------------------------------------------------------------------------------------------------------

MERCI !

  la ségrégation a diminué pour les immigrés. L'une des questions majeures qui se pose lorsque l'on étudie le phénomène de ségrégation urbaine est donc celle de sa mesure. En outre, la littérature existante sur la ségrégation urbaine propose de nombreux indices mesurant le degré de ségrégation catégorielle mais peu d'études cependant proposent une mesure de la ségrégation sur une variable continue. Le chapitre 1 revient sur la définition de ségrégation et étudie les propriétés générales d'une famille d'indice de ségrégation basée sur la décomposition d'indices d'inégalité. Nous étudions un indice de ségrégation basé sur le revenu le Neighborhood Sorting Index (NSI), introduit par Jargowsky (1996), ainsi que ses interprétations intuitives. Cet indice permet de mesurer le degré de ségrégation économique des individus en fournissant une mesure d'une variable continue. Il est défini comme la racine carrée du ratio de la variance des revenus moyens entre les quartiers sur la variance des revenus des individus dans la ville. L'utilisation du NSI est ensuite illustrée par une application empirique qui mesure et compare le niveau de ségrégation économique en France dans les trente plus grandes aires urbaines françaises entre 2001 et 2009. 2 Identité L'intérêt des économistes pour les questions d'identité est récent et croissant.La notion d'identité peut être difficile à saisir. Elle est multiple : l'identité sociale, l'identité de genre, l'identité ethnique ou l'identité nationale. Il est par conséquent difficile de mesurer cette variable. Dans leur article fondateur, Akerlof & Kranton (2000) tentent de proposer une définition claire de l'identité, ils la définissent comme le sentiment que l'on a de soi et proposent d'intégrer cette variable à la fonction d'utilité. L'identité peut avoir un effet important sur les choix des individus et peut par conséquent impacter leurs résultats socio-économiques tels que leur niveau de salaire, leur accès à l'emploi etc. L'identité est un concept qu'il est difficile de mesurer, de plus en plus étudiée dans le contexte de la migration on s'intéresse souvent à l'identité ethnique. En migrant, les individus peuvent faire face à un arbitrage entre adopter la culture d'accueil Introduction Générale ou préserver leur héritage culturel. Le résultat de cet arbitrage peut se traduire sous 4 formes d'acculturation définies par Berry (1997) : l'intégration où les individus adoptent la culture d'accueil tout en préservant leur héritage culturel, l'assimilation où les individus adoptent la culture d'accueil en s'éloignant de leur culture d'origine, la séparation où les individus maintiennent leur héritage culturel et n'adoptent pas la culture d'accueil ou la marginalisation où les individus s'écartent à la fois de leur culture d'origine et de la culture d'accueil. Le résultat de cet arbitrage peut avoir des effets importants sur les résultats socio-économiques des individus (Pendakur & Pendakur (2005), Nekby & Rodin (2007), Manning & Roy (2010), Battu & Zenou (2010)). Il convient donc de développer des outils pour mesurer cette distance identitaire, jusqu'ici l'identité ethnique est souvent approchée par la réponse à la question je me sens [français, marocain, italien...] , qui est également appelée identité nationale. D'autres mesures approchent l'identité à travers la construction d'indices basés sur les caractéristiques identitaires utilisées pour se définir (langue, couleur de peau, origines...) a travers des analyses factorielles. Ces mesures de l'identité ethnique peuvent s'apparenter à la ségrégation dans la mesure où elles capturent une distance au groupe majoritaire. Dans le chapitre 2 nous proposons une mesure de l'identité ethnique. La notion d'identité ethnique est le plus souvent approchée empiriquement par une variable binaire traduisant le sentiment national (la réponse à la question : je me sens [français/ italien/ Marocain ...]). Ce chapitre propose une méthodologie permettant d'étudier le degré d'assimilation des immigrés en France, ainsi que des descendants d'immigrés. A travers l'analyse de données originales (fournies par la base Trajectoires et Origines) nous construisons un indice qui permet une mesure continue de l'identité ethnique. L'indice que nous construisons est basé sur une analyse factorielle qui permet de prendre en compte le caractère multi-dimensionnel de l'identité en analysant les caractéristiques mentionnées par les individus pour se définir. Nous proposons une comparaison de cet indice avec d'autres mesures de l'identité existant dans la littérature (notamment la variable binaire "je me sens français") et soulignons leur caractère complémentaire. En outre, nous montrons que l'assimilation et le sentiment d'être français ne coïncident pas toujours. Il semble que plus le pays d'origine est distant, à la fois en termes économiques et culturels, plus le sentiment d'être français est fort et plus le degré d'assimilation est faible. Nous étudions ensuite les déterminants de l'identité à travers l'analyse de certaines caractéristiques socio-démographiques. Nous montrons également que l'identité des enfants d'immigrés converge vers celle des natifs, que celle ci soit approchée par le sentiment national ou le degré d'assimilation.

  measures introduced by Jargowsky & Kim (2009), which allows us to compare cities on the basis of the breakdown of individuals who differ in terms of income among a given set of spatial areas. We propose an approach of measuring segregation by income based on transformations of the breakdown of a population among local areas. These transformations capture two dimensions of the segregative phenomenon. First, change in segregation may be the result of changes in the "allocation" of individuals among areas while the income distribution among the individuals remains the same. Second, changes in the income distribution (e.g., progressive or regressive transfer) among immobile individuals result in segregation change.We first study the sensitiveness of the family of segregation measures considered with respect to movements of individual(s). In particular, we argue that a segregation measure should decrease if a rich individual moves from an area -where she is richer than the average individual -to a poorer one or if a poor individual moves from an area -where she is poorer than the average individual -to a richer one. Moreover, we consider the impact of a switch of two individuals, which requires that a segregation measure decreases if a rich individual living in a rich area and a poor individual living in a poor area exchange their location.The second type of transformations considered leaves the breakdown of individuals unchanged but affects the income distribution among individuals. We study the sensitiveness of the segregation measures relatively to an income transfer between two individuals located in the same local area. Any income transfer which is progressive in the usual sense of Pigou-Dalton contributes to increase segregation. The rationale of this requirement lies to the fact that such a transfer increases the homogeneity of the area and hence lowers its social mixing. On the contrary, an income transfer from a poor to a rich individual decreases segregation because it reduces the homogeneity of the local area. This family of segregation indices is then illustrated measuring and comparing the segregation in the 30 largest French urban areas from 2000 to 2008. More precisely we use the

  The simplest transformation illustrated by Example 1 is the unilateral movement of one individual from one area to another one. Definition 1.2. Movement of one individual. Let (P, Y ) and ( P , Y ) two cities and k an individual located in area p. The city ( P , Y ) is obtained from the city (P, Y ) by

  Definition 1.4 (Switch of two individuals). : Let (P, Y ) and ( P , Y ) two cities, within which two individuals k and h are located in area p and q respectively. The city ( P , Y ) is obtained from the city (P, Y ) by means of a switch of two individuals if :

Definition 1 .

 1 6 (Within-area income transfer). : Let (P, Y ) and (P, Y ) two cities and two individuals k and h located in area p. The city (P, Y ) is obtained from the city (P, Y ) by means of within-area income transfer if, for any δ ∈ R + :

Proposition 1 .

 1 9 (Sensitivity to areas aggregation). : Let (P, Y ) and ( P , Y ) two cities such that ( P , Y ) obtained from (P, Y ) by means of areas aggregation, then : Chapitre 1 : Income segregation in large French cities (a) S I (P, Y ) = S I ( P , Y ) if µ p = µ q (b) S I (P, Y ) > S I ( P , Y ) if µ p = µ q

Figure 1 . 1 :

 11 Figure 1.1: Ranking correlation between GSI and NSI (IRIS scale)

  Figures 1.1 and 1.2 illustrate the correlation between the ranks of the two indices for both level (IRIS and Grand Quartier ). Both indices are strongly correlated, indeed, the

Figure 1 . 2 :

 12 Figure 1.2: Ranking correlation between GSI and NSI (Grand quartier scale)

  On the contrary, Dunkerque appears less segregated regarding the GSI than measured with the NSI.According to the GSI, Bayonne, Limoges and Saint Etienne are the less segregated cities. In 2008, 31% of the overall income inequality in the city, as measured by the Gini Inequality coefficient, is explained by inequality between neighborhoods. While in Paris, the most segregated city, we can explain 56% of the overall inequality by inequality between areas.According to the NSI, the cities of Bayonne, Nice and Clermont-Ferrand are the less segregated cities throughout the considered period, while the most segregated urban areas are Le Havre and Lille. In 2008, while 16% of the overall inequality as measured by the standard-deviation is explained by inequality between areas in Bayonne, the less segregated city of our sample, we can explain 36% of overall inequality observed in Le Havre by inequality between areas. Thus, the highest NSI is 2.25 times higher than the lowest NSI in 2008. As we see in figure1.4 it is not surprising to observe that NSI values are not volatile. Few exceptions concern Nantes, Amiens, Montpellier or Strasbourg, for which NSI values follow a more unstable trend. Figure1.3 gives also interesting information on the change in ranking of cities. We notice that the ranking according to the NSI is not stable across the period. Bayonne, Nice or Lille are few exceptions of segregation stability. Montpellier, Nantes or Strasbourg observe a strong degree of segregation volatily. Some cities are less and less segregated compared to other cities : such is the case of Lyon and Grenoble. On the contrary, cities like Paris see their rank increasing. However, as we can deduce from the figure 1.4, these changes might be explained rather by close NSI's values, for which a small change in the NSI's value can cause important changes in the ranking.

Figure 1 . 3 :

 13 Figure 1.3: Ranking over time (IRIS scale)

Figures 1 .

 1 Figures 1.5 and 1.6 depict, for both indices, the relation between both scales in terms of values which illustrates the proposition 1.9. With respect to this proposition, migrating from IRIS scale to Grand Quartier scale should not increase the segregation. Indeed, all the points are located under the first bisector. This figure highlights also the strong correlation between segregation index calculated on the basis of IRIS and on the basis of Grand Quartier. The unweighted coefficient is equal to 0.8859 for the NSI and 0.8835 for the GSI (for all cities and for all years) and are significantly different to zero (p-value < 0.001).

Figure 1 . 6 :

 16 Figure 1.6: The value of NSI according to the scale area unit

Figure 1 . 7 :

 17 Figure 1.7: Correlation between GSI and Coefficient of Variation (IRIS scale)

Figure 1 . 8 :

 18 Figure 1.8: Correlation between NSI and Coefficient of Variation (IRIS scale)

  Then, S I (P, Y ) = S I (P, Y ). Proof. By definition Y µ = Y µ . If I respects symmetry, I(Y ) = I( Y ) and then S I (P, Y ) = S I (P, Y ). QED. Symmetry between areas. Let (P, Y ) and (P, Ỹ ) two cities such that Y = DY with D an areas' permutation matrix. Then, S I (P, Y ) = S I (P, Y ). Proof. If I respects symmetry, I(Y µ ) = I( Y µ ) and then S I (P, Y ) = S I (P, Y ). QED. Proposition 1.11 (Principles of population). : Within-area replication invariance. Let (P, Y ) and ( P , Y ) two cities such that, for all j ∈ M and for any α ∈ N + , Y j = (Y j , Y j , ..., Y j α+1 times ) = (y j 1 , ..., y j 1 α+1 times , ..., y j n j , ..., y j n j α+1 times ) Then, S I (P, Y ) = S I ( P , Y ). Area replication invariance. Let (P, Y ) and ( P , Y ) two cities such that, each neighbourhood is replicated times as Y = (Y 1 ; ...; Y 1 +1 times ; ...; Y m ; ...; Y m +1 times ) Then, S I (P, Y ) = S I ( P , Y ). Proof. If I respects Dalton principle of population, I(Y ) = I( Y ) and I(Y µ ) = I(Y µ ).

  of propositions 1.3 and 1.5 (Segregation under movements) 5.2.3 Unilateral movements Proof of part i. of Proposition 1.3. By simplicity, we consider a city with two local areas such that µ 1 < µ 2 . Assume a movement of a rich individual from area 2 to area 1. Denote his income by γ with γ > µ 2 . As, by definition, inequality of overall income distribution remains unchanged, S I (P, Y ) > S I ( P , Y ) if and only if

  5.2.4 Proof of proposition 1.7 (Internal transfer) Proof of part i. of Proposition 1.7. Consider a city with m area and a progressive transfer between two individuals in area p ∈ {1, ..., m}. By definition the distribution of mean incomes is not changed : Y µ = Y µ while the overall inequality reduces according to I that respects the Pigou-Dalton principle : I(Y ) > I( Y ). If Y µ is not of the form Y µ = c1 m (where m is the total number of areas), S I (P, Y ) < S I (P, Y ). If Y µ = c1 m , then S I (P, Y ) = S I (P, Y ) = 0.

  studies,[START_REF] Pendakur | Ethnic identity and the labour market[END_REF],[START_REF] Constant | Measuring ethnic identity and its impact on economic behaviour[END_REF],[START_REF] Nekby | Acculturation identity and labor market outcomes[END_REF],[START_REF] Manning | Culture clash or culture club ? national identity in britain*[END_REF],[START_REF] Battu | Oppositional identities and employment for ethnic minorities : Evidence from england*[END_REF],[START_REF] Casey | Immigrants' identity, economic outcomes and the transmission of identity across generations[END_REF]). In most of these works, the empirical measure of ethnic identity is based on the answer to the question "Do you think of yourself as [natives' citizenship] ?" Moreover, although estimation of the impact of ethnic identity on the socioeconomic integration of immigrants raises econometric issues, the literature stresses a significant and negative influence of ethnic identity[START_REF] Nekby | Acculturation identity and labor market outcomes[END_REF],[START_REF] Constant | Ethnosizing immigrants[END_REF],[START_REF] Casey | Immigrants' identity, economic outcomes and the transmission of identity across generations[END_REF],[START_REF] Battu | Oppositional identities and employment for ethnic minorities : Evidence from england*[END_REF],[START_REF] Bisin | Ethnic identity and labour market outcomes of immigrants in europe[END_REF]).

  [START_REF] Fryer | An economic analysis of" acting white[END_REF] propose theoretical frameworks -not specifically in immigration contexts -to explain individuals' socio-economic outcomes through identity. Identity refers to the sense of belonging to a given group. More particularly, ethnic identity is activated when ethnic groups have to cohabit together which is an obvious consequence of immigration. While migrating, an individual might face a trade-off between conforming to the host culture or preserve her own cultural heritage such that it could even lead to adopt oppositional identities[START_REF] Battu | Oppositional identities and employment for ethnic minorities : Evidence from england*[END_REF]). Consequently, ethnic identity may have direct implications on economic outcomes[START_REF] Pendakur | Ethnic identity and the labour market[END_REF][START_REF] Constant | Measuring ethnic identity and its impact on economic behaviour[END_REF],[START_REF] Nekby | Acculturation identity and labor market outcomes[END_REF],[START_REF] Battu | Oppositional identities and employment for ethnic minorities : Evidence from england*[END_REF],[START_REF] Casey | Immigrants' identity, economic outcomes and the transmission of identity across generations[END_REF],[START_REF] Bisin | Ethnic identity and labour market outcomes of immigrants in europe[END_REF]). Empirically, immigrant's assimilation is often approached by the national identity[START_REF] Manning | Culture clash or culture club ? national identity in britain*[END_REF],Casey & Dustmann (2010),Bisin et al. (

  ,[START_REF] Nekby | Acculturation identity and labor market outcomes[END_REF]) using[START_REF] Berry | Immigration, acculturation, and adaptation[END_REF]'s typology.[START_REF] Constant | Measuring ethnic identity and its impact on economic behaviour[END_REF] have introduced the ethnosizer for commitment with home or host identity measurement. It allows a ranking of individuals regarding this commitment among four states of acculturation : integration (commitment with both host and home culture), assimilation (commitment with host culture only), separation (commitment with host culture), or marginalization (no commitment with either host or home culture). To compute the index they defined a priori identity features such as spoken language, religion, societal interaction... They are then able to emphasize different pre-migration -religious cults, origins -and post-migration determinants -age, education, and hours worked. Our methodology is different and less subjective since we do not have postulate which characteristic should be regarded as typically native or typically immigrant.

3. 1

 1 Data and sample Our work is based on the French Trajectoires et Origines (TeO, thereafter) crosssectional survey developed in 2008 which focuses on integration and discrimination issues. It offers a very large set of variables about today's first and second generation of immigrants in France. It has been conducted by two main French statistical institutes, INSEE and INED. The scope of the survey is the set of people from 18 to 60 years old residing in metropolitan France according to the 2007 French national census. Survey areas have been chosen -countryside and cities -to be representative of the structure of the whole country. It voluntarily over-samples immigrants and descendants of immigrants but representative weights have been calculated to improve analysis. The major difficulty was the construction of the second generation sample due to their statistical invisibility in French censuses. This has been fixed by assembling information about parents' birth country, nationality, and information about respondents' current situation. Only one person in the household has been interviewed but information about other members in the housing is available. Finally, 21761 respondents have been kept in the overall sample, including 8456 immigrants, 8161 descendants, 712 DOM 2 natives, 651 descendants of DOM natives and 3781 respondents whom both parents are born French and called French natives. After our own selection (some necessary answers about respondants' self image were missing), our final sample is composed of 6964 descendents of immigrants, 6868 immigrants and 3545 natives.

  2. "Départements d'Outre-Mer", that is French Overseas Departments.

-

  otherwise ;-Language spoken by parents during childhood ; -Parents' origins ; -Discrimination feeling, 2 types (due to skin color and due to origin) ; -Proportion of immigrants in living area, 1 when respondent says that at least half of her neighhorbood inhabitants are immigrants ; -Mother education, 1 if higher than certificate of general education, Mixed origin, 1 if resposdent han exactly one of her parents who is a French native and 0 otherwise ;

  have pointed out the drawbacks of such a method to measure trust. Indeed, responses are difficult to interpret and the variation in the answers may come from various sources as the different understanding of what it means to be trusted or the different interpretation of who comprises "most people". Moreover variation in the answers can also come from the fact that people are not willing to answer truthfully to such a question or have different ability to elicit trustworthy behavior from other people.An other approach to measure trust has thus been developped and is based on experimental games. Introduced as a laboratory experiment by[START_REF] Berg | Trust, reciprocity, and social history[END_REF] the trust game consists in a game where two players are anonymously paired. The first mover decides how much on his initial endowment of 10 euros he wants to pass to a second player, the receiver. The second player receives this amount tripled by the experimentalist and decides how much of this transfer he wants to send back to the sender. The sender thus receives : his endowment -his transfer + the back transfer sent by the receiver. The receiver earns : the intitial endowment + the transfer multiplied by the experimenterthe back transfer. Therefore, decisions from the sender constitute a measure of trust as it measures the amount someone is inclined to send expecting his partner being reciprocal.

Chapter 3 :

 3 Segregation and Trust : An experiment in French secondary schools 71 neigborhood where school S is located is characterized by a strong level of inequality, indeed the interdecile ratio is equal to 16.64.

Figure 3 . 1 :

 31 Figure 3.1: Map of Rennes

Chapter 3 :Figure 3 . 2 :

 332 Figure 3.2: Neighborhood residency of teenagers (%) (a) stands for teenagers from school M, (b) for teenagers from school S

Figure 3 . 3 :

 33 Figure 3.3: Father's Socio-Professional Category 0 stands for unemployed, 1 for blue-collar workers, 2 for employees, 3 for executives and 4 for retired.

Figure 3 .

 3 Figure 3.3 shows the different Socio-Professional Category of participants' fathers, 0 stands for unemployed, 1 for blue-collar workers, 2 for employees, 3 for executives and 4 for retired. We can see that most fathers in school S are blue-collar workers while in school M most fathers occupy an job of executive or assimilated.

Figure 3 . 4 :

 34 Figure 3.4: Sequence of the game

Figure 3 .

 3 5 represents the repartition of these amounts. The amount sent on average by players A from school M is higher than the amount sent by players A from school S. The figure also shows that the distribution of the transfers is relatively concentrated in the bottom (around 2) for the subjects from school S. By contrast, the amounts sent by players A from school M are more spread around the upward of the distribution (3 or 4). Wilcoxon tests confirm Chapter 3 : Segregation and Trust : An experiment in French secondary schools the robustness of this result when player B being in the same school (p = 0.0472) or, in a lesser extent, player B being in a different school (p = 0.1068). Interestingly, players

Figure 3 . 5 :

 35 Figure 3.5: Distribution transfers A

Figure 3 .

 3 Figure 3.6 shows the average percentage of back transfers from player B according to the number of points sent by player A. As we used a contingent response method, we have information about the distribution of back-transfers from player B regarding the amount potentially sent by player A.

  Année de naissance : ……………… Lieu de naissance : ……………………….Combien as-tu de frères et soeurs ? …………. Frère(s) et …………… soeur(s) Combien de tes frères et soeurs vivent avec toi à la maison ? ……….Quel est le métier de tes parents ou tuteurs légaux? Père : …………………………………………….. Mère : ……………………………………………..Moi et le collègeDepuis combien de temps es-tu inscrit dans ce collège ? ……………………………………….. Avant d'entrer au collège, dans quelle école primaire étais-tu ? Nom de l'école : …………………………………………… Ville de l'école : ………………………………………… Aimerais-tu changer de collège ?  Oui  Non Si tu devais changer de collège, parmi les collèges suivants, dans lequel souhaiterais-tu aller ? t-il un autre collège où tu souhaiterais aller ? ……………………………. Moi et mon quartier Voici la carte des quartiers rennais,  Entoure en rouge le quartier où tu habites  Fais une croix dans le ou les quartiers où habitent tes amis (y compris le tien)  Souligne le ou les quartiers où tu n'es jamais allé Si tu habites à Rennes, dans quel quartier habites-tu ? …………………………………………………………. Depuis combien de temps y habites-tu ? ……………………………………………………………………………… Si tu habites dans une autre commune, quel est le nom de cette commune ? …………………………….. Depuis combien de temps y habites-tu ? ……………………………………………………………………………… Aimerais-tu déménager ?  Oui  Non Si tu devais déménager, indiques si tu aimerais habiter dans les quartiers suivants : , combien y a-t-il de garçons que tu considères comme tes meilleurs amis ? ………………………….. Et combien y a-t-il de filles que tu considères comme tes meilleures amies ? ……………………………………. Parmi tes meilleurs amis ou amies ,  Combien sont dans ton collège ? ………………  Combien sont dans un autre collège ? ………………  Combien habitent dans ton quartier ? ………………  Combien habitent dans un autre quartier rennais ? ………………  Combien habitent hors de Rennes ? ………………………… Ce questionnaire est maintenant terminé, nous te remercions d'y avoir répondu. Aurais-tu des critiques, des suggestions ? Certains problèmes qui te paraissent important auraient-ils dû être évoqués

94Chapter 3 :

 3 Segregation and Trust : An experiment in French secondary schools Si le joueur B vient de ton collège, combien de points souhaites-tu lui envoyer de cette thèse est à l'intersection de l'étude de la ségrégation urbaine et de la prise en compte de l'identité dans la compréhension des phénomènes et interactions économiques. Rédigée sous la forme de trois essais qui peuvent se lire de façon indépendante, elle propose dans un premier chapitre une analyse de la ségrégation résidentielle en France. Nous avons proposé une étude d'une famille d'indices de ségrégation basée sur la décomposition d'indices d'inégalité. Revenant sur la définition de la ségrégation, nous proposons de mesurer la ségrégation basée sur une variable continue, le revenu. Ce type d'études est rare en France où la ségrégation est le plus souvent mesurée selon des catégories (CSP, origine ethnique). L'importance de la ségrégation et l'objectif de mixité sociale dans le débat public rendent pourtant nécessaire ce type d'étude afin d'évaluer les politiques publiques et mesurer l'ampleur du phénomène. Nous contribuons au débat en proposant une mesure de la ségrégation résidentielle en France dans les 30 plus grandes aires urbaines sur la période 2001-2008, cette mesure permet notamment de voir que le phénomène a peu augmenté voir diminué, et de comparer les villes entre elles. Nous proposons ensuite dans un second chapitre une étude de l'identité ethnique des individus en France. Les questions d'identité sont récentes en économie mais de plus en plus développées, définies comme le sentiment que l'on a de soi par Akerlof & Kranton (2000), cette variable peut être intégrée dans la fonction d'utilité des individus. Au coeur du débat politique, la notion d'identité est importante notamment car elle a des effets sur les préférences des individus et impactent donc leurs choix et par conséquent leurs résultats socio-économiques. Il semble donc important de pouvoir mesurer cette variable notamment en vue de la mise en place de politiques publiques. L'objet du chapitre 2 est double, nous proposons tout d'abord un apport méthodologique sur la mesure de l'identité ethnique. Elle intéresse les économistes notamment dans les études sur l'intégration des migrants, qui en migrant peuvent faire face à un arbitrage entre adopter la culture d'accueil ou conserver leur héritage culturel. Le résultat de cet arbitrage a des conséquences sur leurs résultats socio-économiques. Le plus souvent approchée par l'identité nationale-la réponse à la question je me sens [français, marocain, italien...]-ethnique est difficile à mesurer. Certaines études proposent de mesurer l'identité via une analyse factorielle sur des critères identitaires définis a priori, c'est le cas notamment de l'ethnosizer de Constant et al. (2009). Similairement, nous proposons une mesure de l'identité ethnique via un indice construit grâce à une analyse factorielle sur des critères identitaires définis a posteriori, résultant de cette analyse factorielle même. Cet indice construit à partir de l'analyse des réponses à la question parmi ces 14 caractéristiques, lesquelles vous définissent le plus obtenues dans la base de données originale Trajectoires et Origines (TeO) permet de capturer une certaine distance identitaire entre les migrants et les natifs. Cette distance identitaire est associée à la notion d'assimilation, c'est à dire la proximité à la culture d'accueil majoritaire. Nous comparons cet indice d'assimilation à la mseure plus courante d'identité nationale. Nous montrons que l'assimilation et le sentiment d'être français ne coïncident pas toujours. Il semble que plus le pays d'origine est distant, à la fois en termes économiques et culturels, plus le sentiment d'être français est fort et plus le degré d'assimilation est faible. Dans un second temps nous nous intéressons à la formation de l'identité en étudiant les déterminants de l'assimilation. Nous proposons d'étudier l'impact de certaines caractéristiques socio-démographiques sur le degré d'assimilation des individus. Nous montrons notamment que l'identité des enfants d'immigrés converge vers celle des natifs, que celle ci soit approchée par le sentiment national ou le degré d'assimilation. Enfin dans un troisième chapitre nous mêlons l'étude de l'identité et de la ségrégation en nous intéressant aux effets de la ségrégation sur les préférences individuelles et notamment le degré de confiance aux autres. L'absence de confiance peut avoir des effets importants sur les interactions économiques et par là même avoir des conséquences sur les résultats socio-économiques des individus. En outre, les individus peuvent discriminer leurs semblables selon leur identité sociale, c'est à dire le groupe auquel ils appartiennent. Tajfel (1970) a d'ailleurs montré dans son paradigme du groupe minimal que de la discrimination entre groupes pouvait avoir lieu même pour des groupes créés sur des critères artificiels comme une couleur de ralliement. Des groupes sociaux peuvent être basés sur différents critères comme l'origine ethnique, le lieu de résidence, ou bien encore, comme c'est le cas dans notre étude, sur le collège d'appartenance. Nous avons mené une étude expérimentale dans des collèges rennais afin d'étudier l'existence de favoritisme intra-groupe ainsi qu'évaluer les effets de la ségrégation sur la confiance aux autres. Nous nous intéressons à des collégiens afin de réduire les effets d'endogénéité sur les choix de localisation des individus. L'expérience de terrain a été réalisée au sein de deux collèges qui se différencient par leur localisation géographique, étant situés dans des quartiers différents en termes de ségrégation. Nous montrons que les collégiens du collège ségrégé font globalement moins confiance que les collégiens dans le collège mixte. Nous ne trouvons pas d'évidence claire pour l'existence de favoritisme intra-groupe, nous observons cependant que les participants du collège ségrégé se comportent de manière

3. 1

 1 Map of Rennes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Neighborhood residency of teenagers (%) (a) stands for teenagers from school M, (b) for teenagers from school S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Father's Socio-Professional Category 0 stands for unemployed, 1 for blue-collar workers, 2 for employees, 3 for executives and 4 for retired. . . . . . . . . . . . . . . . . . . . . . . 3.4 Sequence of the game . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Distribution transfers A . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Distribution back transfers players B . . . . . . . . . . . . . . . . . . . . 3.7 Sequence of experiments . . . . . . . . . . . . . . . . . . . . . . . . . . Liste des tableaux 1.1 The data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Income segregation and income inequality (weighted mean) . . . . . . . 1.3 Mean Gini Inequality coefficients and coefficient of variation of individual and neighborhood income distributions, and economic segregation measures 1.4 Pearson's correlation coefficients (IRIS scale) . . . . . . . . . . . . . . . 1.5 Pearson's correlation coefficients (Grand Quartier scale) . . . . . . . . . 1.6 NSI and GSI values per region, 2008 . . . . . . . . . . . . . . . . . . . . 1.7 Tobit regressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Weights for assimilation index . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Predictions of each attrbiute by the index only . . . . . . . . . . . . . . 2.3 Means of ethnic identity measures . . . . . . . . . . . . . . . . . . . . . 2.4 Weighted shares of origins . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 National identity and assimilation inded for the whole population . . . . 2.6 Comparison of Identities between First and Second Generations . . . . . 3.1 Neighborhoods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 School comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 School' areas comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Transfers players A (%) . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Back transfer from player B ( % of the transfer) . . . . . . . . . . . . . . 3.6 Expected and actual returns . . . . . . . . . . . . . . . . . . . . . . . . . 3.7 Favoritism players A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8 Favoritism Players B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.9 Favoritism according to the payment decisions . . . . . . . . . . . . . . 3.10 Players B' favoritism (%) . . . . . . . . . . . . . . . . . . . . . . . . . .

Table 1 .

 1

	City	population Nb of	∆ IRIS	Nb of	∆	∆ pop	Pop.
			IRIS		quar-	quar-	(%)	Included
					tier	tier		(%)
	Paris	6099092.53 3728.00	24	617.14	12	28.54	93.23
	Marseille 766363.26	487.00	3	129.71	1	8.61	85.34
	Lyon	694787.91	411.43	6	154.43	2	9.04	77.37
	Nice	544977.76	301.29	8	52.00	3	18.61	84.35
	Lille	534558.39	367.29	6	113.71	0	13.65	85.42
	Bordeaux 439039.29	257.14	5	50.14	0	10.72	86.55
	Toulouse 369451.76	212.00	2	72.43	0	9.62	70.57
	Toulon	305651.26	180.71	1	26.00	1	4.67	82.51
	Nantes	298931.66	166.86	3	35.00	1	14.94	83.41
	Strasbourg 228236.56	139.71	3	45.86	0	0.30	85.03
	Rouen	217186.77	141.29	7	46.14	2	12.56	87.67
	Grenoble 202446.64	131.43	15	25.57	4	13.13	75.11
	Tours	162520.91	104.86	2	37.14	2	4.15	83.47
	Rennes	157381.83	103.14	6	20.00	0	10.08	93.71
	Saint-	146181.40	97.29	2	30.57	1	6.86	78.18
	Etienne
	Clermont 142212.33	74.43	1	30.14	0	2.77	85.00
	Le Havre 141094.70	95.86	19	28.43	6	45.56	90.46
	Montpellier 140584.80	78.14	26	27.43	3	14.05	73.81
	Dijon	133689.73	87.86	4	26.29	0	0.26	89.01
	Orleans	127882.80	77.86	7	33.00	3	14.12	74.51
	Mulhouse 118953.31	74.57	3	24.00	0	1.93	77.91
	Reims	116454.09	75.57	3	42.86	1	-0.92	89.19
	Brest	114776.97	72.71	18	6.00	5	16.17	88.30
	Angers	106392.99	68.71	2	15.00	0	6.94	76.39
	Limoges	102001.40	65.14	133	24.86	41	10.89	89.55
	Bayonne	100702.46	58.43	11	16.14	4	11.83	78.51
	Le Mans 100576.13	67.57	1	26.00	0	5.83	79.93
	Caen	98755.80	69.43	15	30.00	5	26.13	82.18
	Dunkerque 97341.70	61.14	4	28.71	0	7.79	82.57
	Amiens	79778.21	53.86	4	21.00	2	6.80	81.95

1: The data A slightly decrease in segregation. Table 1.2 presents the evolution of the mean values of both segregation indices and some inequality index. Each city is weighted by the size of its population in 2006 in order to estimate the average segregation experienced by people. Whatever the geographical scale, income-based segregation measured through the NSI increases between 2001 and 2004 and then decreases. In 2001, 32% of income inequality (as measured by coefficient of variation) can be explained by the inequality between IRIS, while this rate is 30% in 2008. Segregation measured by the GSI is rather stable over the period : indeed, in 2001 and in 2008, 49% of income inequality (as measured by the Gini Inequality index) can be explained by the inequality between neighborhoods. Chapitre 1 : Income segregation in large French cities At the same time, inequality as measured by Gini Inequality index and the coefficient of variation increases over the considered period.

Table 1 .

 1

2: Income segregation and income inequality (weighted mean)

Table 1 . 3 :

 13 Mean Gini Inequality coefficients and coefficient of variation of individual and neighborhood income distributions, and economic segregation measures

	Urban Area Income	Neighborhood	GSI	Individual	Neighborhood	NSI
		Inequality	Inequality		Household	Mean	In-
					Income	come
	Paris	0.42	0.23	0.55	0.0057	0.0018		0.32
	Marseille	0.40	0.20	0.50	0.0234	0.0085		0.37
	Lyon	0.37	0.17	0.47	0.0285	0.0090		0.32
	Nice	0.39	0.15	0.38	0.0400	0.0097		0.24
	Lille	0.39	0.21	0.54	0.0326	0.0128		0.39
	Bordeaux	0.35	0.14	0.40	0.0441	0.0116		0.26
	Toulouse	0.36	0.14	0.40	0.0528	0.0145		0.28
	Toulon	0.36	0.14	0.40	0.0513	0.0153		0.30
	Nantes	0.34	0.15	0.43	0.0663	0.0182		0.28
	Strasbourg	0.39	0.19	0.49	0.0917	0.0305		0.34
	Rouen	0.36	0.18	0.50	0.0778	0.0288		0.37
	Grenoble	0.35	0.15	0.43	0.0844	0.0273		0.33
	Tours	0.34	0.15	0.45	0.0998	0.0325		0.33
	Rennes	0.36	0.15	0.41	0.1272	0.0361		0.29
	Saint-	0.35	0.13	0.36	0.0981	0.0250		0.26
	Etienne
	Clermont	0.35	0.14	0.39	0.1426	0.0343		0.25
	Le Havre	0.37	0.20	0.53	0.1049	0.0423		0.41
	Montpellier 0.41	0.17	0.42	0.1308	0.0395		0.31
	Dijon	0.34	0.14	0.43	0.1276	0.0391		0.31
	Orleans	0.34	0.14	0.42	0.1257	0.0387		0.31
	Mulhouse	0.36	0.18	0.50	0.1363	0.0505		0.37
	Reims	0.37	0.18	0.48	0.1567	0.0512		0.33
	Brest	0.33	0.12	0.38	0.1239	0.0360		0.29
	Angers	0.35	0.15	0.43	0.1504	0.0470		0.31
	Limoges	0.35	0.13	0.36	0.1655	0.0444		0.27
	Bayonne	0.35	0.11	0.31	0.2043	0.0396		0.20
	Le Mans	0.34	0.15	0.43	0.1487	0.0484		0.33
	Caen	0.36	0.16	0.45	0.1584	0.0524		0.33
	Dunkerque	0.36	0.15	0.42	0.1298	0.0443		0.34
	Amiens	0.40	0.20	0.50	0.2460	0.0798		0.34
			Gini Segregation NSI	Gini Inequality
		GSI	1.0000
		NSI	0.7780 1.0000
		Gini Inequality	0.5401 0.2294	1.0000

Table 1.4: Pearson's correlation coefficients (IRIS scale)

Table 1

 1

.5: Pearson's correlation coefficients (Grand Quartier scale)

Table 1 .

 1 6 presents mean value of NSI and GSI for each large region in 2008. We divide France into 4 large regions : 11 North and Bassin Parisien (9 cities), West (9 cities), East (7 cities) and Mediterranean region (5 cities). 12 Northern cities seem to be more segregated than other cities and western cities seem to be the most mixed of French cities.

However we can note that standard-deviation of NSI values is larger within western cities than within other regions. 13 Table

1

.6 shows also the decomposition of the variance of the NSI values into within and between regions. The variability of NSI values among French cities at the IRIS level is mainly explained by variability within regions than between regions : around 30% of the variance of the IRIS -based NSI values and around 42% of the variance of the IRIS -based GSI values can be explained by variance between regions. Hence, even if the number of observation per group is small, we are not able to identify some clusters of segregated or mixed cities. We can illustrate this point by the following examples. In the Mediterranean region, Marseille is higly segregated (IRIS -based NSI value is equal to 0.37) whereas Nice is one of the most mixed cities (IRIS -based NSI value of 0.24).

Table 2 .

 2

	Identity	Weights based on
	attributes	MCA
	Religion	-4.019
	Skin color	-3.852
	Nationality	-2.547
	Origins	-1.831
	Region	-0.394
	Gender	0.039
	Family	0.498
	Health state	0.648
	Education	0.831
	Town/Neighborhood	0.843
	Generation	1.580
	Political view	1.725
	Job occupation	2.207
	Hobbies	2.378

1: Weights for assimilation index Results for MCA-based weighting procedure are presented in table 2.1. There are 9

Table 2 .

 2

	Predictions of each attrbiute by the
		index only
	Good predictions	Not selected	Selected Total
	Religion	77.18	91.14	84.16
	Skin color	73.16	89.90	81.53
	Hobby	71.54	80.51	76.03
	Job occupation	78.00	69.85	73.93
	Nationality	75.44	68.48	71.96
	Generation	70.25	66.14	68.20
	Origins	49.38	80.19	64.79
	Political view	85.98	42.72	64.35
	Quartier	58.27	63.27	60.77
	Education	58.20	62.45	60.32
	Health	82.66	28.38	55.52
	Family	56.50	52.32	54.41
	Region	68.93	36.54	52.73
	Gender	66.14	35.37	50.75
	Total	69.40	61.95	65.67

2: Predictions of each attrbiute by the index only check whether or not predicted values of these simple models match actual answers of respondents. 2.2 gives the percentages of correct predictions for each identity attributes.

Table 2 . 3 :

 23 Means of ethnic identity measures

Table 2 .

 2 [START_REF]Ta décision et la sienne détermineront la valeur de ton bon d'achat ainsi que la valeur du sien. Chaque point gagné te rapporte 60 centimes d'euros supplémentaires. Par exemple, si le jeu te permet de gagner 5 points, tu gagnes un bon d'achat d'une valeur de 13 euros : 10 euros + 5 points x 60 centimes[END_REF] gives weighted means of our both endogenous measures of ethnic identity.Obviously, weights have important impacts on statistics for the whole sample because of over-representation of immigrants in the survey. The proportion of respondents which agrees with the sentence "I feel French" largely corresponds to majority (93.75%, 97.87% for natives and 93.12% for denscendants). One could consider the proportion of first generations which agrees as low (63.33%) but it is quite similar with the value found

	by Manning & Roy (2010) or Battu & Zenou (2010) for British national identity and
	much higher than what Casey & Dustmann (2010) obtain for German national identity
	among immigrants with very similar questions in both cases.

Table 2

 2

.4 allows for analyzing the changes of the structure of the French immigration.

Indeed, here are presented origins of parents. If we compare second and first generations origins, we then roughly consider two different, although wide, waves of immigration (in average, around the late 60's for second generations' parents, and in the late 80's for first generations). Maghreb immigration has slightly decreased in proportion of overall immigration while the proportion of western European immigration is almost divided by two. Eastern Europe immigration stays at a relative low revel when Sub-Saharan's, Asian's and Turkish's have significantly increased. Finally, 41% of second generations' mothers or fathers are French.

Complementary tables of descriptive statistics are available in the Appendix. We notably observe that average time since arrival of first generations is quite high (almost 21 years).

Table 2 .

 2

		Whole	1st	2nd
		Sample	Generation	Generation
	Other Africa	6.66	10.10	3.30
	Northern America	0.70	0.81	0.58
	South America	1.98	3.11	0.70
	Asia	4.98	7.81	2.26
	Eastern Europe	7.11	6.27	7.95
	Western Europe	40.14	27.72	52.26
	North Africa	29.57	31.36	27.91
	Middle East	1.82	2.52	1.14
	Sahel	3.04	4.00	2.10
	Turkey	4.01	6.30	1.80
		100.00	100.00	100.00

4: Weighted shares of origins the work of some French researchers (notably Lagrange (

2013

)) who pointed out a more diffitult integration of Sahelian natives due to cultural gaps. 41.28% of first generations immigrants already acquired French citizenship at the time of the survey. The literature regularly points out the importance of the citizenship's acquisition on national identity of immigrants. Furthermore, we observed that 83.4% of immigrants with French citizenship claim national identity against 49.2% for those without. This is going to be verified by further econometric analysis.

Table 6

 6

		(continued)
	Comparison of Identities between First and Second Generations
		National Identity	Assimilation index
		1st	2rd	1st	2nd
		Generations Marginal	Genenations Marginal	Generations	Generations
				Estimate	Estimate
	Importance of religion in received	effect	effect
	education	-0.0215**	-0.00819*	-0.541***	-0.471***
		(-2.70)	(-2.53)	(-11.04)	(-5.06)
	Mother religion (ref. atheist)
	Christian	-0.0270	0.00990	0.221	0.160
		(-0.61)	(0.70)	(0.86)	(0.55)
	Muslim	0.00315	-0.0211	0.661	-0.347
		(0.05)	(-0.97)	(1.60)	(-1.05)
	Buddhist	-0.0681	-0.0384	1.011*	-0.468
		(-0.66)	(-0.47)	(1.96)	(-0.95)
	Other	-0.0509	-0.0102	0.605	0.597
		(-0.76)	(-0.50)	(1.42)	(1.10)
	Father religion (ref. atheist)
	Christian	0.0722	-0.00933	0.0467	0.606**
		(1.91)	(-0.64)	(0.21)	(2.63)
	Muslim	0.0456	-0.0118	-0.632	-0.122
		(0.74)	(-0.65)	(-1.58)	(-0.47)
	Buddhist	-0.0718	-0.00360	-0.294	-0.0161
		(-0.70)	(-0.09)	(-0.58)	(-0.04)
	Other	0.0391	-0.0272	-0.102	-0.421
		(0.73)	(-1.20)	(-0.28)	(-1.35)
	Parents' language (ref. French)
	European	-0.100*	-0.0746**	0.0530	-0.393
		(-2.52)	(-2.79)	(0.24)	(-1.65)
	Arab	-0.0771	-0.0202	-0.231	-0.866***
		(-1.49)	(-1.49)	(-0.59)	(-3.99)
	Berber	-0.119	-0.0372	-0.637	-0.236
		(-1.83)	(-1.31)	(-1.35)	(-0.58)
	Sahel	-0.121	-0.0270	-0.466	0.239
		(-1.80)	(-0.92)	(-0.98)	(0.44)
	African	-0.117*	-0.0547	0.0554	-1.786**
		(-2.38)	(-1.13)	(0.18)	(-3.09)
	Asian	-0.143**	-0.0000113	-0.128	0.0240
		(-2.71)	(-0.00)	(-0.37)	(0.06)
	Turkish	-0.261**	-0.0790	-0.0790	-1.371**
		(-3.25)	(-1.31)	(-0.18)	(-2.92)
	Other	-0.171	-	-0.270	-
		(-1.46)	-	(-0.35)	-

Table 3 . 1 :

 31 Neighborhoods

Table 3 . 2 :

 32 School comparisona. Based on parents' socio-professional group[START_REF] Merle | Carte scolaire et ségrégation sociale des établissements. une analyse monographique des collèges rennais[END_REF]

	.2 ).

Table 3 . 3 :

 33 School' areas comparison

Table 3

 3

		.4: Transfers players A (%)
	M	S

Table 3 .

 3 5 shows the average back transfer rates of players B. The first remark is that players belonging to school M seem to behave similarly whatever the school belonging of player A. A Wilcoxon test enables to accept the hypothesis which states that the rate of return are identical whatever the school belonging of player A (p = 0.9655). By contrast, players from school S seem to transfer back a higher amount to players A located in a different school, though this difference is not statistically significant (p = 0.5880,

	Wilcoxon test)

Table 3 .

 3

		Same school Different school
	All players	47.31	50.65
	School M	47.40	47.11
	School S	47.24	53.81

5: Back transfer from player B ( % of the transfer)

Table 3 .

 3 Chapter 3 :Segregation and Trust : An experiment in French secondary schools 93 Intra-group favoritism Egalitarianism intra-group discrimination

		M	S	M	S	M	S
	1	25	18.52	58.33 51.85 16.67	29.63
	2	25	25.93	50	37.04	25	37.04
	3 16.67	44.44	54.17 18.52 29.17	37.04
	4	25	29.63	41.67 37.04 33.33	33.33

10: Players B' favoritism (%)

  Table des figures 1.1 Ranking correlation between GSI and NSI (IRIS scale) . . . . . . . . . . 1.2 Ranking correlation between GSI and NSI (Grand quartier scale) . . . . 1.3 Ranking over time (IRIS scale) . . . . . . . . . . . . . . . . . . . . . . . 1.4 Value over time (IRIS scale) . . . . . . . . . . . . . . . . . . . . . . . . 1.5 The value of GSI according to the scale area unit . . . . . . . . . . . . . 1.6 The value of NSI according to the scale area unit . . . . . . . . . . . . . 1.7 Correlation between GSI and Coefficient of Variation (IRIS scale) . . . 1.8 Correlation between NSI and Coefficient of Variation (IRIS scale) . . .

& Grenet (2011)). D'autre part,[START_REF] Schelling | Dynamic models of segregation[END_REF] montre qu'un équilibre ségrégé peut se produire même si individuellement les agents ont des préférences pour la mixité. Basant son analyse sur un échiquier avec des pions de deux couleurs différentes représentant des individus,[START_REF] Schelling | Dynamic models of segregation[END_REF] montre encore qu'un équilibre ségrégé se produit lorsque les agents décident de bouger s'ils deviennent minoritaires. Dès lors on atteint une situation de ségrégation alors que les agents n'ont a priori pas de préférence pour la ségrégation.En France le phénomène de ségrégation est au coeur du débat public depuis plus de vingt ans et l'objectif de mixité sociale est poursuivi à travers l'adoption de politiques de la ville qui ciblent des territoires prioritaires. Cet objectif de mixité s'est notamment traduit par l'adoption de la loi Solidarité et Renouvellement Urbain (SRU) en 2000. Cette

Note the coefficient of correlation between Gini Inequality coefficient values and Coefficient of Variation values are in average equal to 0.68

See Noiriel (2002)).

One might think that skin-color is particularly discriminating since it would target particular population. Around 36% of sub-Saharan migrants choose this feature against nearly 10% of French. As regard to the relatively limited gap between the previous proportions we do not think that this feature is biased by restrictiveness.

moins égalitaire favorisant cependant autant les collégiens d'un collège différent que du même collège.

Remerciements

the next section while considering only immigrants. What is actually primordial is not the religion but the importance of it in respondent childhood education.

6 National identity and assimilation : first and second generations This section investigates the determinants of ethnic identity for first and second generations of immigrants table (2.6) and allows innovative information about their situation in France. We are also able to challenge previous conclusions of the literature. Unfortunately, we do not have panel data and immigration structure has changed between first and second generations of the sample, comparisons in terms of intergenerational integration between these two groups are thus fragile.

Differences between second and first generations

The determinants of ethnic identity do not have the same impact on first and second generations. Origins well explain identity of first generations (with positive signs for rational identity and negative ones for the index, this result is developed in the next subsection) but do not influence second generations' one. This is an evidence for the process of assimilation since the inertia of home culture decreases among time and generations.

Chapter 3 : Segregation and Trust : An experiment in French secondary schools

Player A from the same school (a) We study now whether the players behave differently regarding the school belonging of their partner. We distinguish 3 types of attitudes :

-intra-group favoritism : player A always sends more to player B if B is in the same school than in a different school. Respectively player B always send more to a player A from the same school.

-egalitarian behavior : Player A always send the same amount to a player B from the same school and from a different school. Similarly for player B.

-intra-group discrimination : Player A always sends more to a player B from a different school than from the same school. Respectively player B always favor a player A from a different school.

Chapter 3 :Segregation and Trust : An experiment in French secondary schools 81 Table 3.7 and 3.8 show the repartition of players regarding these 3 attitudes. Our results can be summarized the following way :

Result 3. Players from the non segregated school (M) adopt more frequently an egualitarian attitude than players from the segregated school (S). These latest discriminate players from a different school as much as players from their school.

Players A. A majority of players from school M (62,5%) adopt an egalitarian attitude,that is to say they send as many points to a player B in the same school as a player B in a different school. A quarter of them discriminate in favor of their own group while 12.5% discriminate in favor of the other group. Tests of proportion enables to say that a significant higher proportion of players from school M adopt an egalitarian behavior than a discriminant behavior (in favor or against their own group) : p = 0, 0088 (equality versus intra-group favoritism) and p = 0, 0003 (equality versus inter-group favoritism)

Concerning players from school S, they uniformly distribute between the 3 attitudes.

A χ 2 test of goodness-of-fit indicates that the observed distribution is not significantly different from a uniform distribution (p = 0, 9608). Players B. Each player B had to take 8 decisions according to the (hypothetic) transfer of player A and regarding the school belonging of the latest. We compare the amount sent back to a player A from the same school to the amount sent to a player A from a different school, given the transfer from player A. We can thus classify the behavior of player B in 4 different cases (each one characterised by the amount of the transfer from player A).

School M School

Essays on segregation and identity in France

This thesis focuses on the study of urban segregation, ie the isolation both social and spatial of certain groups of individuals within cities. Also, to characterize groups of individuals and measure their degree of social integration, this thesis focuses on the definition and measurement of identity, defined as a person' sense of self. In the first chapter we focus on a measure of urban segregation, proposing a theoretical and empirical analysis of an index of Economic segregation on a continuous variable (the income) in France. We then are interested in a second chapter by the social integration of immigrants and children of immigrants in France where the ethnic identity of individuals is an expression of this integration. This chapter introduces an index that allows continuous measurement of ethnic identity and captures a certain distance in identity. We compare this index with other usual measures in the literature and study the socio-economic determinants of ethnic identity. Finally, in the third chapter, we focus on the effects of urban segregation in the degree of cooperation and trust of individuals. We study the potential impact of the neighborhood residency of a person on his trust . For this, we perform an experimental study in different schools in Rennes among teenagers.

Keywords : Segregation ; Income ; Identity ; Ethnic Identity ; Assimilation ; Migrants ; City.