Amélie Banc

Bernard Desbat

Denis Renard

Yves Popineau

Cécile Mangavel

Laurence Navailles

Exploring the Interactions of Gliadins with Model Membranes: Effect of Confined Geometry and Interfaces

Mechanisms leading to the assembly of wheat storage proteins into proteins bodies within the endoplasmic reticulum of endosperm cells are unresolved today. In this work, physical chemistry parameters which could be involved in these processes were explored. In order to model the confined environment of proteins within the endoplasmic reticulum, the dynamic behavior of γ-gliadins inserted inside lyotropic lamellar phases was studied using FRAP experiments. The evolution of the diffusion coefficient as a function of the lamellar periodicity enabled to propose the hypothesis of an interaction between γ-gliadins and membranes. This interaction was further studied with the help of phospholipid Langmuir monolayers. γand ω-gliadins were injected under DMPC and DMPG monolayers and the 2D systems were studied by Brewter Angle Microscopy (BAM), Polarization Modulation Infrared Reflection-Absorption Spectroscopy (PM-IRRAS), and surface tension measurements. Results showed that both gliadins adsorbed under phospholipid monolayers, considered as biological membrane models, and formed micrometer-sized domains at equilibrium. However, their thicknesses, probed by reflectance measurements, were different: ω-gliadins aggregates displayed a constant thickness, consistent with a monolayer, while the thickness of γ-gliadins aggregates increased with the quantity of protein injected. These different behaviors could find some explanations in the difference of aminoacid sequence distribution: an alternate repeated -unrepeated domain within γ-gliadin sequence, while one unique repeated domain was present within ω-gliadin sequence. All these findings enabled to propose a model of gliadins selfassembly via a membrane interface and to highlight the predominant role of wheat prolamin repeated domain in the membrane interaction. In the biological context, these results would mean that the repeated domain could be considered as an anchor for the interaction with the endoplasmic reticulum membrane and a nucleus point for the formation and growth of protein bodies within endosperm cells.

Introduction

Wheat storage proteins (WSP), constituting gluten, are very important for various technological applications ranging from baking performances 1 , to the elaboration of biomaterials 2 , and the development of new drug delivery systems 3 . Moreover, as wheat is the world's largest crop, these storage proteins are the major source of dietary protein for human and livestock. Most of WSP are classified as prolamins because of their high proportions of proline and glutamine. Despite their high proportion in polar glutamine residues, prolamins are poorly soluble in water. However they can be dissolved in water-alcohol mixtures or in low pH solutions [START_REF] Osborne | The vegetable proteins[END_REF] . WSP display a very extensive polymorphism, but they present a common feature which is the presence of repeated amino acid sequences in their primary structures. Prolamins are subdivided into two groups based on their ability to form polymeric systems by means of intermolecular disulfide bonds between protein subunits 5 . Gliadins are monomeric proteins, whereas glutenins are polymeric ones. Gliadins account for about half of the gluten proteins, and are subdivided into four types according to their electrophoretic mobility in acid-polyacrylamide gel electrophoresis, commonly denoted as α-, β-, γ-, and ωgliadins. α-, βand γgliadins have similar primary structures. They are composed of a short N-terminal domain, a repetitive domain which contains repeated motifs rich in proline, glutamine and phenylalanine, and a non-repetitive domain which includes all intramolecular disulphide bonds. Their primary structure indicates that the non-repetitive domain is more hydrophobic than the repetitive one, suggesting an amphiphilic feature of these gliadins. ω-gliadins principally consist of proline and glutamine residues, and are made up almost entirely of repeated domains without cysteines to form disulphide bonds 6 . ω-gliadins are globally more polar than α-, βand γ-gliadins [START_REF] Popineau | High performance liquid chromatography of cereal and legume proteins[END_REF] .

In the biological context, WSP serve as amino acid source for germination, and are principally stored within protein bodies in developing grains, before their maturity. Protein bodies (PB) are micrometer-sized organelles emerging from endoplasmic reticulum membranes, and may contain up to 80% of proteins [START_REF] Galili | [END_REF] . The mechanisms leading to the formation of PB, and the organization of storage proteins inside the organelles, are not well understood today. An accumulation of proteins within the endoplasmic reticulum (ER), leading to the emergence of protein bodies in the cytoplasm, is suggested. However, due to the absence of a retention signal in the sequence of these proteins, the sequestration and the accumulation processes of proteins in the lumen of the ER are unexplained 9 . Today, understanding the mechanisms involved in the unconventional protein traffic pathways which lead to PB formation, is a great challenge in plant biology 10 . Moreover, the organization of WSP in the biological context, as well as their composition, should be important for wheat grain quality. The aim of the study is to elucidate physical chemical parameters involved in the organization of WSP in the cellular context. The formation of natural-like PB with prolamins expressed in different heterologous systems 11,12,13 suggested that the mechanism involved was controlled by the intrinsic structure of proteins as well as by the ER environment. The strategy of this work was thus to study the behavior of model WSP in a confined environment similar to the ER, in order to identify key parameters of the accumulation process. Considering the high membrane surface in the ER, the interactions between WSP and membranes were more particularly studied. To our knowledge, the hypothesis of such interactions was scarcely studied. Kogan et al 14 revealed the interaction between a peptide corresponding to the repetitive domain of γ-zein (a maize storage protein) with soybean phosphatidylcholine liposomes. In the case of wheat, it was observed that total gliadins could modify mechanical properties of giant unilamellar vesicles membranes 15 . In our study, model WSP used were γ-gliadins and ωgliadins. γ-gliadins are considered as an ancestral form of storage proteins, and were shown to be able to form alone PB in heterologous systems 9 . ω-gliadins were also used because their involvement in PB formation could be different due to their fully repetitive sequence. This assumption is supported by the different surface properties of γand ω-gliadins at the air-water interface 16 . Furthermore, ω-gliadins should be considered as a model of the repetitive domain of γ-gliadins. In a first part, lyotropic lamellar phases, consisting of stacks of surfactant bilayers separated by aqueous layers, were used as an ER model environment for gliadins. This 3D approach enabled us to study both the confinement effect on the proteins assembly, and to suggest an interaction between gliadins and membranes. However, the results obtained with this approach being not sufficient to firmly conclude on the gliadin-membrane interaction, in a second part, a 2D approach was carried out to look at the protein behavior at the water lipid interface. In this case, 1,2-Dimyristoyl-sn-Glycero-3-Phosphocholine (DMPC) and 1,2-Dimyristoyl-

sn-Glycero-3-[Phospho-rac-(1-glycerol)]

(DMPG) monolayers were used as ER model membranes. DMPC was chosen as it represents the major phospholipid contained in plant ER membranes 17 , while DMPG was selected in order to study the effect of negative charges generally observed in biological membranes.

Experimental methods

1/ 3D approach: lyotropic lamellar phases system Samples. γand ω-gliadins were purified according to Banc et al 16 procedure. The gliadin components used in this work were not fully sequenced. However it is possible to propose putative sequences (table 1) based on their measured molecular masses, partial sequences and other physicochemical properties with reference to literature 18,19,20,21,22 . γ-gliadin was labeled with tetramethylrhodamine isothiocyanate (TRITC) according to a new procedure adapted for this protein which is not soluble in alkaline aqueous solutions. Briefly, the freezedried γ-gliadin was dissolved at 10 mg/ml in an ethanolbicarbonate buffer (0.1 M, pH 9) mixture 45:55 (v/v) and incubated for 7 hours, at 50°C, with a TRITC solution at 10 mg/ml in DMSO. The molar ratio of TRITC to γ-gliadin in the initial reaction solution was 10. After reaction, the excess reagent was removed by extensive dialysis against a water-ethanol (45:55) solution, and the final molar ratio of TRITC to γ-gliadin, determined by UV spectroscopy, was 1. The lamellar phase system was spontaneously formed with the non-ionic n-pentaethyleneglycol monododecylether surfactant C 12 E 5 (Nikko Ltd), hexanol and water 23,24 . The hexanol/C 12 E 5 weight ratio used was 0.29, and the water content was varied from 40 to 90 wt%. This range of aqueous fractions enabled to obtain monophasic smectic structures with repeat distances d ranging from 5 to 18 nm. Three different probes were mixed with the lyotropic lamellar formulations at constant concentration (0.08% (w/w)): The rhodamine-labeled γ-gliadin (γ-gliadin-TRITC), the rhodamine dye TRITC (mixed isomers, purchased from Aldrich) and the hydrophobic probe, rhodamine 1,2 dihexadecanoyl-sn-glycero-3phosphoethanolamine (DHPE-TRITC, purchased from Invitrogen -Molecular Probes). After mixing, samples were let several days to reach equilibrium. X-ray scattering. Small angle x-ray scattering experiments (Nanostar, Bruker) were performed in order to describe the host phase nature and to measure the lamellar spacing (d) of lamellar phase systems. Samples prepared with various water contents display various water layer thicknesses (d w ). The quantity d w was deduced from the swelling behavior established using x-ray experiments as follows: the stacking period d of the lamellar phase was first obtained from the value q max of the first order Bragg peak as d = 2π/q max . Repeating the measurement for different water concentrations, the bilayer thickness δ was extracted from the swelling law d = δ/φ m, with φ m the membrane volume fraction. The water layer thickness was finally deduced using the relation d w = d-δ. Optical microscopy. Polarized light and fluorescence microscopy observations were done on a Leica SP2 confocal laser scanning microscope. For observations, flat capillaries (thickness e = 50 µm) were filled with the lamellar phase samples and sealed with a UV-curing adhesive (Norland Optical Adhesive 81).

Diffusion coefficients determination using FRAP measurements.FRAP measurements were performed using a confocal laser scanning microscope (CLSM) that gives high spatial resolution 25 and allows surgical bleaching. In order to measure the translational diffusion coefficient parallel to the layers (D ┴ , i.e. perpendicular to the optical axis), homeotropically oriented lamellar phases were used. In flat capillaries, the lamellar phase naturally adopted homeotropic anchoring (stacking axis perpendicular to the walls) and well oriented monodomains were thus obtained. The homeotropic orientation was checked using the optical polarized light microscopy technique, so that the laser beam was parallel to the normal of the layers. The bleaching and imaging were performed on a Leica SP2 confocal microscope with an oil immersion x63 objective lens (numerical aperture 1.4). A spot area of nearly 2 µm in radius was bleached during a time τ (in the range 1 to 10 s, depending on the sample). The image acquisition was made by scanning the field with a confocal photomultiplier (acquisition time of a few seconds) after a time t (1.635 s) had elapsed. Analysis of data was performed according to the Moreau et al 26 method. In a first approximation, the lateral width of the laser beam spot was neglected. Secondly the permeation through the bilayers was considered to be so small that the diffusion coefficient for motions in the direction parallel to the optical axis (D ⁄ ⁄ ) was assumed negligible compared to the translational diffusion (D ┴ ) for species diffusing between nanometered-separated membranes. As a consequence, the concentration of bleached dyes c(r, t) versus space and time, initially nonzero only within the point-like laser spot, is found by integrating Fick's law in the 2D-space perpendicular to the optical axis, which leads to: when the bleaching duration was extremely short. In eq. (1), r is the distance from the center of the bleaching point, t the time, D ┴ the diffusion coefficient in the layer plane, and c 0 a normalization constant depending mainly on dye concentration, power of the bleaching radiation, etc. For the sake of simplicity, the depletion in fluorescence intensity at time t after a photo bleaching of finite duration τ is represented as the superimposition of time-translated expressions similar to eq. ( 1), namely: with, t > τ, and I 0 a normalization constant. Using this scheme, the fluorescence intensity could therefore be described by the equation: with E 1 the exponential integral function of order 1. The diffusion coefficient D ┴ was deduced from the recorded images by a numerical fitting using eq. ( 3), with only two fitting parameters, namely I 0 as an arbitrary intensity scale and σ 2 ≡ 4D ┴ t, since the bleaching duration τ was known.

(1)

(2)

(3) 2/ 2D approach: Langmuir films system Materials.Experiments were done in a circular Teflon® trough 51 mm radius, filled with 8 mL of subphase. The subphase was constituted of a 50 mM pH 7.2 phosphate buffer previously filtered through a glass microfibre filter (GF/F, Whatman). The water used was purified from a milliQ system (Millipore, Molsheim, France) with a nominal resistivity of 18.2 MΩ.cm. Phospholipids monolayers were prepared with DMPC or DMPG purchased from Avanti Polar Lipids. Phospholipids were previously dissolved in chloroform (for DMPC), or chloroform:ethanol 4:1 (v/v) (for DMPG) at 0.5 mg/ml, and spread at the air-water interface using a Hamilton microsyringe according to the Langmuir method. The volume injected was adjusted in order to obtain the required monolayer pressure. Proteins used were γ-gliadins and ω-gliadins purified according to the Banc et al procedure 16 . Freeze-dried proteins were dissolved in a 48:52 (v/v) water:ethanol mixture at a concentration C = 1 mg/mL, and filtered through a 0.45 µm porosity filter (Millipore). After an equilibration time of the phospholipid monolayer, protein solutions were injected into the subphase using a Hamilton microsyringe. The surface pressure (π) was monitored by a Wilhelmy surface balance using a filter paper plate (Whatman). Brewster Angle Microscopy.The surfaces of the films were observed using the Brewster angle microscope BAM2 plus (NFT, Göttingen, Germany) equipped with a frequency doubled Nd:YAG laser with a wavelength of 532 nm and a charge-coupled device (CCD) camera with a x10 magnification lens. The exposure time (ET), depending on the image luminosity, was adjusted from 20 to 0.5 ms to avoid saturation of the camera.The spatial lateral resolution of the Brewster angle microscope was 2 µm, and the image size was 400 x 650 µm². The BAM images were coded in grey level. To determine the reflectance of layers at the surface, the calibration procedure of the BAM software was used to determine the linear function between the reflectance and the grey level. This function was established by comparison between the experimental curve of the grey level as a function of the incidence angle and the Fresnel curve (curve of the reflectance as a function of the incidence angle) that can be fitted by a parabola around the Brewster angle minimum. PM-IRRAS. Spectra were recorded on a Nicolet 870 Fourier transform infrared (FT-IR) spectrometer by coaddition of 600 scans at a resolution of 8 cm -1 . The details of the optical setup, the experimental procedure, and the two-channel processing of the detected intensity have been already described 27 . PM-IRRAS is a technique sensitive to the orientation of the transition moment at the water surface, and hence the molecular groups themselves. Briefly, the surface selection rule indicates positive bands for transition moment lying in the surface plane whereas negative bands are attributed to transition moments perpendicular to the surface. For an intermediate orientation of the transition dipole moment, the two contributions are competing and the absorption band vanishes when the transition dipole moment is tilted at 39° from the surface normal of the water subphase. PM-IRRAS device allows obtaining of the differential reflectivity spectrum:

∆R/R= [(Rp-Rs)/(Rp+Rs)].J 2 (4)
with Rp the p-polarized reflectance, Rs the s-polarized reflectance and J 2 the Bessel function.

To remove the contribution of the subphase absorption and the dependence on the Bessel function, the film spectra were divided by that of the subphase. The water vapor contribution on each film spectrum was removed by subtraction of water vapor spectrum.

Results

1/ 3D approach: lamellar phase system Structural characterization. In order to study the behavior of model gliadins inside a membrane confined environment, lyotropic lamellar phases were formulated with labeled γ-gliadins. Hydrophilic and hydrophobic model probes were also prepared in the lamellar system to support the analysis. Firstly, a characterization of the samples was performed to determine whether gliadins were inserted inside the lamellar phase or notFigure 1 displays microscopic observations of gliadin doped lamellar systems. The typical texture of defects of the lamellar structure [START_REF] De Gennes | The Physics of Liquid Crystal[END_REF] (oily streaks) appears using polarized light microscopy (Fig. 1a). The fluorescence intensity is homogeneous in homeotropic domains (Fig. 1b) when the membranes are parallel to the glass plates (i.e. the normal of the layer is parallel to the optical axes), and bright fluorescent spots are observed in the vicinity of the lamellar phase grain boundaries. These observations indicate a biphasic system of gliadins inserted inside the lamellar phase and aggregated gliadins outside the lamellar phase. The protein should be partially excluded from the lamellar phase so that the texture looses its homogeneity. This phenomenon is more pronounced in diluted systems. For the hydrophilic (TRITC) and hydrophobic (DHPE-TRITC) probes, a monophasic doped lamellar phase with the probe totally inserted inside the lamellar phase is always characterized. The lamellar structure of doped samples was also checked by x-ray diffraction experiments. Figure 2 displays typical x-ray diffraction results obtained for lamellar systems formulated with γ-gliadin. Bragg peaks observed in Fig. 2a are consistent with the lamellar structure of the host phase. An intensity increase of the small angle scattering with dilution of the systems is also observed. Though not investigated in details, it may be correlated to the presence of large protein aggregates between lamellar phase grain boundaries observed by fluorescence microscopy. Fig. 2b compares the swelling law d vs 1/ φ m for the gliadin doped lamellar system and the undoped system previously studied by Freyssingeas et al 24 . The membrane thickness δ is found to be equal to 2.9 and 3.0 nm for the undoped and doped system, respectively. It turns out that the stacking periods are not significantly modified after addition of either protein (Fig. 2b) or probes (data not shown). The most important result is that gliadins may be inserted inside the lamellar phase for a large range of dilutions. Dynamic inside the lamellar phases. The dynamic of the γgliadins inserted into lyotropic lamellar phases with various water contents was studied by FRAP experiments. As the image analysis is based on the Fick's law and equation ( 3), the Brownian dynamic of the different labeled molecules inside lamellar systems was checked measuring the parameter σ 2 as a function of time: The Gaussian broadening should be a simple linear function of the elapsed time t. Figure 3 shows the evolution of σ 2 versus time for the γ-gliadin-TRITC protein, TRITC and DHPE-TRITC probes inserted in the C 12 E 5 /Hexanol system with a water layer thickness (d w ) equal to 8 nm. From the observed linear behavior, unambiguous values for the diffusion coefficient could be deduced with our FRAP analysis method. Using FRAP experiments, the diffusion coefficient D ┴ of each probe as a function of the water layer thickness d w of the C 12 E 5 /Hexanol/Water lamellar phase was measured. For the TRITC dye, the molecules should be encapsulated inside the water layer of the lamellar structure 26 . Despite the large error bars, it can be observed that at large d w , the D ┴ values asymptotically approach 120 x 10 -12 m 2 /s; at lower d w , the diffusion coefficient D ┴ significantly and steadily decreases; and a quasi-plateau, where D ┴ exhibits little variations with d w, is reached for d w < 4.7 nm (vertical full line in Fig. 4). The first (dilute) regime can be qualitatively explained by Faxén's model [START_REF] Faxén | Low Reynolds number hydrodynamics[END_REF] for the 2D selfdiffusion of a colloidal particle symmetrically confined between two rigid walls. According to this model, at high dw values the translational diffusion coefficient of the diffusing object D ┴ tends towards the 3D free-diffusion coefficient value. The second (concentrated or confined) regime, when the self-diffusion coefficient remains nearly constant for small membrane separations, was explained by the confinement (d w < particle diameter) of particles between fluid membranes 26 . According to the authors, the limit between the two regimes is thus directly correlated to the diameter of the particle. It is interesting to note that the transition in our system apparently occurs for a d w value (4.7 nm, vertical full line in Fig. 4) larger than the expected hydrodynamic diameter of the TRITC dye [START_REF] Karolin | [END_REF]31,32 (ca. 1 nm).

At the same time, the diffusion coefficient for large d w values is close to 120 x 10 -12 m 2 /s. This asymptotic value is much lower than the 3D free-diffusion coefficient D 0 (ca. 425 x 10 -12 m 2 /s) of TRITC calculated using the Stokes-Einstein equation (in water at 20°C). This equation relates the free diffusion coefficient of a hard sphere in a Newtonian fluid to the hydrodynamic radius, in the colloidal range in which the sphere is subject to Brownian motion:

where For the DHPE-TRITC probe, the diffusion coefficient is mostly independent on swelling (Fig. 4, empty squares).

The values are small (ca. 20 x 10 -12 m 2 /s) and do not vary with the confinement, behavior in agreement with amphiphilic probes diffusing along the bilayers. Interestingly, the same behavior is observed for the γgliadin-TRITC protein (Fig. 4, filled diamonds) encapsulated inside the C 12 E 5 /Hexanol/water lamellar phase. The diffusion coefficient value does not vary with d w , and is equal to 30 x 10 -12 m 2 /s, a small value again. This invariance of the diffusion coefficient clearly indicates that γ-gliadin do not freely diffuse in the water layer of the lamellar structure. Either the proteins are in interaction with the bilayers, or they form large objects soluble in the aqueous medium which remain geometrically confined by adjacent bilayers in the whole range of d w studied. In order to confirm and decipher a potential membrane-gliadin interaction, a complementary 2D approach was performed using different kinds of gliadins (γ-and ω-gliadins) and phospholipids (DMPC and DMPG).

2/ Langmuir films

Interfacial pressure 2D experiments were carried out using DMPC or DMPG monolayers at the air-water interface, as model membranes. This increase of pressure can be ascribed to an insertion of gliadins inside the monolayer. When the DMPC monolayer has an initial pressure of 35 mN/m, even if a perturbation is firstly observed, the surface pressure is finally unmodified after a short equilibration time. At this higher pressure, γ-gliadins can not penetrate into the DMPC monolayer. The same behavior was observed with the DMPG monolayer. Keller et al 33 previously found that a complex gliadin fraction could not insert into lipid or emulsifier monolayers above a critical surface pressure.

The gliadin insertion into DMPC or DMPG monolayers depends on interfacial pressure, as observed for numerous proteins 34,35,36 . In some cases, however the peptides expelled from the lipid monolayer remained adsorbed at the monolayer 36 . Because the biological membrane pressure is considered ranged from 25 to 35 mN/m 37 , it can be supposed that γ-gliadins do not insert into biological membranes. In this range of surface pressures, ω-gliadins exhibit the same behavior as γ-gliadins. Only the system with a 35 mN/m initial pressure was further characterized because our study is related to the behavior of gliadins in the ER lumen.

BAM measurements. The effect of the injection of gliadins under DMPC monolayers was observed by Brewster Angle Microscopy. At 35 mN/m, DMPC monolayer displays a homogeneous aspect, with constant grey level (data not shown). After the injection of gliadins under the monolayer, appareances and disappearances of luminous dots, like blinking, was observed. As the reflectivity intensity observed by BAM is correlated to the refractive index and the thickness of the interfacial film, this phenomenon can be attributed to adsorption-desorption cycles of gliadins under the monolayer. After an equilibration time, the stabilized system displays bright dots on a field which has the same grey level as the pure DMPC monolayer (Fig. 6). Considering that the interfacial pressure is unchanged with the injection of gliadins, luminous dots can be ascribed to the gliadin adsorption under the phospholipidic monolayer. Moreover, the observation of the stabilized system by BAM with crossed polarizer and analyzer shows a dark picture (Fig. 6 c,f). This observation means that gliadin dots would be flat and smooth, because rough aggregates would induce scattering and depolarization of the incident light. Figure 6 (a,b,d,e) presents BAM pictures obtained after the injection of different quantities of γand ω-gliadins under the monolayer. In all cases, the diameter of bright dots is limited to few microns and it appears impossible to form a homogeneous protein film under the phospholipidic monolayer whereas such a film was formed with the same quantity of gliadin injected at the air-water interface 16 . For low protein quantities injected, both γand ω-gliadin systems present similar pictures, characterized by luminous dots with a micrometric radius. For higher gliadin quantities injected, γ-gliadin-DMPC monolayer system displays more numerous larger and brighter dots than ω-gliadin-DMPC monolayer system. The local reflectance intensity of the dots as a function of the injected gliadin quantity, and the reflectance -thickness relationship are plotted in Fig. 7. The reflectance-thickness relationship is based on Fresnel equations and values were calculated by a software developed by Buffeteau et al 38 .

The plot shows a periodical function indicating several thicknesses values for one reflectance value (Fig. 7b). The reflectance of γ-gliadin dots increases with the quantity of gliadin injected, whereas the reflectance of ω-gliadin dots is constant (Fig. 7a). The increase of reflectivity with the addition of γ-gliadins has to be attributed to an increase of thickness, rather than a decrease in thickness. In the thickness range presented, there are two regions in the periodical function where the reflectivity increases with the thickness. Considering a progressive thickness growth, to reach the high thicknesses regions, the reflectivity should have first increased then decreased. This behavior was not encountered in our study. Moreover, the reflectance values measured in the γ-gliadin system, ranging from 0 to 3.10 -4 , are very low compared to the global reflectance range (ranging from 0 to 2.5.10 -3 ). These reflectance values suggest very thin objects. The thickness values were estimated thanks to the following equation 39 , which establishes a relationship between the reflectance and the square of the thickness, for a thin, single-layered interfacial film:

where I 0 and I R are the incident and the reflected intensity, n 1, n 2 the refractive indices of the film (1) and the subphase (2), λ the wavelength of the incident light and d the thickness of the film. Parameters used where λ = 532 nm, n 2 = 1.333 and n 1 = 1.47. The n 1 value is chosen as the refractive index of biological materials is known to be comprised between 1.43 and 1.47 39 , and the protein-lipid monolayer assembly is considered to be continuous. As a consequence, the n 1 refractive index value is an estimation which implies an uncertainty in the thickness value calculated. The DMPC monolayer thickness value thus obtained is 2.2 nm, a value in agreement with those found in literature 40 . The average thicknesses corresponding to the dots reflectance are comprised between 8 and 20 nm in the presence of γ-gliadins and about 6 nm in the presence of ω-gliadins. Considering the DMPC monolayer thickness, the γ-gliadin aggregates thickness grows approximately from 6 to 18 nm with the addition of proteins, whereas the ω-gliadin aggregates thickness is constant and approximately equals to 4 nm. With low quantities of γand ω-gliadins injected, the aggregates thicknesses suggest gliadin monolayers adsorbed under the DMPC monolayer.

With high quantities of γ-gliadins injected, but not ωgliadins, the calculated thickness suggests a multilayer structure of the protein aggregates. Brewster Angle microscopic observations of systems made with DMPG monolayers were also carried out. Observations were qualitatively the same as those performed using DMPC monolayers. It was also observed the formation of flat, circular, micrometric gliadin aggregates under the lipidic monolayer, whose reflectivity depended on the quantity of protein injected in the γ-gliadin case only. PM-IRRAS spectra. The γ-gliadin -DMPC monolayer system was studied by PM-IRRAS. The protein signal was very difficult to obtain, probably due to the low thickness of the aggregates and their low surface representativeness. Figure 8 displays PMIRRAS spectra of the pure DMPC monolayer (a), the ratio between the spectrum obtained after the injection of 40µl of γ-gliadins under a 35 mN/m DMPC monolayer and the DMPC spectrum (b) , and the spectrum of γ-gliadins alone at the air-water interface (c).

The DMPC spectrum displays characteristic bands at 1729, 1468, 1230 cm -1 (fig. 8a). These bands are assigned, respectively, to the stretching of the C=O ester bonds, the CH 2 bending mode, and the antisymmetric P=O stretching vibration 41 . The γ-gliadin under the DMPC monolayer spectrum (fig. 8b) displays a band at 1665 cm -1 ascribed to the amide I band of the protein, and no band attributed to the DMPC monolayer. The presence of the amide band proves that proteins are not far from the air-liquid interface, whereas the absence of DMPC bands indicates that the DMPC signal is unmodified by protein adsorption and suggests thus a weak interaction between lipids and proteins. The maximum intensity of the amide I band appears at 1665 cm -1 , indicating a secondary structure rich in β-turns and/or small α-helices. This band appears similar to the band obtained for γ-gliadins alone injected at the air-water interface at 6300 Ų/molecule (Fig. 8b) (this molecular area roughly corresponds to a γ-gliadins injection of 2µg in the trough used for experiments made with a lipid monolayer). In both cases, the amide II band is absent. This absence can be assigned to a specific orientation of secondary structures. Our previous PM-IRRAS spectrum analysis of the γ-gliadins at the air-water interface indicates that secondary structures are flat oriented relative to the interface 16 . Considering the similarity of γ-gliadins amide bands at both air-water and DMPC-water interfaces, it can be concluded that γ-gliadins adsorbed under a DMPC monolayer is structured in β-turns and small α-helices, flat oriented relative to the phospholipidic monolayer plane.

Discussion

The 3D approach developed in this study shows that γgliadins can be partially inserted within a non-ionic lyotropic lamellar phase in a large range of dilutions.

Whereas the bilayer thickness is constant and equal to 2.9 nm, the most confined system displays a water layer thickness of 1.8 nm. These dimensions, smaller than the dimensions of gliadin estimated in different solvants 42 , suggests that gliadins inserted inside the lamellar phase adopt a thinner, and consequently more anisotropic conformation than in solution. Such an elongated conformation would be consistent with the thickness of γgliadin monolayers adsorbed at the air-water interface measured at low compression levels 16 . However, the dynamical study using FRAP measurements of the gliadins-lyotropic lamellar phase system also suggests additional hypotheses, stipulating that gliadin do not freely diffuse in the aqueous layer:

(1) γ-gliadins form large objects, soluble into water, which are geometrically confined between bilayers in the whole range of dw studied, (2) γ-gliadins are embedded into bilayers, (3) γ-gliadins are close to the polar head-water interface interacting with the bilayers from their water side. The size of γ-gliadins in our system is unknown but it is important to note that gliadins can adopt very different conformations and sizes according to the nature of the solvent and the ionic strength 42 . In a good solvent, like 70% (v/v) aqueous ethanol, SAXS measurements 43 showed that the dimensions of γ-gliadins were d (diameter)=3,35nm and L(length)=12,5nm assuming a rod model. γ-gliadins can also display smaller dimensions, for example, in an acetic acid-10mM NaCl solvent, the hydrodynamic radius can be estimated to 3 nm 42 .

Hypothesis (1) can be examined considering either gliadin aggregates or unfolded gliadin monomers. Taking into account the dimensions measured in a good solvent, dynamic data of gliadins in the lamellar phase can be interpreted as the result of the confined diffusion of anisotropic objects 26 , which would be sterically prohibited from having their long axis parallel to the staking axis of the lamellar phase. Within the framework of hypothesis (1), however, the diffusion of confined objects is estimated to be similar to that of the same objects embedded into membranes, and current models 44,45,46 indicate that, for a given membrane system, a larger object always displays a lower diffusion coefficient than a smaller object. As a consequence, with hypothesis (1), and similarly with hypothesis (2), the protein diffusion coefficient is predicted to be smaller than for lipids embedded inside bilayers. Despite the high error bar of measurements, the reverse tendency is unambiguously observed experimentally in Fig. 4. As a further argument against hypothesis 2, transmembrane domains are not predicted in γ-gliadin sequence by the method of Zao and London 47 . That is why the hypothesis of monomeric protein close to the polar heads -water interface, interacting with the bilayers can be privileged. This interaction would induce the elongated conformation previously suggested. In a second time, the gliadin-membrane interaction study was completed by the 2D approach using DMPC and DMPG phospholipids. Results indicate an insertion of gliadins for monolayer pressures below 20mN/m and an adsorption of gliadins under the monolayer for pressures above. Different authors, on different systems and with different experimental methods, determined bilayermonolayer equivalence pressures in the range of 25-35mN/m 48,49,50,51 . This suggests that the equivalent pressure of bilayers in the lamellar phase is higher than 20mN/m and confirm that gliadins are in interaction with membranes, without being embedded inside them. BAM observations indicate that both γ and ω-gliadins locally adsorb under lipid monolayers to form small domains with a limited lateral expansion. This behavior suggests a nucleation-growth mechanism for the formation of gliadins aggregates under the membrane. The limited lateral growth can be attributed to an important line tension between the adsorbed gliadins aggregates and the subphase molecules in interaction with polar heads of phospholipids. The thickness of these domains was estimated by reflectivity measurements and indicated different behaviors according to the gliadin type. Initially, γand ω-gliadins adsorb as monolayers under the lipidic monolayer. With increasing gliadin quantity injected into the subphase, the γ-gliadins aggregate thickness grows whereas ω-gliadins aggregate thickness remains constant. Considering that γ-gliadins display an amphiphilic structure made of a hydrophobic, non-repetitive domain, and a more hydrophilic, repetitive domain, and that ω-gliadins are essentially composed of a repetitive domain, a model is proposed to explain our experimental observations (Scheme 1). The interaction between protein and membrane, observed using both γ-and ω-gliadins, could be ascribed to an interaction between polar heads of phospholipids and the repetitive domain of gliadins. This hypothesis would be in agreement with biological studies showing that the repetitive domain of gliadins is crucial for protein bodies formation in wheat 52,53 . The exact nature of the interaction between lipids and gliadins could not be solved in our study. However, the low net charge of gliadins at the pH conditions of our experiments (γ-gliadin: +2, γ-gliadin's repetitive domain: +5, ω-gliadin: -2), and the similar observations obtained using both zwiterrionic and negatively charged monolayers exclude a predominance of electrostatic interactions. In addition, PMIRRAS measurements suggest weak gliadinmembrane interactions. Fernandez et al 54 showed that the extent of protein deposition on the lipid bilayer is strongly correlated with the average extent of underwrapping of backbone hydrogen bonds in the native structure of a protein. According to authors 55,56 , intramolecular hydrogen bonds that are not properly desolvated by surrounding hydrophobic groups are available to benefit from further protection by another body, like lipid bilayers, since an exogenous removal of surrounding water enhances their electrostatic stability. The extent of unprotected intramolecular hydrogen bonds is not known for gliadins, as these proteins were never crystallized. However, this content can be expected important as the primary structure of gliadin repetitive domains contains many glutamines, which are susceptible to form hydrogen bonds (47% and 43%, for γand ω-gliadins respectively), and few hydrophobic residues to protect intramolecular hydrogen bonds (16% and 18% for γand ω-gliadins respectively). Moreover, the secondary structure of wheat storage proteins repetitive domains is known to be very instable 57 and extended due to prolines and glutamines residues 58 . The proposed repetitive domain -membrane interaction could thus be explained by the protection of hydrogen bonds. Finally, the thickness growth, observed only with γgliadins, could be ascribed to the non-repetitive domain. A multilayer structure, characterized by a stacking of repetitive and non repetitive domains, is thus proposed. In this multilayer structure model, hydrophobic interactions are considered to be predominant in the interaction between non-repetitive domains, whereas the interaction between repetitive domains should be explained by the under-wrapped hydrogen bond model, previously described for the protein membrane interaction. The different abilities of γand ω-gliadins to accumulate via an interface were previously observed at the air-water interface where gliadins form homogeneous monolayers 16 . Under lateral compression, γ-gliadins monolayer forms thicker film whereas ω-gliadins monolayer collapses. The accumulation mechanism, at the air-water interface under compression could also be due to the amphiphilic character of γ-gliadins. The interaction of gliadin with membranes was previously suggested by suction experiments on giant phospholipidic vesicles in presence of gliadins 15 . Authors interpreted the modification of mechanical properties of vesicles as an insertion of gliadins inside the bilayer.

However our results clearly indicate that γand ω-gliadins do not penetrate into membranes with pressure higher than the critical pressure of 20 mN/m. An insertion of gliadins in vesicle membranes can be considered only if local low pressures (<20mN/m) are induced by the suction action. Moreover, the modification of mechanical properties observed by the authors does not seem contradictory with the hypothesis of an adsorption of protein on the bilayer. In summary, in this study the gliadin-membrane interaction was highlighted with two contrasting model membranes and the formation of local aggregates under the membrane was demonstrated. We propose that such processes happen in the biological context of the ER during the accumulation of prolamins in developing wheat grains. The gliadinmembrane interaction would be mediated by the repetitive domain of gliadins, and could act as a anchor for gliadins on the ER membrane and as a nucleus point for the growth of prolamin assemblies leading the protein bodies formation. The amphiphilic character of γ-gliadins would be at the origin of the accumulation process in the ER of endosperm cells.

Conclusions

The demonstration of γand ω-gliadins-membrane interaction, using a combined 3D approach using lamellar phases and a 2D approach using Langmuir phospholipid films, could explain the initiation of prolamins assembly within the endoplasmic reticulum of wheat endosperm cells. Moreover, the aggregate thickness growth observed in our prolamins-membrane model systems could represent a mechanism of the accumulation process occurring in the biological context. A model of accumulation process based on the amphiphilic nature of γ-gliadins is proposed. Further studies will be needed to confirm this hypothetical model of prolamins accumulation from a membrane, and in particular by better characterizing gliadin aggregates using techniques which provide local informations such as AFM and microspectroscopies.

Figure 1 .

 1 Figure 1. Images obtained using optical microscopes for the C 12 E 5 /Hexanol/water/γ-gliadin-TRITC system for three different water layer thicknesses (d w ). (a) Polarized light microscope and (b) Confocal fluorescent optical microscope.

Figure 2 .

 2 Figure 2. X-rays scattering experiments of γ-gliadins doped lamellar phases. (a) Bragg peaks of the γ-gliadin-TRITC protein inside the C 12 E 5 /Hexanol/water lamellar system for three different water layer thicknesses (d w ). (b) Evolution of the d-spacing as a function of the water content. Empty circles correspond to the protein doped lamellar phase and filled diamonds correspond to the same lamellar phase without proteins (Freyssingeas et al 19 data). The solid lines correspond to a linear fit using d = δ/φm.

Figure 3 .

 3 Figure 3. Gaussian broadening σ 2 versus time resulting from fits according to equation (3). The lines correspond to simple linear fits; C 12 E 5 / Hexanol / water / TRITC system (empty circles), C 12 E 5 / Hexanol / water / γ-gliadin-TRITC system (filled diamonds), C 12 E 5 / Hexanol / water / DHPE-TRITC system (empty squares).

  k B is the Boltzmann constant, T the temperature, ζ the drag coefficient η 0 the viscosity of the fluid and R H the hydrodynamic radius. With D ┴ = 120 x 10 -12 m 2 /s, R H calculated from equation 5 is 1.8 nm and should give a transition between the dilute and confined regimes for d w = 2R H = 3.6 nm, a value consistently close to the d w value (ca. 4.7 nm) measured for the TRITC dye encapsulated inside the lamellar phase. Taking into account the hydrodynamic radius R H for the rhodamine dye (ca. 0.5 nm), it is therefore assumed that TRITC is present in an aggregated form inside the aqueous layer of the lamellar phase. The TRITC aggregation occurring in water, and being self-consistent with the chemical structure of the fluorophore, could also explain the large error bars obtained for diffusion coefficient from FRAP measurements.

Figure 4 .

 4 Figure 4. Diffusion coefficients D ┴ derived from FRAP experiments as a function of the water layer thickness d w for three different doped C 12 E 5 /hexanol/water lamellar phases: free TRITC (empty circles), the γ-gliadin-TRITC (filled diamonds) and the DHPE-TRITC (empty squares). Vertical solid line drawn correspond to d w = 4.7 nm.

  Figure 5 displays the interfacial pressure evolution as function of time with the injection of (5) γ-gliadin solution under DMPC monolayers. When the phospholipid monolayer has an initial pressure of 20 mN/m, the γ-gliadin injection induces an abrupt increase of the interfacial pressure followed by stabilization at about 25 mN/m.

Figure 5 .

 5 Figure 5. Evolution of the interfacial pressure Π (mN/m) as a function of time (s) with the injection of γ-gliadin (arrow) under DMPC monolayers at 20 mN/m (thin curve) and 35 mN/m (thick curve).

Figure 6 .

 6 Figure 6. Brewster angle microscopy images of gliadins injected under a DMPC monolayer at Π = 35 mN/m. (a) 10µg ωgliadin injected (b) 100µg ω-gliadin injected (c) 100µg ω-gliadin injected, observed between crossed polariser and analyser (d) 10µg γ-gliadin injected (e) 100µg γ-gliadin injected (f) 100µg γ-gliadin injected, observed between crossed polariser and analyser (Exposure Time= 1/50s).

Figure 7 .

 7 Figure 7. (a) Evolution of the local reflectance of aggregates (luminous dots) versus gliadin quantity injected. Filled dots: γ-gliadin, unfilled dots: ω-gliadin. (b) Brewster Angle Microscopy model of reflectance versus thickness (incidence wavelengh λ = 532 nm, incidence angle θ = 53.17°, film refractive index n=1.47).

Figure 8 .

 8 Figure 8. PM-IRRAS spectra: (a) DMPC monolayer at 40 mN/m (b) γ-gliadins (40µg) injected under a 35 mN/m DMPC monolayer (spectrum divided by that of the DMPC monolayer) (c) γ-gliadins alone injected at the air-water interface.

Scheme 1 .

 1 Scheme 1. Model of gliadins self-assembly via a lipidic membrane interface. (a) In the case of γ-gliadins, where the molecule is represented with the hydrophobic globular domain in yellow, and the more hydrophilic extended domain in red, the formation of a multilayer structure of γgliadins under the lipidic membrane would occur through mainly hydrophobic interactions. (b) In the case of ωgliadins, where the molecule is represented in red due to its unique low hydrophobic extented domain, the formation of a ω-gliadin multilayer under the lipidic membrane would be inhibited due to the absence of hydrophobic domains within the sequence.

Acknowledgments

Financial support for this work was provided by INRA and CNRS within the framework of the Groupement De Recherches Assemblages de Macromolécules Végétales (GDR AMV). We are grateful to Mr Jean-Pierre Compoint and Mrs Dominique Melcion for the purification of gliadins. We also gratefully acknowledge Prof. F. Nallet for the final manuscript correction.


Christian Belzil
email: christian.belzil@polytechnique.edu

François Poinas
email: poinas@gate.cnrs.fr

Education and Early Career Outcomes of Second-Generation Immigrants in France

Keywords: JEL classification: I2, J15, J24, J41 Second-generation immigrants, schooling attainments, fixed term employment

We estimate a flexible dynamic model of education choices and early career employment outcomes of the French population. Individuals are allowed to choose between 4 options: continue to the next grade, accept a permanent contract, accept a temporary contract, or withdraw from the labor force (a residual state). Our analysis focuses on the comparison between French Second-Generation Immigrants whose parents are born in Africa and Frenchnatives. We find that schooling attainments explain around two thirds of the differences in access to early career employment stability. However, one third cannot be linked to observed investment in human capital.

Introduction

Continental European labor markets are often pictured as being characterized by a relatively low degree of flexibility, when compared to Anglo-Saxon countries. This is particularly the case for France and Italy (OECD, 1999, Table 2.2). This inflexibility is particularly acute at the firing level. In practice, it implies that individuals holding employment must be paid relatively high severance pay in case employment downsizing is necessary.1 As a consequence, firms may be reluctant to grant permanent contracts to new hires and favor limited term contracts.2 This theoretical prediction is largely supported by the data. About 30% of newly hired workers in the French labor market get a permanent contract for their first job, although the share of permanent contracts in total employment is 86% (INSEE, Enquête emploi, 2005).

At the same time, the high incidence of criminal activities and social turmoil in areas densely populated with immigrants has pushed French policy makers to question the level of integration of second generation immigrants. In 1999, the unemployment rate of second generation immigrants aged 19-29 was 30% (nearly 40% if the parents came from Algeria or Morocco), whereas it was 20% for children with both parents born in France. This inequality is also noticeable at the level of early career employment contracts. For instance, only 23% of second generation immigrants with both parents born in an African country get a permanent contract for their first job compared to 32% for young workers with both parents born in France. While discrimination has been advanced as a possible cause, potential differences in pre-market skill investment (such as differences in education) may also be important. From an economist perspective, differences in early career outcomes, between natives and second generation immigrants, which persist after conditioning on education, are particularly interesting. It is those differences that are important to quantify.

The poor performance of second generation immigrants has also attracted attention in European countries, like Denmark [START_REF] Nielsen | The School-to-Work Transition of 2nd Generation Immigrants in Denmark[END_REF] and the Netherlands [START_REF] Van Ours | The Educational Attainment of Second-Generation Immigrants in The Netherlands[END_REF]. In the United States, the economic performances of second generation immigrants appear to have been much better. For instance, [START_REF] Chiswick | Educational Attainment: Analysis by Immigrant Generation[END_REF] and [START_REF] Card | Is the New Immigration Really So Bad?[END_REF] find no gap in schooling attainments and wages between second generation immigrants and US-natives.

Surprisingly, and despite the recent incidence of violent crimes in French banlieues, very few economists have investigated the relative performance of second generation immigrants in France. As of now, Aeberhardt and Pouget (2007) and Aeberhardt et al. (2007) are the only recent papers studying the wage gap between second generation immigrants and children of parents born in France. Both papers are based on econometric models in which schooling is assumed to be exogenous.

In this paper, we perform an econometric analysis of individual educational choices and early labor market outcomes. We estimate a reduced-form dynamic model of education and early career outcomes. We focus on the nature of the early career employment contracts and more precisely whether the term of the contract is fixed (limited) or permanent (unlimited). We model individual trajectories as a collection of sequential dynamic discrete choices, in the spirit of [START_REF] Cameron | The Dynamics of Educational Attainment for Black, Hispanic, and White Males[END_REF]Heckman (1998, 2001). We consider two sub-populations that are indexed by the country of origin of the parents: "French-natives" (those for whom both parents were born in France with French citizenship), and "African-natives" (those for whom both parents were born in an African country with a non-French citizenship).

At the outset, it should be pointed out that the model is very flexible. It assumes that, for each grade level completed, individuals are allowed to choose within a set that contains 4 options: i) continue to the next grade, ii) accept a Permanent Contract (PC), iii) accept a Fixed Term Contract (FTC), or iv) withdraw from the labor force (a residual state). So, given a completed grade level, each choice (each element in the set) has its own latent utility equation, which is parameterized as a function of a large set of parental background variables and unobserved heterogeneity. As in a standard Roy model, there exists a different set of equations for each possible grade level. This model allows us to measure separate effects of education level on the employment outcome probabilities. For instance, the effect of completed education on the likelihood of a particular early career outcome (say obtaining a permanent contract) is not captured by a single parameter but by a collection of several parameters characterizing individual unobserved abilities, and other parameters measuring the effect of parents' occupation, location and geographical origin on a given outcome. As a consequence, the model contains a very large number of parameters. 3Our general objective is to explain the schooling and employment outcomes of second generation immigrants from Africa and French-natives. We ask the following questions. Do parents' background and unobserved skills and motivation explain schooling attainments in the same way for Frenchnatives and African-natives? Is the schooling gap between French-natives and second generation immigrants sufficient to explain the early career employment gap? If not, what is the impact of education relative to other factors?

We now summarize the main findings. First, the relative impacts of observed and unobserved factors on the probability of reaching a particular grade level appear to be similar across groups. Around 60% of the crosssectional variance of the probability of completing five years of college is explained by parents' background, 15% by early cognitive skills and 25% by unobserved skills and motivation. For lower schooling attainments, like completing secondary school and more, the impact of parents' background is lower for both sub-samples (around 30%), whereas early cognitive skills have a stronger impact for African-native attainments (59% vs. 37 for Frenchnatives), and unobserved skills a smaller impact (15 vs. 34%).

Second, the schooling gap between French and African-natives is not sufficient to explain the early career employment gap. 68% of the cross-sectional variance in the probability of obtaining a Permanent Contract as a first contract in the labor market is explained by schooling attainments. However, 32% of the differences across groups are associated to returns to observed or unobserved factors. This is much harder to explain. While this "employment quality gap" may be associated to differences in skills that prevail after conditioning on schooling, it may also be attributed to factors such as discrimination and the like.

Third, the share of the cross-sectional variance in the probability of obtaining a Permanent Contract decreases with experience. After two years in the labor market, it represents 62%, which implies that returns to other observable and unobservable factors, such as experience, are higher (38%).

In the following section, we introduce the database used in this article. The econometric model is described in the next part. Then, we present the results of estimations and conclude.

2 The Data: Génération 98

Our work is based on Génération 98, a large scale survey conducted in France by Céreq. 4 It provides detailed information on the socio-demographic background and employment characteristics of young individuals who left school in the year 1998 and were interrogated in early 2001. Re-interviews have been conducted for half of the sample in 2003, but we do not use them here since we focus on employment conditions during the first two years after school completion. The aim of Génération 98 is to document many aspects of early labor market transitions. In particular, Génération 98 provides information on spells of employment, unemployment, and training experienced between school completion (labor market entrance) and the date of the survey. Therefore, information on three years of the generation's working life is available and each period of employment is well documented. The personal labor market history of survey respondents has been reconstructed, month by month, during the period 1998-2001.

Because Génération 98 is a national survey of those who left the educational system at a particular point in time (1998), all individuals faced the same labor market conditions after 1998.

Parents' Country of Origin

Our sample is composed of 42,674 individuals. The group of French-natives contains 40,525 individuals whose both parents were born in France and had the French citizenship at birth. The second group is composed of 2,149 African-natives, i.e. whose both parents were born in an African country and did not have the French citizenship at birth. Individuals belonging to this last group are also called second generation immigrants from Africa.

Education

In order to model education, we use the highest educational level (reached in 1998). The educational level variable falls in 7 categories: 1) no qualification; 2) vocational high school degree; 3) high school degree (baccalauréat, A level); 4) some college but leaving higher education without graduating; 5) technical or vocational college or ordinary college (baccalauréat and 2 years); 6) those graduated who completed 3 or 4 years of college and 7) those who completed 5 years of college and more, elite business or engineering school university degrees.

Employment Contracts

The data contain information on the nature of the employment contract at the beginning of each employment spell, as well as changes in the contract type within the spells. We create two categories of contracts, distinguished by their term, defined when the contract is signed by the employer and the employee.

The Permanent Contracts (PC) category regroups the CDI (contracts with indefinite duration) as well as contracts held by civil servants. The duration of a CDI is not set ex-ante and the employer has to pay a firing cost if he wants to lay-off a worker employed under such a contract.

The category named Fixed Term Contracts (FTC) refers to all types of contracts whose term is defined ex-ante. It regroups the CDD (contracts with limited duration), which is the most common form of fixed term employment, but also subsidized contracts, apprenticeship contracts and self-employment. Contrary to a CDI, no cost is supported by the employer at the end of a CDD, but CDD have to be used under some restrictions. According to the French legislation, a CDD cannot be used to fill a job that would exist under normal and permanent business conditions for a given firm. Moreover, a CDD can be renewed only once, and the maximum employment duration under a CDD can not exceed 18 months.

The Econometric Model

We model schooling decisions as a sequential dynamic discrete choice model. 5 At each grade level, individuals are assumed to make a choice between obtaining more schooling and labor market work. We model three different post-schooling outcomes: i) employed in a Permanent Contract (PC), ii) employed in a Fixed Term Contract (FTC) and iii) out of the labor force (Out), a residual state. 6 Because the model is interpreted as the reduced-form of a more involved structure, the terms choices and outcomes may be used interchangeably. 7 To estimate the model, we use several observable factors: family characteristics (parents' occupation and location), gender, immigration status and a cognitive skill indicator: "late at school". This variable indicates if the individual enters secondary school after being 11 years old, which is the "normal" age at which children attain this level without schooling delay. On top of these observable variables, we have to introduce an individual unobserved time invariant heterogeneity term, in order to control for educational selectivity. Indeed, there are unobservable factors, such as "motivation" or "ability", that influence schooling decisions at each grade level. Cameron and Heckman (1998) explain that ignoring these effects creates an omitted variable bias that understates the true effects of family background variables on educational attainments, especially at higher grades. Indeed, ability and family characteristics are negatively correlated at higher grades: individuals with low family background characteristics continue schooling only if they have a high ability.

As in [START_REF] Cameron | The Dynamics of Educational Attainment for Black, Hispanic, and White Males[END_REF]Heckman (1998, 2001), the model is specified as a sequence of multinomial logistic probabilities with unobserved heterogeneity. Let C be the set of choices at the end of each grade level:

C = {s, c 1 , c 2 , c 3 } c 1 , c 2
and c 3 are the 3 employment outcomes (respectively employed in a permanent job, employed in a fixed term job and out of the labor force), 5 Modeling schooling decisions as a reduced-form transition (hazard) model has been done in [START_REF] Cameron | The Dynamics of Educational Attainment for Black, Hispanic, and White Males[END_REF]Heckman (1998, 2001), [START_REF] Belzil | Testing the Specification of the Mincerian Wage Equation[END_REF]. 6 We do not distinguish here between unemployed workers who choose not to work, and unemployed workers who are searching for a job.

7 For instance, the data does not allow us to distinguish individuals who accept limited term contracts because they received no permanent contract offer from those who actually accept a limited term contract over a permanent one.

whereas s corresponds to continuing schooling to the next grade level.8 At the end of grade g, g = 1, . . . , 7, where 1 is the lowest grade, the optimal choice for an individual i is the following:

c i,g = arg max c∈C U * i,g,c (1)
where U * i,g,c is the utility from choosing option c, given completion of grade g. The expression of this latent variable is given by:

U * i,g,c = X i β g,c + ν i,g,c (2)
where X i is a vector of observed variables, β g,c is a vector of parameters measuring the effects of these variables, and ν i,g,c is unobservable by the econometrician. The structure adopted for ν i,g,c is

ν i,g,c = α g,c θ i + i,g,c
where θ i is the individual specific effect, constant across grades and contractual outcomes, and which is orthogonal to the i.i.d. error term, denoted i,g,c . This particular form implies an individual specific intercept term,

γ i,g,c = α g,c θ i .
Then, assuming that i,g,c is an iid extreme value variable, we can write the probability that an individual i exits to the outcome c once he achieved grade g as an extension of [START_REF] Mcfadden | Conditional Logit Analysis of Qualitative Choice Behavior[END_REF] conditional logit model:

Pr (D i,g,c = 1|X i , θ i ) =                exp (X i β g,c + γ i,g,c ) 1 + c 3 a=c 1 exp (X i β g,a + γ i,g,a )
for c = c 1 , . . . , c 3

1 1 + c 3 a=c 1 exp (X i β g,a + γ i,g,a ) for c = s (3) where D i,g,c = 1 if individual i's outcome after grade g is c ∈ C, i.e. if c i,g = c.
The probability that individual i exits to the optimal outcome ĉ, after having completed the optimal grade level ĝ defines the contribution to the likelihood for an individual i. Precisely, the individual likelihood is

L i (X i , θ i ) = ĝ-1 b=1 Pr (D i,b,s = 1|X i , θ i ) • Pr (D i,ĝ,ĉ = 1|X i , θ i )
where D i,b,s is an indicator that is equal to 1 when an individual i, who has already completed grade level b, chooses to continue in school (chooses option s).

Unobserved Heterogeneity

In the spirit of [START_REF] Heckman | A Method for Minimizing the Impact of Distributional Assumptions in Econometric Models for Duration Data[END_REF], we adopt a discrete distribution for unobserved heterogeneity. Assuming that there are K types in the population,9 the probability of belonging to type k, p k , is estimated by a logistic distribution function:

p k = exp q k K s=1 exp q s k = 1, . . . , K
where q k 's are parameters to be estimated, with the restriction that q K = 0. Given we use an individual-grade-outcome-specific intercept term in our model specification, γ i,g,c = α g,c θ i , the K types distribution induces the estimation of K type-specific intercepts for each outcome equation at each schooling level. Therefore, unobserved heterogeneity in our model has to be interpreted as a vector of schooling and labor market unobserved skills, ability or motivation, whose dimension is K times the number of latent equations modeled. 10As a consequence, the mixed likelihood, for an individual i, is simply:

L i (X i ) = K k=1 p k • L k i (X i ) (4)
where L k i (X i ) is the contribution of the likelihood for an individual of type k.

The model is estimated by maximization of the sum of all individual (mixed) log likelihoods.

Estimation

Two versions of the model are estimated. In the first one, the contractual outcomes correspond to the contract types at the beginning of the first job after schooling, up to 1 year. As a consequence, the outcome "out of the labor force" concerns individuals who have no job during the year that follows their exit from schooling. In the second version, the outcomes are the employment status exactly two years after the exit from schooling.

For each version of employment outcomes, the model is estimated separately for French and African-natives. Therefore, each group has its own unobserved heterogeneity distribution and parameters. A relatively small number of individuals choose to stop schooling at the end of the fist education level (no qualification) in the two sub-samples. Thus, we do not model employment contract outcomes at this level. As a consequence, the choice set at the end of the first education level is either continuing or stopping schooling.

The estimation output of one set of employment outcomes for one subsample consists of a huge set of estimated parameters. A 2 types unobserved heterogeneity distribution requires the estimation of 271 parameters (290 for a 3 types distribution and 309 for a 4 types distribution). The calculation of the effects of interest, such as the impact of attaining a schooling level on the probability of a particular employment outcome, is not summarized by a single parameter. Instead, it involves the combination of parameters associated to unobserved heterogeneity and parameters measuring the effect of observable characteristics.

Results

In this section, we present the results of the different estimations. We first show results about unobserved heterogeneity and the goodness of fit. Secondly, we study the determinants of schooling choices and explain the differences in schooling attainments between the two sub-samples. Finally, we show results on employment outcomes. In particular, we look at the roles of schooling and origin in explaining both first employment outcomes within the first year, and employment outcomes at two years.

Unobserved Heterogeneity and the Goodness of Fit

Unobserved Heterogeneity

In order to determine the optimal number of types for the unobserved heterogeneity distribution, we compare the estimations of the model with 2, 3 and 4 types for each origin group and each set of employment outcomes (first outcomes within the first year and outcomes at two years).11 The comparison of Bayesian Information Criterion values for the different specifications, shown in Table 1 makes us choosing a 2 types distribution for unobserved heterogeneity.

[TABLE 1 HERE]

Goodness of Fit

From parameter estimates, we compute the simulated schooling grade attainments and employment outcomes for each individual of each sub-sample.

According to the estimated unobserved heterogeneity distribution, a random type is assigned to each individual. Then, for each sub-sample, we build the simulated distributions of schooling attainments and employment outcomes, that we compare with the actual distributions. Tables 2 and3 show the simulated and actual distributions of schooling attainments for French and African-natives respectively, as well as the average grade levels. Tables 4 and5 show the employment outcomes distributions. All those tables contain the type-specific distributions and average grade as well as the average across types in each sub-sample.

For both groups, the actual and average simulated distributions are very close to each other. Indeed, our model is capable of explaining both schooling attainments and employment outcomes almost perfectly. 12Tables 2 and3 show that African-natives are much less educated than French-natives: more than one grade of difference on average. More precisely, 28% of French-natives have at most a vocational high school degree (grades 1 and 2) and 46% get a college diploma (grades 5 to 7), whereas, for Africannatives, those proportions are respectively 54% and 19%. As seen in Tables 4 and5, French-natives are also more often employed in Permanent Contracts (PC) (24% for the first contract vs. 15% for African-natives, and 43% vs. 26% for the contract at two years) and less often unemployed (15% and 16% vs. 23% and 26%).

The type-specific patterns in each sub-sample are also very different, which confirms the importance of controlling for unobserved heterogeneity. For French-natives, type 2 individuals tend to reach higher schooling attainments: their average grade is around 5, whereas it is only 3.6 for type 1's, and their distribution is more oriented towards high education levels. Thus, one could interpret unobserved heterogeneity as unobserved academic skills, where type 2 individuals would correspond to high-skilled individuals. Type 2 individuals are also less often employed in Fixed-Term Contracts (53% vs. 65% for the first contract, and 30% vs. 48% for the contract at 2 years).

For African-natives, the correlation between unobserved heterogeneity and schooling is less clear: the difference between type 1 and 2 average grades is only 0.3. Concerning the grade distribution, even if the proportion of unqualified is three times as high for type 2 as it is for type 1 (30% vs. 10%), there are also more type 2 college graduates (5% vs. 0%). The majority of type 1 individuals are vocational high school graduates (51%, 15% for type 2), and the proportion of general high school graduates is also higher among type 1 individuals (13% vs. 6%).

Concerning the employment outcomes, it turns out that type 2 individuals are much less often firstly employed in PC (8% vs. 22%), and more often unemployed (35% vs. 14%), whereas at 2 years, they are more concerned by permanent employment (35% vs. 18%).

[TABLE 2 HERE] [TABLE 3 HERE] [TABLE 4 HERE] [TABLE 5 HERE]

Schooling Choices

In this sub-section, we first study the impact of the covariates on schooling attainments. Then, we decompose the gaps in the schooling attainments between French and African-natives into two sources: the first one due to behaviors (parameter difference) and the second one due to endowments (covariate difference).

Determinants

At each grade level, the decision of continuing schooling to the next grade is explained by observable covariates (parents' occupation, location, gender and "late at school") as well as unobserved heterogeneity. In order to assess the relative impact of those different factors, we perform a variance decomposition on the attainment of three grade levels: high school completion and above (which corresponds to reaching level 3 or more), higher education diploma and above (level 5 or more) and college graduation (level 7).

We group the dummies for parents' occupation, living in an urban area and gender in a "parents' background" category. 13For each schooling attainment, we regress the simulated grade attainment dummies on each group of explanatory factors separately. Then, we compute the relative share of each group in explaining the grade attainment as the ratio of the corresponding R 2 over the sum of R 2 's of each regression.

Table 6 contains the results of this variance decomposition for French and African-natives separately. The results confirm the importance of unobserved heterogeneity in explaining the schooling attainments for Frenchnatives, where its relative share ranges from 24 to 34%. This share is lower for African-natives (8 to 25%).

Parents' background is a key determinant of the schooling attainments, especially at high grades: it explains 59 and 58% of the variance of reaching college graduation for French and African-natives respectively, whereas it accounts for less than one third of the variance of reaching high school completion (29 and 26%). This pattern may reflect a certain degree of intergenerational immobility: children born from richer and more qualified parents are more likely to obtain a higher education diploma. As a consequence, family background plays a minor role in obtaining low grades, and its importance increases with the grade level.

Early cognitive skills are also a huge determinant of schooling attainments (17 to 37% for French-natives, 17 to 64% for African-natives). Interestingly, the pattern across grades is the opposite of parents' background: the importance of "late at school" is higher at low grades. One possible explanation is that among the set of individuals late at school, are those who are very weak academically, but there may be also a set of individuals who were late for exogenous reasons (some bad luck), and were therefore capable of recuperating. Thus, among the late at school individuals, it is likely to find a higher proportion of weak academic individuals at low grades, and a higher proportion of individuals delayed for exogenous reasons at high grades.

[TABLE 6 HERE]

Then, we merge the simulated samples of French and African-natives and perform a variance decomposition on this full sample. We introduce origin as an explanatory factor, which captures differences in parameters as well as differences in unobserved heterogeneity. Consequently, the relative share of the variance assigned to the "origin" factor is the variance due to the parameters and unobserved heterogeneity together.

The results of the variance decomposition for the full sample are shown in Table 7. The relative shares of parents' background and late at school, and their evolution across the grade levels, are close to the ones we saw in the separate-sample decompositions. The results indicate that, relative to other factors, the impact of ethnic origin is very small: it explains 3 to 5% of the schooling attainments variances. This result suggests that the difference in schooling attainments between French and African-natives is mainly explained by observable characteristics. Our results are consistent with the huge impact of long run factors in explaining schooling attainments, as documented by Cameron and Heckman (1998) and [START_REF] Eckstein | Why Youths Drop out of High School: The Impact of Preferences, Opportunities, and Abilities[END_REF].

[TABLE 7 HERE]

Decomposition of Schooling Gaps Between Origin Groups

In this part, we study schooling attainment gaps between French and Africannatives. We perform a decomposition of the difference in the predicted probabilities of reaching grades 3, 5 and 7. For those three grade levels, we compute the predicted gap, i.e. the gap in the predicted probabilities between the two groups.14 This gap is decomposed into two parts: the part due to behaviors (parameters), and the part due to endowments (covariates). 15Let β A be the estimated parameter vector of individuals with two African parents and β F , the estimated vector for French-natives. Let X A and X F denote their respective covariate distributions and Pr(.) be the probability of interest. The difference in the predicted graduation probabilities can be decomposed into the two following ways:

E X F [Pr(X F β F )] -E X A [Pr(X A β A )] = gap due to behaviors + gap due to endowments = E X F [Pr(X F β F ) -Pr(X F β A )] + [E X F [Pr(X F β A )] -E X A [Pr(X A β A )]] (5) = E X A [Pr(X A β F ) -Pr(X A β A )] + [E X F [Pr(X F β F )] -E X A [Pr(X A β F )]] (6)
In equation ( 5) (resp. ( 6)), the behavior gap is the gap due to parameters when the distribution of African-natives' (resp. French-natives') covariates is set to the distribution of French-natives (resp. African-natives). 16 Table 8 reports the sample analogues of the predicted gaps, and the gaps due to behaviors, computed from both equations ( 5) and ( 6). 17 A positive gap corresponds to a lower probability for African-natives.

For the three schooling grades considered, we can see that African-natives have significant lower probabilities of grade attainment: 26 percentage points for high school completion and more, 28 for obtaining a university diploma, and 9 for college graduation. For the gap in the attainment of high school and more, the difference due to parameters is not significant, which means that the whole gap is explained by differences in the observable characteristics between French and African-natives. Concerning the probability of obtaining a higher education diploma, the difference due to parameters ranges from 10 to 21 percentage points, which corresponds to 36 to 76% of the predicted gap. Finally, 32 to 49% of the college graduation gap, is explained by the parameters.

Those results suggest that, at low schooling levels, only endowments matter for deciding to continue schooling investment, whereas behaviors turn to be important for the continuation decision at higher grades. Moreover, we can seen as abusive. Indeed, unobserved heterogeneity, which is evaluated in our analysis, is considered here as "behaviors", whereas it could also be considered as "endowments". 16 The vectors of parameters, β F and β A , contain the parameters of the unobserved heterogeneity distributions. As a consequence, "gap due to behaviors" corresponds to the difference in probabilities due to behavioral parameters and unobserved heterogeneity.

17 The gap due to endowments is not reported in the table since it equals the difference between the predicted and behavior gaps.

remark that the gap due to parameters is much higher when it is computed with French-natives covariates (5), rather than African-natives's (6). Since French-natives covariates distribution corresponds to a higher socioeconomic background, this result suggests that differences in behaviors between French and African natives play a higher role in the upper scale of the socioeconomic scale.

[TABLE 8 HERE] 6 Employment Outcomes

In this section, we examine the determinants of the employment outcomes for both origin groups, as well as the differences across groups. In particular, we study the impact of schooling, which is treated as endogenous in our model. We show the results that concern both the employment outcomes during the first year after school completion, as well as the employment outcomes two years after.

Impact of Schooling

We compute the type-specific predicted probabilities of being employed in a Permanent Contract, employed in a Fixed Term Contract, and being unemployed. Those probabilities are computed at the sample modes, for the following grade levels: vocational and general high school (grades 2 and 3), low college (dropouts and 2 years graduates -grades 4 and 5), high college (3 years and more -grades 6 and 7). Then, we compute the differences in the contractual outcome probabilities between the grade levels and their standard errors. The differences measure the impact of attaining the next grade level on the probabilities to be employed in a PC, FTC or being unemployed, other factors remaining fixed. The impacts on the probability of being employed in a PC can be interpreted as "returns to schooling" on permanent employment incidence. This term is used about returns of investment in education on earnings. As an illustration, estimation results of Aeberhardt et al. (2007) show positive marginal returns to schooling on wages of both French-natives and second generation immigrants from Africa. Here, however, we do not focus on wages, but we study whether or not investing in education increases the likelihood of being employed in a PC. This issue is of particular interest if workers on the labor market attach more value to jobs offering a stable employment situation.

Table 9 contains results for French-natives and Table 10 results for Africannatives. The next subsection discusses the impact of schooling on employment in a PC and unemployment.

[TABLE 9 HERE] [TABLE 10 HERE]

Permanent Contracts

For French-natives of type 2, low college attainment has a negative impact on the PC employment probability (38 percentage points for the 1st contract, 33 for the contract at 2 years), compared to high school completion. However, continuing from low to high college has a positive impact (40 and 34 percentage points). Those numerical effects have to be interpreted as upper bounds for the whole French-natives sample, since the differences for type 1 have most of the time a reverse sign with a much lower magnitude, which makes them sometimes insignificant.

Concerning African-natives, the high values of the standard errors make the estimates poorly precise. Only the difference in the likelihood of obtaining a PC during the first year after schooling between low and high college for type 2 is significant and high (85 percentage points).

Unemployment/Out of the Labor Force

Increasing the education level has a positive impact on the French-natives probability of being unemployed during the first year after schooling. Indeed, attaining low college increases the probability by 3 percentage points for type 1 and 12 percentage points for type 2, whereas the impact of high college is small (non significant for type 1, 3 percentage points for type 2). Concerning unemployment 2 years after schooling, the impact of low college is negative for type 1 and positive for type 2 (10 percentage points in both cases). The impact of high college has the opposite sign for both types (increase of 10 percentage points for type 1 and decrease of 14 percentage points for type 2).

Again, for African-natives, results are barely significant. We can only note that there is a huge negative impact of low college on the probability of remaining unemployed during the first year after schooling (76 percentage points).

Importance of Schooling vs. Permanent Factors

We now determine the importance of schooling, relative to other factors, in explaining the employment outcomes. We conduct a variance decomposition of the simulated PC outcome. We regress the simulated PC outcome dummy on each group of explanatory factors separately and compute the share of each factor as the ratio between the corresponding R 2 and the sum of R 2 's of each regression. "Simulated schooling" is added as a new group of explanatory factors, on top of the groups already introduced in the variance decomposition of the schooling attainments: parents' background, late at school and unobserved heterogeneity.

Table 11 contains the results of this variance decomposition for French and African-natives separately. Schooling explains a great part compared to other explanatory factors. In particular, its impact is twice as high as the impact of parents' background, except for the 1st contract within the 1st year for African-natives. Delay during primary school has a very small impact on the contractual outcomes (6% and less). This confirms that this variable has to be interpreted mostly as a measure of cognitive skills (as opposed to some sort of labor market skill) , since we already noticed in section 5.2.1 that its impact on schooling attainments was as important as parents' background. Unobserved heterogeneity is a huge determinant: it explains 17 to 20% of the permanent employment probability variance for French-natives (as high as Parents' background) and 30 to 40% for African-natives (as high as schooling).

[TABLE 11 HERE] Then, we do the same decomposition on the full sample, which contains the simulated outcomes of French and African-natives together. Parents' origin is introduced as a new explanatory factor, whereas unobserved heterogeneity is removed, since its distribution is origin specific.

Table 12 contains the results of this variance decomposition. It shows that schooling attainments explain 68% of the cross-sectional variance in employment under a Permanent Contract for the first job after schooling. Thus, 32% of the variance are not explained by observed investment in human capital. Differences in observable characteristics or behaviors and discrimination may be possible explanations of the gap in permanent employment between French and African-natives. Moreover, two years after the exit from school, the schooling impact decreases to 62%. There may be other observable human capital factors, such as experience, that may have a return on the access to permanent employment at that time.

[TABLE 12 HERE] 7 Conclusion

In this paper, we estimated a flexible dynamic model of education choices and early employment contract outcomes. The model was estimated separately for Second-Generation Immigrants born of African parents, and the equivalent sub-population of French-natives.

We found that parental background is the main determinant of schooling attainments at high grade levels for French and African-natives. Compared to other factors, it explains about 60% of the variance of completing five years of college for both French and African-natives. Concerning the attainment of lower grade levels, however, the impact of parental background is much lower (around 30% for the probability of attaining at least secondary education completion) but still the same for both origin groups. At that grade level, the two sub-samples differ according to the size of the relative impact of "delay during primary school" (59% for African-natives, 37% for French-natives) and unobserved heterogeneity (15 and 34% respecively).

Then, we found that origin-specific unobserved heterogeneity and parameters seem to explain a small part of the schooling gap between French and African-natives. Concerning early career employment outcomes, schooling attainments explain 68% of the employment under a Permanent Contract in the whole sample for the first employment period in the labor market after schooling. This result implies that there are still 32% that are not explained by observed investment in human capital. Two years after the exit from school, this unexplained part increases to 38%. Thus, unobserved factors, differences in behavior or discrimination may all be viewed as possible reasons explaining a significant gap in access to early career job stability.

  employment outcome within the first year Pr(PC|s = 4, 5) -Pr(PC|s = 2, 3) 0.050 (0.013) -0.376 (0.017) Pr(FTC|s = 4, 5) -Pr(FTC|s = 2, 3) -0.076 (0.017) 0.258 (0.019) Pr(OUT|s = 4, 5) -Pr(OUT|s = 2, 3) 0.026 (0.011) 0.118 (0.014) Pr(PC|s = 6, 7) -Pr(PC|s = 4Predicted probabilities are computed for a man having a white collar father, a white collar mother, living in a urban area and not having been delayed at school. Note 2: In parenthesis: Standard errors computed using the Cholesky factorization method.

Table 1 :

 1 Bayesian Information Criterion Values for Model SelectionNote: The number of estimated parameters of each specification is 309 for the model with 4 types, 290 for the model with 3 types and 271 for the model with 2 types.

		French-natives	African-natives
	First employment outcome within the first year
	4 types	206644.29	12030.97
	3 types	206528.13	11948.08
	2 types	206326.80	11798.42
		Employment outcome at 2 years
	4 types	214163.45	12511.16
	3 types	213983.91	12380.89
	2 types	213837.91	12281.88

Table 2 :

 2 Actual and Simulated Grade Distributions: French-Natives

		Actual	Simulated Sample
	Grade	Sample	Average Type 1 Type 2
	1	0.060	0.059	0.088	0.000
	2	0.225	0.227	0.315	0.051
	3	0.147	0.147	0.142	0.157
	4	0.108	0.106	0.109	0.101
	5	0.207	0.207	0.152	0.314
	6	0.136	0.137	0.122	0.169
	7	0.118	0.118	0.073	0.207
	Average
	Grade	4.057	4.060	3.579	5.013

Table 6 :

 6 Variance Decomposition of Schooling Attainments by Origin Groups

		French-natives African-natives
	Reaching level 3 or more (high school completion)
	Parents' background	29%	26%
	Late at school	37%	59%
	Unobserved heterogeneity	34%	15%
	Reaching level 5 or more (higher education diploma)
	Parents' background	40%	28%
	Late at school	33%	64%
	Unobserved heterogeneity	28%	8%
	Reaching level 7 or more (college graduate)
	Parents' background	59%	58%
	Late at school	17%	17%
	Unobserved heterogeneity	24%	25%

Table 7 :

 7 Variance Decomposition of Schooling Attainments for the Full Sample Note: In parenthesis: Standard errors computed using the Cholesky factorization method.

	Reaching level 3 or more (high school completion)
	Origin	5%
	Parents' background	42%
	Late at school	53%
	Reaching level 5 or more (higher education diploma)
	Origin	5%
	Parents' background	52%
	Late at school	43%
	Reaching level 7 or more (college graduate)
	Origin	3%
	Parents' background	75%
	Late at school	22%
	Table 8: Schooling Gaps Decompositions
	∆ Pr(s ≥ 3) (high school completion)
	Predicted gap	0.261 (0.095)
	Gap due to behaviors (5)	0.164 (0.088)
	Gap due to behaviors (6)	0.083 (0.095)
	∆ Pr(s ≥ 5) (higher education diploma)
	Predicted gap	0.277 (0.054)
	Gap due to behaviors (5)	0.211 (0.056)
	Gap due to behaviors (6)	0.100 (0.053)
	∆ Pr(s ≥ 7) (college graduate)
	Predicted gap	0.093 (0.014)
	Gap due to behaviors (5)	0.046 (0.021)
	Gap due to behaviors (6)	0.030 (0.014)

Table 9 :

 9 Schooling Returns: French-Natives

Table 11 :

 11 Variance Decomposition of Obtaining a Permanent Contract by

	Origin Groups
		French-natives African-natives
	First employment outcome within the first year
	Parents' background	22%	38%
	Late at school	3%	1%
	Unobserved heterogeneity	17%	30%
	Simulated schooling	59%	32%
	Employment outcome at two years
	Parents' background	19%	19%
	Late at school	6%	0%
	Unobserved heterogeneity	20%	40%
	Simulated schooling	54%	41%

Table 12 :

 12 Variance Decomposition of Obtaining a Permanent Contract for the Full Sample

	First employment outcome within the first year
	Origin	3%
	Parents' background	26%
	Late at school	3%
	Simulated schooling	68%
	Employment outcome at two years
	Origin	6%
	Parents' background	24%
	Late at school	8%
	Simulated schooling	62%

A vast literature deals with the impact of employment protection legislation (in particular firing costs) on unemployment and labor mobility (eg.,[START_REF] Bentolila | Firing Costs and Labour Demand: How Bad is Eurosclerosis?[END_REF][START_REF] Bertola | Job Security, Employment and Wages[END_REF][START_REF] Garibaldi | Job Flow Dynamics and Firing Restrictions[END_REF][START_REF] Mortensen | Unemployment Responses to 'Skill-Biased' Technology Shocks: The Role of Labour Market Policy[END_REF].

2 Indeed, there is a considerable amount of debate going on between European countries about the optimal level of job and social security that the European economy can stand.

At a more philosophical level, the model may be labeled as semi-structural, since it is not based on a formal utility maximization procedure. It is also important to note that because the model is explicitly dynamic (education choices may affect post-schooling choices even after conditioning on unobserved heterogeneity), it cannot be logically estimated by IV techniques (the most popular method of estimation among empirical labor economists). For more details, seeKeane (2007) and[START_REF] Belzil | Calibration and IV Estimation of a Wage Outcome Equation in a Dynamic Environment[END_REF].

French Center for Research on Education, Training and Employment.

At the highest grade, s is excluded from the choice set since continuing schooling is impossible.

In what follows, we estimate the model with different values of K, and determine the optimal number of types using a Bayesian Information Criterion.

"School continuation" is the outcome of reference at the end of each grade level. Therefore, there are 3 latent utility equations modeled at the end of each of the 7 grade levels, corresponding to the 3 employment outcomes.

Since we want to take into account educational selectivity(Cameron and Heckman, 1998), we disregard a model specification without unobserved heterogeneity.

The evident capacity of the model to fit the data is most likely a by-product of its flexibility.

Removing the gender dummy from this category has a very limited impact on the results.

The predicted gaps are very close to the gaps actually observed in the population.

The terminology "behaviors" vs. "endowments" is used here to be consistent with the distinction made in empirical work. Technically speaking, this terminology may be

Note 1: Predicted probabilities are computed for a man having a white collar father, an unemployed mother, living in a urban area and not having been delayed at school. Note 2: In parenthesis: Standard errors computed using the Cholesky factorization method.