S Finazzi

A Le Boité

F Storme

Alexandre Baksic

C Ciuti

Corner space renormalization method for driven-dissipative 2D correlated systems

Keywords:

come

Corner space renormalization method for driven-dissipative 2D correlated systems

Simulating large quantum systems is a challenging task because their complexity grows exponentially with their size. Indeed, the dimension of the Hilbert space for a multipartite system consisting of m subsystems, each of them described by a space of dimension N , is N m . Furthermore, for open systems the physics can no longer be described only in terms of the eigenstates of an Hamiltonian, requiring instead the knowledge of the densitymatrix. In this case, the number of variables to be determined scales as N 2m , namely the square of the size of the Hilbert space.

In the last decades, several methods have been proposed to reduce the complexity of this problem. The first attempt in this direction is the renormalization group technique, proposed by Wilson [1] and successfully applied to the Kondo problem. Numerical implementations of this approach are based on the solution of a system with a smaller Hilbert space, where only the relevant physical states with the lowest energies are retained. Ideally, this procedure can be iterated by arbitrarily growing the size of a block system step by step, for instance by doubling the size of the block at each iteration. However, such a numerical implementation of the real-space renormalization group can yield inaccurate results for the system ground state, because the boundary conditions imposed while solving the smaller system might be inappropriate to describe the doubled one [2]. In the case of one-dimensional systems, a powerful method is represented by the density-matrix renormalization group (DMRG) [3], which is based on the selection of the most probable states of the reduced density-matrix of a block, obtained by determining the ground state of the Hamiltonian of a larger section of the lattice. The generalization to two spatial dimensions is challenging and currently under intense study [4,5]: one approach exploits the artificial description in terms of one-dimensional systems with * Electronic address: cristiano.ciuti@univ-paris-diderot.fr long-range interactions [6], while another is based on the generalization of matrix product states [7] to projected entangled-pair states [8]. These theoretical methods have been extended to 1D dissipative lattice systems by introducing matrix product density operator algorithms [9], time-dependent DMRG [10] and a superoperator renormalization technique [11]. These approaches are aimed at solving the master equation governing the dynamics of the density-matrix of the lattice.

Among driven-dissipative systems, lattices of coupled cavity resonators with quantum optical nonlinearities [12][13][14] are attracting a considerable interest, e.g. for the realization of non-equilibrum strongly correlated photonic phases [15]. In particular, the spectacular rise of circuit QED resonators with superconducting Josephson quantum circuits is very promising in this respect both for the realization of strong correlations and for their control [16,17]. So far, several studies have been devoted to non-equilibrium mean-field-like theories [18][19][20][21][22][23], based on a Gutzwiller factorization of the densitymatrix. Numerical methods beyond mean-field for such systems so far rely on a direct integration of the densitymatrix for small size systems [24,25] or applications of the matrix product operator techniques mentioned above to one-dimensional cavity arrays [26,27].

In this letter, we present a theoretical method to explore the physics of driven-dissipative correlated quantum systems with two spatial dimensions. A corner of the Hilbert space for a lattice system is selected using eigenvectors of the density-matrix solving the master equation for smaller clusters. At each step, two sublattices are merged and M pairs of states are selected to construct a corner basis by maximizing their joint probability. The degree of accuracy can be controlled by enlarging the number of states of the corner space, until convergence is obtained. The method is applied to the driven-dissipative 2D Bose-Hubbard model, which describes, e.g., two-dimensional arrays of coupled cavities with quantum nonlinearities.

The general problem we aim to solve is the Lindblad master equation [START_REF] Walls | Quantum Optics[END_REF] for the density matrix ρ of a drivendissipative manybody quantum system,

dρ dt = i [ρ, Ĥ] + j Ĉj ρ Ĉ † j - 1 2 Ĉ † j Ĉj ρ + ρ Ĉ † j Ĉj ,
where Ĥ is the Hamiltonian of the lattice system and Ĉj are operators describing the relaxation of the system due to the interaction with an external bath. We will consider a zero-temperature reservoir for simplicity, although the case of finite temperature can be treated without major complications. To give an example, in the case of a lattice of optical cavities the jump operators are Ĉj = √ γ j bj , where bj is the photon annihilation operator in the j-th cavity and γ j is the corresponding dissipation rate.

The corner space renormalization algorithm we introduce here is based on the following steps: i) determine the steady-state density-matrix for small lattices, for which a direct, brute-force integration of the master equation is possible; ii) merge spatially two pre-determined lattices and select the M most probable product states spanning the so-called corner space; iii) determine the steady-state solution of the density-matrix in the corner space; iv) increase the dimension M of the corner until convergence of the observables is achieved; v) in order to create a larger lattice, go back to step ii).

Here, we describe in detail the crucial steps iii) and iv), i.e., the selection of the corner space. As sketched in Fig. 1, let us suppose that we know the solution for the steady-state density matrices ρ (A) and ρ (B) represents a manybody state which can have strong correlations within the system A. To select a small 'corner' C(M ) of the larger space H A∪B , we will consider the subspace spanned by the M most probable states of the form |φ

(A) r |φ (B) r ranked according to the joint probability p (A) r p (B) r . Let us call |φ (A) r1 |φ (B) r 1 the most probable product state, i.e. such that p (A) r1 p (B) r 1 ≥ p (A) r p (B) r
for every value of r and r . We will call |φ

(A) r2 |φ (B) r2
the second most probable product state and so on so forth. In other words, we will consider the subspace generated by the orthonormal basis {|φ Carlo sampling when applied. In this example, the dimension of the full Hilbert space is 2 16 = 65536. The case of 65536 states has been solved by an independent Monte Carlo wavefunction code using a Fock basis for the entire space and sparse matrix calculations.

(A) r1 |φ (B) r 1 , |φ (A) r2 |φ (B) r 2 , ..., |φ (A) r M |φ (B) r M }, where p (A) r1 p (B) r 1 ≥ p (A) r2 p (B) r 2 ≥ ... ≥ p (A) r M p (B) r M , i.e. we select the 'Corner' Maximize Hilbert space A B A [ B H A H B ⇢ (A) = X r p (A) r | (A)) r ih (A) r | H A S B = H A ⌦ H B C(M ) = {| (A) r1 i| (B) r 0 1 i, . . . , | (A) rM i| (B) r 0 M i} C(M ) H A S B p (A) r p (B) r 0 ⇢ (B) = X r 0 p (B) r 0 | (B)) r 0 ih (B) r 0 | ……..
M most probable pairs of states 1 . Note that a generic state belonging to the corner space, namely of the form

|Ψ = M s=1 c s |φ (A) rs |φ (B)
r s , can describe strong correlations and quantum entanglement between systems A and B while keeping correlations within A and B. We emphasize that by increasing arbitrarily the number M of states in the corner space, the method becomes exact, because the considered basis spans the entire Hilbert space. Of course, the method is useful only when the number of 1 Note that p (A) r j can be smaller than p states M required to reach convergence is small enough to be treated numerically. This ultimately depends on the degree of correlation of the considered system. Concerning step iii), namely the determination of the steady-state density-matrix, it is worth pointing out that when the number M of states in the corner space is small enough, the master equation can be solved by direct numerical integration in time (M typically up to a few hundreds). For larger values of M (up to a number of the order of 10 4 depending on the sparsity of the Hamiltonian matrices), a more efficient method is based on a stochastic technique [START_REF] Plenio | [END_REF], the so-called Monte Carlo wavefunction algorithm [30][31][32]. Such algorithm computes the density-matrix of the system by averaging over quantum trajectories of the wavefunction in presence of random quantum jumps.

r j p (B) r j ≥ p (A) r j+1 p (B) r j+1 . M n ( b ) g2 g (2) <j,l> 20
As a first illustration of the corner space renormalization method, we show results for the driven-dissipative Bose-Hubbard model in 2D square lattices. The corresponding Hamiltonian ( = 1) in the frame rotating at the pump frequency and in the case of homogeneous pumping reads:

Ĥ = j (-∆ω b † j bj + U 2 b † j b † j bj bj +F ( b † j + bj ))- J z <j,l> b † j b l ,
where ∆ω = ω pω c is the detuning between the pump and the bare boson frequency, U is the on-site bosonboson interaction and F is the pump field. J is the hopping coupling, z is the coordination number and <i,j> denotes the sum over all the couples of nearest neighbors.

For simplicity, we have fixed the phase of the pump in such a way that F is real. Finally, each site is subject to losses with a dissipation rate γ.

In the following, we will consider the case of periodic boundary conditions. In Table I we show results for a 4 × 4 square lattice of hard-core bosons (U = +∞), i.e. for which the maximum number of photons per site to be considered is N max = 1. These results have been obtained starting from a 2×2 lattice for which a brute-force determination of the steady-state solution of the master equation is possible. Merging two 2 × 2 lattices, we get results for a 4 × 2 lattice and, repeating the doubling procedure, for the 4 × 4 case. The dimension of the full Hilbert space for hard-core bosons on a 4 × 4 lattice is 2 16 = 65536. Although very heavy, the master equation resolution in the full Hilbert space has been performed by an independent Monte Carlo wavefunction code using a Fock basis for the entire space and sparse matrix calculations. This way, we have been able to benchmark the results obtained with a small corner to the exact results. The table reports results for the boson population per site n = b † j bj , the real part { ( b j )} of the bosonic coherence and the nearest-neighbor correlation g is trivially equal to 0 since two bosons are not allowed to be on the same site. Note that g

(2) j,l = 1 for a factorized Gutzwiller-like density-matrix ρG = j ρj where ρj is the reduced density-matrix of the j-th site. The meanfield approach is equivalent to taking a self-consistent Gutzwiller density-matrix, assuming all the sites identical. Hence the difference (g

(2)
<j,l> -1) quantifies the degree of correlations beyond mean-field between nearest neighbors. Remarkably, for the parameters given in the caption of Table I, we get a very accurate result for a small number M = 200 (negligibible error for n, 0.1% for the bosonic coherence and 0.3% for g

(2) j,l ). In Table II, we show results for soft-core bosons with a larger hopping coupling (U/γ = 20, J/γ = 3) and a cut-off number N max = 3 of bosons per site (we have verified that this is the cut-off number per site required to get convergence). A cut-off N max = 3 for a 4 × 4 lattice implies a Hilbert space dimension equal to 4 16 4.3 • 10 9 . As shown by the convergence progression in Table II, results with deviations below 1% are reached already for a corner space dimension M = 3200, hence six orders of magnitude smaller than the full Hilbert space for a system exhibiting large correlations (g

(2)
j,l -1 = 0.63).

An example of the temporal dynamics leading to steady-state solutions is reported in Fig. 2, plotting n and g 2 for different lattice sizes. The corner method results are compared with the non-equilibrium mean-field approach used in Refs. [21,23], based on the exact analytical solution of the master equation for the one-site problem [33]. The initial condition for the density-matrix dynamics for the 2 × 2 lattice is the mean-field solution. After a transient, a steady-state solution is obtained. The initial condition for the 4 × 2 lattice is constructed from the steady-state solution of the 2 × 2 lattice and so-on so forth. We have also merged 3 × 1 clusters to get the 3 × 3 lattice and then the 6 × 3 case by doubling. We see that the steady-state observables for the 3 × 3, 4 × 4 and 6×3 lattices with periodic boundary conditions tend to converge to the same value, so the results are already approaching those for a lattice with an infinite number of sites. The finite spatial range of the correlations of the driven-dissipative system is responsible for such relatively quick convergence. For the parameters in Fig. 2, the deviations from the mean-field theory are around Parameters: J/γ = 1 (except the third line with the * sign, obtained with J/γ = 3), F/γ = 2 and ∆ω/γ = 5. The maximum number of bosons per site is Nmax = 1 for hardcore bosons, Nmax = 3 for U/γ = 20, Nmax = 5 for U/γ = 10, Nmax = 4 for U/γ = 1 and 0.5.

20% for n and g 2 . Since the driving is homogeneous and the considered boundary conditions are periodic, shortcomings due to conflicting boundary conditions in the doubling procedure do not apply here. It is insightful to look at the diagonal decomposition of the calculated density-matrix, namely ρ = M r=1 p r |Ψ r Ψ r | where p r ≥ p r+1 . In Fig. 3, we show an example of the probability distribution p r (top panels, logarithmic scale) and the expectation value of the total number of bosons in the lattice (bottom panels) versus the state rank r for a 6 × 3 lattice of soft-core bosons with U = 20γ (left panels) and hard-core bosons (right panels). In both cases, the probability drops sharply by several orders of magnitudes when the rank r is large enough, confirming the achieved convergence of the corner space dimension. In the hard-core boson case, a rather well definite shell structure is apparent. The first state (r = 1), which captures a large part of probability, is followed by shells of states having close probabilities and densities. In the case of a homogeneous system, a factorized Gutzwiller density-matrix with each site having the same reduced-density matrix leads to a shell structure with exactly flat plateaux structures due to symmetry reasons. In fact, a permutation of the role of the different sites does not change the probability of a state and observables like n tot , which is a sum over all the sites. In the right panel of Fig. 3 (hard-core boson case), the situation is qualitatively close to the Gutzwiller case, even though the plateaux are not exactly flat. In the case of soft-core bosons in the left panel of Fig. 3, a first shell is clearly visible, while higher shells merge into a continuous curve where the different quantities increase gradually, denoting a large degree of correlations (indeed

g (2)
<j,l> -1 0.6 in the case considered).

In Table III, we summarize illustrative results for different lattice sizes with periodic boundary conditions and compare them to the Gutzwiller mean-field solutions [21,23], using the same excitation parameters (F/γ = 2 and ∆ω/γ = 5). The convergence of the results with increasing corner dimension M has been checked as well as the required maximum number N max of bosons per site. It is apparent that in the considered case the mean-field theory gives rather good results for hard-core bosons and a large 8×8 lattice, as quantified by a g (2) i,j -1 0.02. Significant deviations are instead present when the on-site interaction U is competing with the hopping coupling J (the cases with U/γ = 20 and J/γ = 1 and 3 in Table III). The value for U/γ = 10 and J/γ = 1 is close to a two-photon resonance [23] and indeed the the population of bosons per site is much higher (close to one boson per site) with the on-site g 2 correlation function quite close to 0.5. For U/γ = 0.5, it is possible to simulate very large lattices (a 16 × 16 lattice is reported) with a very small number of states (M = 400).

In conclusion, we have presented a theoretical method for driven-dissipative 2D correlated lattice systems. The proposed numerical algorithm follows a hybrid real-space renormalization group approach where the states are selected on the basis of joint probabilities. We have successfully demonstrated the efficiency of such a method by applying it to the driven-dissipative Bose-Hubbard model on 2D square lattices. Unlike mean-field theories, where the decoupling approximation is not controlled, the present numerical method allows us to get results with controllable accuracy. The method has therefore the potential to become a precious tool to benchmark analytical theories and study strongly correlated open systems with more than one spatial dimension. Future studies will explore the physics of 2D arrays of nonlinear cavities with complex elementary cells (including disorder), geometric and spin frustration as well as the role of artificial gauge fields in extended lattices.

C. C. acknowledges support from ERC (via the Consolidator Grant 'CORPHO' No. 616233), from ANR (projects QPOL and QUANDYDE) and from Institut Universitaire de France.

  for two lattices A and B. If we want to consider a lattice obtained by merging spatially the two lattices A and B, the corresponding Hilbert space is H (A∪B) = H A ⊗ H B where H A and H B are the Hilbert spaces of A and B. Each density-matrix operator can be diagonalized as ρ (A) = r p r |, where the states |φ (A) r form an orthonormal basis for H A and p (A) r are the corresponding probabilities. Analogous notations hold for the system B. Each ket |φ (A) r

FIG. 1 :

 1 FIG.1: Sketch of the corner space renormalization method.

FIG. 2 :

 2 FIG.2: Evolution of n and g2 versus time t (units of 1/γ) for the driven-dissipative Bose-Hubbard model with periodic boundary conditions on lattices of various size for the following parameters: U/γ = 20, J/γ = 3, F/γ = 2, ∆ω/γ = 5 . Solid lines represents evolutions performed by direct integration of the master equation, while points depict Monte Carlo wavefunction calculations. When error bars are not shown, the statistical error is smaller than the point size. The blackdotted lines represent the mean-field values. The initial conditions are explained in the text.

FIG. 3 :

 3 FIG. 3: Probabilities pr (top panels, logarithmic scale) and expectation value of the total boson population ntot = j nj for the orthonormal eigenvectors |Ψr of the steadystate density-matrix (ρ = r pr|Ψr Ψr| and pr ≥ pr+1). The state rank r is in logarithmic scale. Lattice size: 6 × 3. Driving parameters: F/γ = 2, ∆ω/γ = 5. Left: U/γ = 20 and J/γ = 3. Right: hardcore bosons with J/γ = 1.

.

  For hard-core bosons, the on-site second-order correlation function g 2 =

TABLE II :

 II Parameters: 4 × 4 square lattice with periodic boundary conditions, U/γ = 20, J/γ = 3, F/γ = 2, ∆ω/γ = 5. A number Nmax = 3 of bosons per site has been considered. In this case, the dimension of the full Hilbert space is 4 16 4.3 • 10 9 .

		0.0902	0.1967	1.646	1.28
	50	0.1006	0.1907	1.513	1.34
	100 0.1044	0.1886	1.454	1.26
	200 0.0968	0.1922	1.324	1.51
	400 0.1006	0.1905	1.291	1.51
	800 0.1009(2) 0.1903(3) 1.242(3) 1.57(2)
	1600 0.1014(2) 0.1896(2) 1.226(3) 1.58(2)
	3200 0.1002(2) 0.1897(2) 1.185(2) 1.63(2)
	6400 0.0994(2) 0.1899(2) 1.179(3) 1.63(1)

TABLE III :

 III Steady-state expectation values for lattices (periodic boundary conditions) with different sizes, calculated via the Gutzwiller mean-field theory and the corner space renormalization method. M is the dimension of the corner space.

		Mean-field		Corner method
	U/γ	n	g2	Nsites (M )	n	g2	g	(2) j,l
	∞ 0.0953	0	8 × 4 (1600) 0.09527(2) 8 × 8 (8000) 0.0948(2)	0 0	1.0436(3) 1.0237(6)
	20 0.125 0.836	4 × 4 (3200) 0.1281(4) 0.859(4) 1.172(5) 6 × 3 (6400) 0.1282(9) 0.858(9) 1.173(4)
	20 * 0.0768 0.8879	4 × 4 (6400) 0.0994(2) 1.179(3) 6 × 3 (6400) 0.0992(1) 1.202(4)	1.63(1) 1.65(1)
	10 0.9587 0.6088	4 × 2 (6400) 0.9275(8) 0.631(1) 1.0127(8) 3 × 3 (8000) 0.9281(9) 0.617(1) 1.0069 (6)
	1 0.1156 1.265 16 × 8 (600)	0.1156	1.259	0.9897
	0.5 0.1126 1.112 16 × 16 (400) 0.1126	1.1105	0.9941


Joachim Jarreau
email: joachim.jarreau@univ-amu.fr.

Philippe Combes

Anthony Edo

Denis Fougère

Gianluca Orece

Christian Schluter

The impact of naturalizations on job mobility and wages: evidence from France

Keywords: Immigrant assimilation, labor market, job mobility, wage bargaining. JEL Classication: J31, J61, J68, F22

This paper studies the impact of naturalization on the labor market outcomes of foreign-born workers in France. Using a large panel dataset of workers employed in France over 1993-2001, I nd that naturalization is associated with a sharp increase in job mobility: immigrants tend to change occupations and employers, in the same year as they naturalize. Turning to wages, I nd evidence that naturalization commands a wage premium, which is associated with employment mobility. For workers initially in lowskill occupations, the wage premium is conditional on occupational mobility. For those in middle-or high-skilled occupations, there is also evidence of a wage premium, mostly for foreign women; this premium is associated with moves to a dierent rm. These results suggest that foreign citizenship constrains workers mobility, and are consistent with the hypothesis of a mismatch of foreign workers to their jobs.

Introduction

Several recent studies in immigration countries have found that the acquisition of citizenship by foreigners is associated with higher employment and wages (e.g. [START_REF] Bratsberg | The eect of naturalization on wage growth: A panel study of young male immigrants[END_REF]; [START_REF] Fougere | Naturalization and employment of immigrants in france (1968-1999)[END_REF]; [START_REF] Steinhardt | Does citizenship matter? The economic impact of naturalizations in Germany[END_REF] for the US, France and Germany respectively). These studies use longitudinal data, which allows to control, to some extent, for the selection of individuals into naturalization; thus suggesting that naturalization by itself (rather than individual characteristics of those who choose to naturalize), has, in these countries, a positive impact on the employment prospects of immigrants, and on their wages.

Barriers on access to some jobs, facing foreign workers, are generally cited as the plausible mechanism behind this pattern. Such barriers include legal restrictions -a number of jobs, mostly in the public sector, being open only to nationals, in the US and in European countries. In addition to this legal discrimination, foreign workers may also face discrimination by employers, for example if citizenship is interpreted as a signal for (country-specic) human capital, or for a commitment to stay longer in the country.

These various forms of discrimination may explain the observed employment impact of naturalization. They may also explain the positive wage eect in two cases: if they apply in jobs paying higher wages, for a given employee prole; or, if they have an indirect impact on wages paid in other, non-restricted positions, by lowering the probability of employment for non-citizens, and thus weakening their bargaining position in the jobs which they have access to.

Alternatively, another source of explanation for the wage impact lies in the degree of economic and legal security oered by citizenship, through the assurance of legal stay and access to safety nets. Without citizenship, obtaining and renewing a legal permit to stay may be tied to employment 1 . Consequently, foreign workers may be under more pressure to secure employment, and thus have less time for screening positions; changing jobs may also be seen as a risk, if it implies leaving a permanent contract for a short-term one or a testing period. In the presence of imperfect information on the labor market, this can create mismatch between foreign workers and the positions they occupy. In this case, the wage gap is not caused by discrimination in specic jobs, but rather by a broader form of discrimination on the labor market. This paper contributes to clarify these mechanisms in the French case. A large, administrative dataset of employer data is used, where immigrant and native workers are followed throughout their professional life.

2 The longitudinal (annual) dimension of the data allows to control for individual 1 This is the case in France (see below) 2 The DADS (Déclaration annuelle des données sociales) comprises all data reported by employers in France 2 heterogeneity when measuring the impacts that naturalization has on the careers of immigrants -i.e. on the wages they earn and the types of jobs they hold. I put specic attention to the conjunction between these two impacts, looking at whether the naturalization wage premium is tied to a change of employer or occupation.

3

Results show, rst, that naturalization triggers a sharp increase in job mobility: the probability of changing employer, as well as occupation, increases sharply in the year of naturalization. Table 1 illustrates this point. The probabilities of changing employer, occupation, as well as location, labor contract, or entering the public sector, are computed for all individuals in the sample (including foreigners and naturalized foreign-born), depending on whether they are foreigner, naturalized, or just in the year of naturalization. All these probabilities increase sharply in the precise year of naturalization, a result which will be conrmed later when controlling for a range of individual characteristics.

Second, my results conrm the presence of a naturalization wage premium in the French context, but highlight the importance of accounting for heterogeneity in this relationship. For foreign men, the premium exists mostly for workers initially employed in low-skilled occupations; while among women, by contrast, there is evidence of a premium for those in middle-and highskilled occupations.

Third, results establish a link between the wage premium and job mobility. For workers employed in low-skill occupations in particular, the premium materializes only for those changing occupation in the year of their naturalization: thus naturalization increases wages because it allows to move to a better paid type of job. This suggests a pattern of mismatch (between employee and job), prior to naturalization. The mobility eect is centered on the naturalization year, thus there is no apparent reason (such as skill) why those workers would not have been able to change before; other than the constraint that foreign citizenship exerts on mobility itself. 4 One possible explanation lies in the precarious situation of those with foreign citizenship, due to uncertainty about legal stay and safety nets; this may lead some foreigners to accept jobs not matching their qualications, because they have not the time to search further (or because changing job is risky, if it involves a testing period during which long-term employment is not guaranteed).

The link between mobility and the wage premium also appears to hold in the case of women in about their employees for computation of social contributions. The panel dataset used here follows over time all workers born in October of even years. In most of the empirical analysis I use data for the period 1993-2001, for reasons detailed below.

who change employer (while staying in the same occupation category).

This eect can also be explained by the fact that those workers accept less paying positions because they lack time or security to search for a better match. Alternatively, it could be that citizenship is lifting barriers to specic positions. Restrictions on access to specic professions and public sector jobs, passport requirements for some positions, employer preferences, are among the forms of discrimination (legal or not) that could play a role. The fact that this eect is specic to foreign women suggests that two forms of discriminations, based on gender and nationality, may be interacting here.

The analysis on wages is conducted while controlling for individual heterogeneity using an individual xed-eects model. Thus, the wage increase is not explained by constant individual characteristics associated to the choice to naturalize. However, there remains the possibility that those who eventually naturalize have distinctive wage patterns, for example because they invest more in country-specic human or social capital, in prevision of staying long-term in the country (or to increase their chances of obtaining citizenship). I control for this in several ways. First, I check that both the mobility and the wage eects of naturalization occur at the time of naturalization, and not in the years before. Second, I use specications allowing for individual wage growth to dier for those who eventually naturalize (or, also, for those in particular who change jobs when naturalizing). These tests conrm that the observed wage impacts are not detected in any form (level or growth) before citizenship acquisition. This establishes that naturalization is instrumental in the eects on job mobility and wages I measure, and that these eects are not driven by selection into naturalization.

6 , 1993-2001, except last panel: 2006-2008. Sample includes all foreigners and naturalized individuals, for all individuals being observed two consecutive years; changes are from one year to the next.

Early socio-economic studies of naturalization have studied the determinants, rather than the consequences, of it. Rates of naturalization were found to vary widely across origins, education and cultural backgrounds. Acquisition of the host country citizenship is a choice, which an economist would want to explain by the prospective benets a candidate can expect from it. However, the decision is not primarily an economic one, and could instead be motivated by political factors, symbolic ones. [START_REF] Bernard | Cultural determinants of naturalization[END_REF]'s ndings, of higher naturalization among the high educated, suggests that it could be used as a signal of status, and of willingness to stay, rather than as an instrument for economic progress. [START_REF] Portes | Changing ags: Naturalization and its determinants among mexican immigrants[END_REF] show that naturalization rates are especially low among Mexican immigrants, and show this to be explained by the short distance from origin, and by the temporary nature of the immigrant experience for the majority of them. [START_REF] Diehl | Rights or identity? naturalization processes among labor migrants in germany[END_REF] nd that, among Turkish immigrants in Germany, the propensity to naturalize is higher among those most assimilated (those with German friends, speaking German, Turkish immigrants). Thus, they argue that naturalization is used at the end of the assimilation process, to bring legal status in accordance with a social status already achieved.

One early study of the economic eects of naturalization was [START_REF] Chiswick | The eect of americanization on the earnings of foreign-born men[END_REF], who was interested in the process of assimilation of immigrants. He found evidence of naturalized immigrants having higher wages, but this result obtained in cross-sectional estimation does not establish causality; thus, it does not say whether naturalization is only a sign of assimilation, or as an essential component of it.

More recently, several studies have used longitudinal data to test the hypothesis of naturalization having a direct impact on labor market outcomes. Comparing cross-sectional and panel estimates has allowed to ask whether there was more than selection in the naturalization eect, as well as to infer the direction of selection.

7

Most studies answer positively. [START_REF] Bratsberg | The eect of naturalization on wage growth: A panel study of young male immigrants[END_REF]; [START_REF] Steinhardt | Does citizenship matter? The economic impact of naturalizations in Germany[END_REF] nd a positive impact on wages, in the US and Germany, respectively. Bevelander and Pendakur (2012) nd a positive impact on employment in Sweden. By contrast, [START_REF] Scott | The economics of citizenship: is there a naturalization eect? The economics of citizenship[END_REF] and [START_REF] Engdahl | the impact of naturalisation on labour market outcomes in sweden. Naturalisation: A Passport for the Better Integration of Immigrants[END_REF] nd little or no wage premium of naturalization in the case of Sweden, after controlling for individual heterogeneity. [START_REF] Bratsberg | The labour market outcomes of naturalised citizens in norway[END_REF] nds no positive impact on wages, in the case of Norway, and a small negative impact for some groups. [START_REF] Fougere | Naturalization and employment of immigrants in france (1968-1999)[END_REF] found a positive employment eect in the case of France. [START_REF] Bratsberg | The eect of naturalization on wage growth: A panel study of young male immigrants[END_REF] use a small sample from a longitudinal survey, the NLSY, focused on Youth in the US (along with CPS data used in cross-section). [START_REF] Steinhardt | Does citizenship matter? The economic impact of naturalizations in Germany[END_REF] is using administrative data, similar to those used here, for Germany. Both are using the panel dimension to control for individual characteristics entering into the self-selection of candidates for naturalization.

The evidence in this paper of a wage premium of naturalization is broadly in line with their results. However, the present paper shows the premium to be signicant only for some specic occupation groups, and to be conditional on employment mobility patterns; by contrast, these two studies do not explicitly test for such heterogeneity. Therefore, the comparison raises the possibility that their estimates reect an average of dierent premia across heterogeneous groups. [START_REF] Bratsberg | The eect of naturalization on wage growth: A panel study of young male immigrants[END_REF] also nd, in cross-sectional data, that the probability of holding a public-sector job, a white-collar one, or a unionized one, is higher for naturalized immigrants.

They interpret this as evidence that the wage premium results from access to those job categories, with citizenship lifting specic barriers to better-paid positions. The present paper tests this hypothesis, and conrms it only partly. It establishes the link between the wage premium and job mobility. Mobility across occupations is one of important channels; on the contrary, access to public sector does not seem to play a major role.

The next section presents some background on French naturalization laws. Section 3 discusses the data and the empirical methodology. Section 4 presents the empirical results. The last section concludes.

2 Naturalization and the labor market: the French context a discretionary decision by the administration, and can be refused even if these requirements are fullled. In particular, the criteria of cultural assimilation and of professional integration (insertion professionnelle) are to be appreciated by the prefet. For example, the nature of employment or of the labor contract do not explicitly enter the legal requirements; however, short-term or low-pay contracts can be a motive for rejection.

10

The process of naturalization can be long. The ocial maximum delay is of 18 months after the request is received. However, delays to submit the request may also add some time. [START_REF] Hagedorn | Republicanism and the politics of citizenship in germany and france: Convergence or divergence[END_REF] indicates that the waiting time for the applicants amounted in 1997 to seven months for an initial meeting with a sta member and additional eight months to have the obligatory interview in which assimilation potential and personal motivation is examined. In addition, informal sources, such as associations, indicate that several applications are often necessary before obtaining a positive result.

11 [START_REF] Fougere | Naturalization and employment of immigrants in france (1968-1999)[END_REF] 13 These include physicians and surgeons, pharmacists, notaries, architects, insurance ocers, managers of a private research laboratory, or of a rm in the funerals, explosives, or fund escorting.

14 However, as underlined by Haut conseil à l'Intégration (1998), the dierence in labor market 10 This is indicated by associations providing advice to immigrants, such as www.info-droits-etrangers.org/.

11 Ocial gures on rates of refusal are not made public.

12 Employment restrictions to non-citizens apply in e.g. Austria, Belgium, Canada, Germany, the US and Sweden.

See [START_REF] Kogan | Ex-yugoslavs in the austrian and swedish labour markets: the signicance of the period of migration and the eect of citizenship acquisition[END_REF][START_REF] Corluy | Employment chances and changes of immigrants in belgium: The impact of citizenship[END_REF][START_REF] Devoretz | The economic causes and consequences of canadian citizenship[END_REF][START_REF] Euwals | Citizenship and labor market position: Turkish immigrants in germany and the netherlands1[END_REF][START_REF] Steinhardt | Does citizenship matter? The economic impact of naturalizations in Germany[END_REF][START_REF] Bevelander | Naturalisation and socioeconomic integration: The case of the netherlands[END_REF][START_REF] Scott | The economics of citizenship: is there a naturalization eect? The economics of citizenship[END_REF] 13 Such legislation has accumulated since the late 19th century, with numerous laws targeting specic profes- sions, motivated partly by concerns regarding national sovereignty and security (weapons trade), xenophobia, and corporatist lobbying.

In the public sector, non-EU nationals generally are denied access to titulaire positions (permanent contracts for public servants), but not to contract jobs (status similar to private sector employment). This also applies to public rms such as the national railroads, energy, and air ight companies.

14 By contrast, in the US, most similar restrictions for private sector professions have been repealed, according to [START_REF] Yang | Explaining immigrant naturalization[END_REF] outcomes (in particular unemployment) between foreigners and nationals cannot be explained entirely by legal discrimination. Several studies have brought evidence of discrimination at hiring against immigrants: see e.g. [START_REF] Cediey | Les discriminations à raison de lorigine dans les embauches en france. une enquête nationale par tests de discrimination selon la méthode du bureau international du travail[END_REF].

In addition, labor market outcomes may dier for non-nationals due to dierences in exit options. Even though, as acknowledged by Haut conseil à l'Intégration (1998), discrimination in access to welfare benets have been essentially removed, some minor dierences subsist. For example, access to the minimum income allocation (RMI, now RSA) is conditional, for foreigners without resident status, on having spent at least 3 years in the country [START_REF] Math | Minima sociaux: nouvelle préférence nationale? Plein droit[END_REF].

15 Haut conseil à l'Intégration (1998) also points out that delays in registering individuals or in the renewal of permits to stay may disrupt access to benets.

Another factor is the link between employment and residency permits. Tow main types of permit exist for non-EU nationals in France. The rst if the residence status which guarantees authorization to stay for ten years, and may be requested after 5 years of legal stay in the territory;

the second is a temporary one-year card which needs to be renewed every year upon examination of the individual's situation. For non-students, stable employment is one of the conditions for renewal (as well as for obtention of residency card).

In accordance with citizenship opening wider employment opportunities, Fougere and Sa (2009) nd higher employment probabilities for naturalized immigrants.

3 Data and Methodology

The main dataset I use is the panel from the Déclaration annuelle des données sociales (DADS).

The DADS dataset is a large administrative dataset of matched employer-employee information collected by the Institut National de la Statistique et des Etudes Economiques (INSEE). These data are based upon mandatory employer reports of earnings of each employee subject to French payroll taxes. Thus, they comprise all legally declared employees in French establishments. Among these, the INSEE builds a panel dataset with a randomly selected 1/12th of workers, which can be followed in time. I use this panel dataset in this paper.

15 This duration was brought to 5 years in 2004.

16 This is consistent with studies in other European countries, e.g. [START_REF] Bevelander | Naturalisation and socioeconomic integration: The case of the netherlands[END_REF]; Bevelander and Pendakur (2012).

Denition of Immigrants

For each individual, the dataset records personal characteristics -gender, age, year of entry in the labor force -job characteristics, including occupation type, net annual earnings, and the employer, including the location, industry and size of the employing establishment. The panel covers the period 1993-2008. However, the nationality variable, allowing us to identify immigrants and naturalization events, is not recorded in the years 2002 to 2005. In order to have a continuous sample of years, I therefore restrict the analysis to the period 1993-2001. The only exception will concern the study on the eect of naturalization on changes in job contracts (short-term, long-term and temporary contracts), as this variable is only recorded after 2005.

Recorded in the data is the French or foreign nationality of each employee.

I focus on workers

recorded as foreign at some point in the data, i.e. foreign and naturalized individuals.

Note that in France, jus soli implies that individuals born of foreign parents in France can acquire French nationality, by right, at 18. Thus, I consider very few such cases, as I focus on working individuals, (less than 0.5% of observations under 18). This study is thus essentially about rst-generation immigrants.

One issue with this variable is that it is not always well recorded by employers, as it is an information required in the forms but not relevant for the computation of employer contributions.

The presence of inconsistencies in the panel dataset e.g., people recorded as switching from foreigner to national several times is a sign of measurement error. This is particularly an issue for the identication of naturalization events.

I address this issue by eliminating all series of the variable nationality which seem suspicious: whenever an individual is observed switching from French to foreigner, I get rid of the data series for this individual. Although there may be occurrences of individuals changing nationality in this direction, I expect that a number of these cases are due either to misrecording (i.e., an individual incorrectly recorded as French, then later correctly as foreign), or to individuals having double nationalities, and being recorded alternatively as one or the other. This also eliminates all cases of multiple switching.

18

An additional issue with this variable is that I do not observe individuals with the nationality of a European union (EU) member country. This is an issue as one expects an EU nationality to entail much less constraints on the labor market as a non-EU one.

19 My approach is the following.

22

In some results, I will also make use of the ner classication of occupations (2-digit CSP code) provided in the data. For example, the blue-collar low-skilled category breaks down into qualied/non-qualied workers in industrial/craftmanship sector; drivers; transportation workers; and agricultural workers.

Main employment

The DADS data contains information on every (legal) employment for each worker. Many workers thus appear to have several positions in a given year, either because they changed employment during the year, or because they held several positions simultaneously. In the empirical analysis I retain only one position per worker and year, denoted the worker's main employment. This position

The Empirical Methodology

Naturalization and mobility I rst investigate the link between naturalization and mobility -i.e., the propensity to change occupation, employer, location, or sector. Table 1 suggests that such a link exists. I test whether this link still holds when controlling for worker characteristics, by tting the following logit model by maximum likelihood :

P [mobility it ] = F (α.F oreign it + γ.N at it + β.X it + δ t ), (1)
where F (z) = e z 1+e z is the cumulative logistic distribution. P [mobility it ] is the probability that individual i changes occupation, employer, location... between year t and t + 1.24 F oreign it is an indicator of foreign citizenship, and N at it equals 1 in the year of naturalization. Thus the model estimates whether the propensity to change is dierent in the year an individual acquires French citizenship, relative to the mobility level of naturalized workers. X it denotes a set of controls, which will include age and age squared, and indicator variables for the region (of work), occupational category, and sector of employment. δ t denotes year xed-eects, to control for the time shocks to employment mobility. In addition, I also include variables N at i,t-1 and N at i,t+1 as regressors in order to test whether the eect is also observed one year before/after naturalization.

Naturalization and wages To capture the eect of citizenship acquisition on annual wages, I use a baseline wage equation of the type:

ln w it = α.CT Z it + β.X it + δ t + δ i + ξ it , (2)
with w it the hourly wage of worker i in her main employed position in year t. CT Z it is a binary indicator of French citizenship.

25 Thus, coecient α measures the average dierence between postand pre-naturalization log wages for a given worker, controlling for individual characteristics and the variables in X it . X it is a vector of controls, which include experience (number of years since rst entry in the labor force in France), tenure (number of years spent in the same rm), and their squares. δ t denote year xed eects. δ i is the individual time-invariant component of the error term, and ξ it an idiosyncratic disturbance.

Identication of α in this equation relies on the assumption that the acquisition of French citizenship is correlated with constant individual characteristics, but not with time-varying, individual unobserved determinants of wages. This may not be true if, for example, naturalized workers have a dierent pattern of human capital accumulation. One would then expect to measure a dierent time trend for wages of naturalized workers, even before naturalization takes place. This concern will be addressed in the robustness checks section, in particular by adding to the above model interactions between experience and indicator variables for workers who eventually naturalize.

Results show that the wage eects of naturalization vary across occupation groups. For this reason, the model will be estimated separately by occupation, grouping workers by their initial occupation in the data.

26

Next, I will decompose the impact of naturalization, by distinguishing cases where citizenship acquisition is accompanied by mobility, i.e. a change of occupation and/or of employer. This is done with the following specication: 4 Empirical Results

ln w it = α mob .CT Z it .D mob i + α nomob .CT Z it .D nomob i + β.X it + δ t + δ i + ξ it , (3)

The Impact of Naturalization on Mobility

First, I document the fact that naturalization coincides, for many individuals, with mobility along several dimensions: the probability of moving to a dierent employer and type of job (occupation), as well as changing contract type, and location, is much higher in the year of naturalization, than at any other time.

In table 3, I use the specication shown in equation 1 to test for the link between naturalization and mobility, which was suggested in table 1. Results conrm that the mobility of immigrant workers is higher in the year of naturalization. For example, the odds of changing occupation are multiplied by 2.9 for foreign men in the year of naturalization.

26 Alternatively one may estimate a model with all workers and interaction terms to allow for dierent impacts.

The method here is preferred as it allows for the impact of control variables, e.g. experience and tenure, to also vary across occupations.

The probability to move to a dierent rm, occupation, or sector, increases in the same year that naturalization occurs; the eects on year earlier or later are much smaller or non signicant. This is consistent with naturalization facilitating mobility, rather than the other way around. If, for example, employment changes were decided to increase one's chance of obtaining citizenship, then we should expect to nd most of the mobility eect appear on the Naturalization t -1 variable.

More generally, one could think that citizenship acquisition is a decision which is part of a broader change undertaken by an individual, possibly involving a change of job, location, etc. But if this were solely the result of an individual decision, then there would be no reason to wait for the naturalization to occur before these other changes. One would then expect to nd job mobility preceding naturalization, especially given the delay between the rst demand and obtention of the nationality, which in France is often of two years or more. Instead, these results suggest that obtaining the nationality is what makes professional mobility possible.

The eect is not due to a correlation with age, which the model controls for. Nor is it explained by the fact that those naturalizing have particular types of occupation, location, or sector employment, which would be associated with higher mobility: including indicator variables for year, region, sector and occupation in these regressions rules out this possibility.

Next, I look at this mobility eect across occupation groups. As we have just seen that occupation changes, in particular, were higher when naturalizing, a natural question is whether this eect concerns foreign workers in all occupation groups, and in which direction these changes occurs.

In table 4, I split the sample into groups by occupation, i.e. the initial occupation of each foreign worker in the sample, and estimates the probability of moving to a dierent occupation.

The naturalization eect on mobility is detected in all groups (except for women in high-skill occupations). However, one notes that this eect is stronger in the low-skilled than the highskilled occupations. For instance, the odds of changing occupation are multiplied by more than 3 in the year of naturalization, for foreign men in low-skilled blue-collar jobs; for those in high-skilled positions, the factor is less than 2.

Finally, in table 5, I look at employer mobility across occupation groups. The pattern found here is the opposite: mobility is signicantly higher at naturalization, for all groups of workers (except women in low-skilled blue-collar occupations); but the eect tends to increase when moving up the skill level of jobs. The employer mobility eect is larger for workers initially in middle-and high-skilled occupation groups, than for those in low-skilled ones.

Taken together, these results suggest that the incidence of foreign citizenship on employment Results in line 1 of tables 6 and 7 show that the overall eect of naturalizations (citizenship) on wages is limited: the only signicant impact is found for women initially in middle-skilled occupations.

In the lower parts of the tables, I then decompose the citizenship variable according to the mobility pattern at the time of naturalization, using the model of equation ( 3). This allows to measure dierent eects of citizenship depending on the mobility behavior in the year of naturalization. I distinguish up to three cases: occupation change, same occupation but employer change, and same occupation and employer.

This reveals the presence of wage gains conditional on some specic mobility patterns. Namely, there is a signicant citizenship premium, of about 8%, for men in low-skill white-collar occupations, when naturalization coincides with occupational mobility. Note that this eect does not hold when including occupation xed-eects, indicating that the wage increase is entirely explained by average pay dierences between occupation classes. In addition, there is indication of a wage gain for men in high-skill occupations, of about 4%, under the condition of no occupation, and no employer mobility at the time of naturalization.

In the case of women, the decomposition also reveals the presence of a wage premium conditional on some mobility patterns. Women in middle-skilled occupations benet from a naturalization premium when they move to a dierent employing rm at the time of naturalization. The gain is substantial (about 14%). A similar eect is found for women in high-skill occupations, of even larger amplitude. Note that such large eects are obtained by focusing on individuals most likely to obtain a pay rise, which thus yields larger coecients than in overall estimates without decomposition.

These results reveal the extent of heterogeneity in the wage eects of citizenship, and the need to account for this heterogeneity in measuring them. Dierences across occupation groups appear to be important in the citizenship eect on wages, yet they are not taken into account in previous studies. Neither is the link between the impact on mobility and wages accounted for. The results here suggest that this may partly explain the small eects measured in some cases (e.g. [START_REF] Scott | The economics of citizenship: is there a naturalization eect? The economics of citizenship[END_REF]; [START_REF] Engdahl | the impact of naturalisation on labour market outcomes in sweden. Naturalisation: A Passport for the Better Integration of Immigrants[END_REF]): if the impacts on wages and on employment mobility are tied together, then measuring the wage eect alone may fail to detect a signicant eect.

These results suggest several potential mechanisms. The pattern for low-skilled occupations is consistent with a mismatch between some foreign workers and their employment: the immediate mobility response, in the naturalization year, suggests that foreign citizenship is what prevented those workers from moving up to higher-qualied occupations before. This upward mobility is associated with a wage gain, which is largely explained by the average wage levels of their initial and nal occupations (so that including occupation xed-eects makes the coecient non signicant).

The gains found for women in higher-skilled occupations suggests a second, distinct mechanism by which foreign citizenship constrains mobility and wages. One possibility is that this pattern could be due to barriers specic to some jobs -e.g., some of the public or private sector activities restricted to nationals (see section 2). Other forms of discrimination may be at work. Robustness checks First, I test whether the measured eect on wages actually follows naturalization, or precedes it. One would expect to nd an anticipated eect, if for example, a decision to settle permanently in the country and to assimilate leads to wage growth and, eventually, to naturalization. Results on mobility, in the previous section, have already given an indication on this, by showing that the increase in the propensity to change employment as mostly taking place in the year of naturalization and not earlier. Since we found that the wage premium was tied to mobility, it seems likely that the wage eect should not precede naturalization either.

In table 8, I use the same model as before, testing whether a worker's hourly wage is higher after s/he has naturalized; this variable Citizenship is interacted with an indicator for occupational mobility (change in 1-digit occupation class) at the time of naturalization. In addition, I include a variable Citizenship (t-3) which switches to one 3 years before naturalization. This variable is similarly interacted with the same indicator of occupational mobility at the time of naturalization.

The previous results are mostly unaected. As before, a signicant wage premium is found for men in the low-skilled white-collar group, associated with occupational mobility; and for women in the middle-and high-skilled groups, associated with no change of occupation. There is no sign of these eects starting before naturalization.

27

This is further conrmed when one excludes all observations after naturalization has occurred (keeping only workers when still foreign), which is done in the columns 5 to 8 of the table: there is no sign of a signicant wage hike preceding naturalization.

Second, the issue of selection is addressed more broadly. In general one may suspect that individuals who naturalize at some point have faster wage growth, for instance because they accumulate more country-specic human capital, even before naturalization occurs. I test for this in tables 9 and 10, where 3 models of increasing exibility are estimated. I rst add to the model interaction terms of experience (and its square) with individual indicators for those individuals who naturalize at some point (equal to constant 1 also before naturalization). Second, I add the possibility that those who change occupation in the year of naturalization, have faster wage growth;

this is done by adding the interaction of experience with an indicator for individuals who changed occupation in the year of naturalization 28 . Finally, I allow for wage growth to dier also after naturalization (adding a term experience x post-naturalization x indicator for naturalization with occupational change).

27 Similar tests for an eect 4, 2, 1 year before naturalization have been conducted and conrm the results shown here. They are available upon request.

Results conrm the robustness of the previous ndings and clarify the patterns. For men in low-skilled white-collar occupations, the last panel indicates that the wage premium is entirely driven by faster wage growth after naturalization. Allowing for faster wage growth (along the career) for those naturalizing does not aect the coecient previously found (rst panel), but adding the mobility distinction does 29 (second panel).

Thus, for this category of workers, it appears that naturalization has a positive eect on wages mainly through occupation mobility, which delivers a gain in wages through faster wage growth.

For women in middle-skilled occupations, by contrast, results in the third panel indicate that the premium previously found is essentially immediate, as it is captured by the citizenship variable more than by post-naturalization eects on wage growth. This eect is robust to the alternative specications tested.

30

Overall, these tests conrm that the previous results on naturalization wage premia, are not attributable to the selection of naturalization candidates, nor on patterns of assimilation or investment which could start before naturalization takes place.

29 This seems to be due to the experience term capturing part of the post-naturalization wage growth acceleration.

30 The specic eect found for women suggests that the eects of foreign citizenship may be compounded by other factors, e.g. gender-based discrimination, or professional choices within couples; so as to make this eect apparent for women but not for men in similar occupations. Lack of information on e.g. family background in the data prevents us from testing this. 31 Wages of foreign (non naturalized) workers are signicantly lower than those of natives, in most categories of work. Note that this can be attributable both to selection eects -e.g. lower levels of human capital of foreign workers -and/or to various forms of discrimination.

Interestingly, naturalization is associated to little wage gains in Low-skilled occupations. This is consistent with previous results in panel regressions, which indicated that the naturalization premium, in these occupations, was obtained only by those workers who moved to dierent types of work.

By contrast, larger gains are associated to citizenship in Middle-skilled and High-skilled occupations. This is most striking for women in middle-and High-skilled positions. These results are consistent with those in the previous section, but may also be reecting, to some extent, a selection on talent in higher-skill positions.

31 Note that the samples here contain only workers who are still present in the dataset after 2005. This allows to exclude individuals observed with a EU nationality (this variable being available only after 2005). increase sharply in the year of the naturalization. The precise timing of events rule out alternative explanations based on human capital accumulation. In addition, I nd, consistently with previous studies, a substantial wage increase upon naturalization. The magnitude and conditions of this wage increase vary across job types. Among men initially employed in low-skill occupations, there is a wage increase conditional on occupational mobility. The premium is of the order of 8% in permanent terms, and is driven by faster wage growth (of about 3% per year) after naturalization.

In addition, there is evidence of a premium for women in middle-and high-skilled occupations.

This eect is larger (about 0.13%), immediate, and most pronounced for workers changing employer at the time of naturalization. These eects are not explained by selection patterns, nor by dierences in wage trajectories before naturalization. Overall, there results conrm that foreign citizenship acts as a barrier to mobility on the labor market. They establish the link between such barriers and the wage premium associated with naturalization. Several mechanisms could be at work to create a mismatch between foreign workers and their job.

  of value 1 if individual i naturalized and changed occupation in the same year (D mob i ), or naturalized but without occupational change (D nomob i ). One has CT Z it .D mob i + CT Z it .D nomob i = CT Z it for all individuals i in the sample.

  Impact of Naturalization on WagesI now look at the relationship between citizenship and wages. I ask whether a wage gain from naturalization appears in France, as is the case in several countries studied in previous studies. I also want to ask whether this potential wage gain is linked to the mobility patterns -changes of occupation, of rm -identied in the previous section. To this purpose, I use panel regressions with individual xed-eects, on the sample of foreign-born workers in France; the model used is the one described in equation 2.

  -skilled, MS: low-skilled, LSW/B: low-skilled blue/white-collar. See text for denition of occupational categories. 31 This paper has studied the impact of naturalizations on the labor market outcomes of immigrants in France. I use of a large, representative longitudinal database of employees in France over 1993-2008, constructed from social security records, to study the impact of citizenship acquisitions on job characteristics and on wages. The longitudinal dimension allows to disentangle causal impacts of citizenship from selection eects. I nd that naturalizations are associated to a large increase in mobility: the probabilities to change occupations ; employing rm; contract type, and location, all

Table 1 :

 1 Mobility rates: changing employer, contract type, location

	Status	Foreigner	Naturalization	Citizen
	Changing employer
	Staying with same employer	113,632	3,668	20,707
	Changing employer	27,208	2,959	4,631
	P[changing](%)	19.3	44.6	18.3
	Changing occupation (1-digit)
	Same occ.	128,709	5,113	22,311
	Changed occ.	10,842	1,347	2,634
	P[changing] (%)	7.8	20.9	10.6
	Changing location ( département)
	Same dept	128,280	5,206	23,258
	Changed dept.	12,536	1,418	2,077
	P[changing] (%)	8.9	21.4	8.2
	Changing sector of employment
	Same sector	119,723	4,210	21,558
	changing	21,015	2,413	3,761
	P[changing](%)	14.9	36.4	14.8
	Entering public sector
	No	139,981	6,476	25,138
	Yes	479	127	161
	P[enter](%)	0.3	1.9	0.6
	Changing labor contract (2006-2008)
	Same contract	112,238	10,394	39,186
	changing contract	20,478	3,461	3,386
	P[changing](%)	15.43	25.0	7.9

Source: panel DADS

  note that the average length of sojourn in France prior to naturaliza-

	tion is approximately 17 years, much longer than in Canada or the US. The rate of naturalized
	foreign-born was 75% in the 1996 Canadian census, compared to 40% in France.
	As is the case in other immigration countries, a number of jobs are restricted to nationals,
	mostly in the public sector.	12 A report from the Haut Conseil à l'Intégration indicated in 1998
	that the stock of jobs available to non-European foreigners is reduced by 23% (Haut conseil à

l

'Intégration, 1998)

. Groupe d'Etude sur les

Discriminations (2000)

nds a gure of 30%, showing that, in addition to public servant positions being restricted to nationals (or EU nationals), successive legislation has created restrictions in numerous private sector professions.

  Information on EU nationality is actually recorded in the most recent years of the data, after 2005, which I am not using for the analysis (I focus on the 1993-2001 period, oering a longer time horizon). Therefore, in the 1993-2001 data I use, I get rid of individuals observed later -after 2005

	-as EU nationals.	20
	Finally, the dataset is formed of individuals who have been recorded as foreigners at some point
	in the data. This is because I am mainly interested in observing the impact of naturalization in
	time: therefore, I compare workers who naturalize with those who remain non-citizens.
	3.2 Occupation variables

I consider four main categories of occupation:

21 Blue-collar low-skilled workers, i.e. manual occupa- tions; White-collar low-skilled workers, including commercial employees, personal service workers, oce employees in public and private sector. Middle-skilled professions; including intermediary ofce workers in private and public sectors, technical workers, foremen; and high-skilled professions, including lawyers, health, professionals, public sector managing personnel, scientists, engineers and technical managers.

  20 In average, 60% of individuals present in the data over 1993-2001 are still being observed after 2005.21 These are based on the 1-digit classication of catégories socio-professionnelles dened by the INSEE and pro- the one with the most recorded worked days in the year; if there are several such positions, I select the one with most hours; and nally, the one with highest pay, if there still remain several Table2documents the distribution of the main variables of interest and controls, for the sample of foreign-born workers. Note that low-skilled occupations represent the large majority of positions held by foreign-born workers. For comparison, the lower panel displays the distribution of occupations among native workers, (i.e. excluding foreigners and naturalized individuals), this data being used in the last section of the empirical exercise. Shares of natives employed in low-skilled blue-collar positions are much lower than among foreign-born, in particular for women.

	candidates.	23
	3.4 Descriptive statistics
	vided in the data. See http://www.insee.fr/fr/methodes/default.asp?page=nomenclatures/pcs2003/pcs2003.htm
	for details.
	The category of managers and CEOs will not be considered. It represents less than 2% of the observations in the
	sample of immigrants used here.

is 23 I also eliminate observations with less than 50 or more than 2500 hours worked per year. The maximum of 2500 hours is a correction applied by INSEE.

Table 2 :

 2 Descriptive statistics

	Foreign-born	Men		Women
		Mean	SD	Mean	SD
	Age	40.9	11.2	39.1	11.3
	Experience	11.8	8.2	8.9	7.7
	Tenure	4.9	6.7	3.7	5.2
	Occupation categories	Men		Women
		N	%	N	%
	High-skilled	13,831	9.5	5,512	7.5
	Medium-skilled	15,229	10.4	9,128	12.5
	Low-skilled white-collar	20,680	14.1	30,662	41.8
	Low-skilled blue-collar	93,856	64.2	27,558	37.6
	CEOs	2,629	1.8	447	0.6
	Total	146,225	100	73,307	100
	Natives	Men		Women
		N	%	N	%
	High-skilled	281,838	12.5	138,051	7.2
	Medium-skilled	467,086	20.7	449,412	23.4
	Low-skilled white-collar	365,136	16.2	1,039,525	54
	Low-skilled blue-collar	1,106,908	49.1	288,065	14.9
	CEOs	32,913	1.5	8,846	0.5
	Total	2,253,881	100	1,923,899	100
	Sample includes data for 1993-2001. Main employment observa-
	tions. Foreign-born denotes workers recorded at least once as for-
	eign in the data. Note: observations for CEOs are not used in the
	empirical analysis.

Table 3

 3

			: Naturalization and mobility
				(1)	(2)	(3)	(4)
					Probability of changing
			employer	occupation	location	sector
				Panel A: Men
	Naturalization		2.60	2.89	2.56	2.68
				(0.00)	(0.00)	(0.00)	(0.00)
	Naturalization: T-1	1.39	1.80	1.36	1.42
				(0.00)	(0.00)	(0.00)	(0.00)
	Naturalization: T+1	1.14	0.99	1.29	1.13
				(0.05)	(0.87)	(0.01)	(0.14)
	Foreign			1.42	0.70	1.30	1.09
				(0.00)	(0.00)	(0.00)	(0.10)
	Baseline odds		.18	.05	.07	.08
	Observations		64093	63808	64090	61672
	Pseudo R 2		0.059	0.061	0.078	0.057
				Panel B: Women
	Naturalization		2.71	2.44	2.33	2.77
				(0.00)	(0.00)	(0.00)	(0.00)
	Naturalization: T-1	1.12	1.27	1.08	1.26
				(0.13)	(0.01)	(0.46)	(0.01)
	Naturalization: T+1	1.35	1.01	1.46	1.23
				(0.00)	(0.96)	(0.00)	(0.04)
	Foreign			1.50	1.03	1.60	1.17
				(0.00)	(0.64)	(0.00)	(0.01)
	Baseline odds		0.21	0.09	0.09	0.10
	Observations		28666	28447	28636	27639
	Pseudo R 2		0.052	0.036	0.066	0.051
	Fixed eects			Year,region
	Exponentiated coecients. Standard errors in parentheses
	c p<0.1,	b p<0.05,	a p<0.01
	Logit model on probability of mobility between year t and t+1, table displays odds
	ratios. Sample: DADS data, foreign-born workers, 1993-2001. Baseline odds are
	computed as the median predicted value ( p/(1-p)) among foreign, non naturalizing

workers. Model includes age, age squared as controls. Observations with missing information on employment in the following year are dropped from the sample. Naturalization equals 1 in t for a worker who is foreign in t and French in t+1. 1-digit occupation has four categories: High-skilled, middle-skilled, low-skilled white/bluecollar. Location: région of employment. Sector: NES classication. See section 3 for details on occupational categories. 18 workers. Model includes age, age squared as controls. Sample in each column includes all foreign workers rst observed in a given occupation, e.g. low-skilled blue-collar for column 1. Workers are classied by rst observed occupation category. Variable denitions as in table 3.

Table 5

 5

		: Employer mobility
		(1)	(2)	(3)	(4)
		Probability of changing employer
	Occupation	LS blue collar	LS white collar	Med-skill	High-Skill
		Men
	Naturalization	1.60	1.41	2.61	2.03
		(0.00)	(0.02)	(0.00)	(0.00)
	Naturalization: T-1	1.06	1.18	1.44	1.80
		(0.51)	(0.42)	(0.10)	(0.01)
	Naturalization: T+1	1.32	0.69	1.04	0.73
		(0.02)	(0.15)	(0.85)	(0.23)
	Foreign	1.58	1.14	0.81	0.68
		(0.00)	(0.33)	(0.13)	(0.01)
	Baseline odds	0.10	0.10	0.06	0.08
	Observations	44357	7958	6247	5455
	Pseudo R 2	0.021	0.024	0.027	0.033
		Women
	Naturalization	1.19	1.84	1.70	3.21
		(0.13)	(0.00)	(0.01)	(0.00)
	Naturalization: T-1	0.81	0.85	1.41	1.51
		(0.23)	(0.32)	(0.22)	(0.37)
	Naturalization: T+1	1.32	1.37	1.44	1.01
		(0.21)	(0.05)	(0.22)	(0.98)
	Foreign	2.22	1.20	1.18	0.59
		(0.00)	(0.08)	(0.43)	(0.04)
	Observations	11624	12197	3065	1640
	Pseudo R 2	0.025	0.034	0.049	0.060
	Baseline odds	0.16	0.08	0.08	0.08
	Fixed eects		Year,region
	Exponentiated coecients. p -values in parentheses
	Logit model on probability of changing occupation (1-digit csp category) between year t and
	t+1, table displays odds ratios. Sample: foreign-born workers, 1993-2001. Baseline odds
	are computed as the median predicted value ( p/(1 -p)) among foreign, non naturalizing
	workers. Model includes age, age squared as controls. Sample in each column includes all

foreign workers rst observed in a given occupation, e.g. low-skilled blue-collar for column 1. Workers are classied by rst observed occupation category. Variable denitions as in table 3.

Table 6 :

 6 Naturalization and wages (Men, 1993-2001)

	log hourly wage

equals 1 for individuals changing employer (rm) in the same year as naturalization, without changing occupation. Model includes year xed-eects, experience, tenure and their squares. HS= High-skilled occupations, MS: middle-skilled, LSW/B: lowskilled white/blue-collar occupations. See text for denitions of occupational categories.

Table 7 :

 7 Naturalization and wages (Women, 1993-2001)

	log hourly wage

Table 8 :

 8 Naturalization and wages: t vs. t -3

	log hourly wage

Table 9 :

 9 Naturalization and wages: selection and wage dynamics -Men

	log hourly wage

ralized, nat'd w/ mobility. (Post-nat experience x mobility): years since naturalization * dummy for occupational change in the naturalization year.

Table 10 :

 10 Naturalization and wages: selection wand wage dynamics -Women Comparing the wages of foreign-born and native workers I now turn to specications including natives. Do the wage gains from naturalization, found in the previous section, reect a catching-up of foreign wages to natives' ? Does naturalization partly or fully close the foreign-native wage gap? This is the question here.it are indicator variables for the four categories of occupation: High-skilled, Medium- skilled, and Low-skilled blue/white-collar. F oreign it indicates a foreign-born worker, and N at it a naturalized worker (for whom F oreign is still one). X it are controls, including age, experience, tenure, and their squares.Coecient α o measures the wage gap between foreign and native workers, in occupation o. The wage level of naturalized workers, relative to natives, is given by α o + β o . Note that I cannot use xed-eects to control for individual heterogeneity anymore (as such heterogeneity would encompass nationality). Thus, these measurements are inuenced by selection, e.g. dierences in human capital, between foreigners and citizens.Results are displayed in table 11.

			log hourly wage
	Occupation	LSB	LSW	MS	HS
	Ctz. x mobility	0.02	0.04	0.02	-0.34
		(0.63)	(0.18)	(0.75)	(0.08)
	Ctz. x	-0.01	0.01	0.17	0.27
	empl. mob	(0.65)	(0.55)	(0.04)	(0.01)
	Ctz. x	0.04	-0.00	0.07	0.00
	no empl. mob.	(0.00)	(0.74)	(0.10)	(0.98)
	Expce x	-0.01	0.01	-0.01	-0.00
	naturalized	(0.15)	(0.34)	(0.71)	(0.97)
	Ctz. x	0.05	0.02	-0.05	-0.25
	occ. mobility	(0.30)	(0.55)	(0.60)	(0.17)
	Ctz. x	0.02	0.00	0.12	0.05
	no occ. mobility	(0.28)	(0.87)	(0.00)	(0.28)
	Expce. x	-0.00	0.00	-0.01	0.02
	naturalized	(0.44)	(0.59)	(0.66)	(0.34)
	Expce. x	-0.01	0.01	0.00	-0.10
	mobility nat'd	(0.20)	(0.25)	(0.93)	(0.04)
	Ctz. x	0.05	0.01	-0.06	-0.20
	occ. mobility	(0.34)	(0.83)	(0.53)	(0.33)
	Ctz. x	0.02	0.00	0.12	0.05
	no occ. mobility	(0.15)	(0.93)	(0.00)	(0.29)
	Expce. x	-0.00	0.00	-0.02	0.01
	nat'd	(0.93)	(0.67)	(0.02)	(0.40)
	Expce. x	-0.02	-0.01	0.02	-0.01
	mobility x nat'd	(0.03)	(0.60)	(0.34)	(0.55)
	Post-nat expce x	0.00	0.02	0.03	-0.05
	mobility	(0.70)	(0.10)	(0.35)	(0.17)
	Post-nat expce x	-0.01	0.00	0.01	0.00
	no mobility	(0.30)	(0.77)	(0.26)	(0.79)
	Observations	18834	19459	4686	3022
	p -values in parentheses. Standard errors clustered at individual
	(worker) level.
	See table 9 for description of variables.
			29

Table 11 :

 11 Wages: foreign-born vs. natives (1993Wages: foreign-born vs. natives ( -2001) )

					log hourly wage
				Men				Women
	Foreign-born x HS	-0.046	a	-0.033	a	0.003	-0.065 a
		(0.006)	(0.005)	(0.008)	(0.008)
	Naturalized x HS	0.071 a	0.055	a	0.142	a	0.149	a
		(0.011)	(0.010)	(0.016)	(0.015)
	Foreign-born x MS	-0.069 a	-0.054	a	-0.007	-0.048 a
		(0.005)	(0.005)	(0.006)	(0.006)
	Naturalized x MS	0.040 a	0.022	b	0.023	b	0.019	c
		(0.010)	(0.009)	(0.011)	(0.011)
	Foreign-born x LSW	-0.133	a	-0.094	a	-0.023	a	-0.040	a
		(0.004)	(0.004)	(0.003)	(0.003)
	Naturalized x LSW	0.033	a	0.002	0.011	-0.007
		(0.010)	(0.010)	(0.007)	(0.007)
	Foreign-born x LSB	-0.024	a	-0.066	a	-0.018	a	-0.032	a
		(0.002)	(0.002)	(0.003)	(0.004)
	Naturalized x LSB	-0.005	0.014 b	-0.003	0.008
		(0.006)	(0.006)	(0.011)	(0.011)
	Fixed eects				Occupation, year
	Firm f.e.				yes					yes
	Observations	2206449	2206449	1848775	1848775
	R 2	0.449	0.342	0.310	0.218
	Standard errors in parentheses

As individuals born in France to foreign parents become French at 18, very few such cases are considered here (less than 0.5% observations at age under 18). This study is thus essentially about naturalizations of workers born abroad, i.e. about rst-generation, not second-generation immigrants.

In addition, I also conduct robustness checks to verify that the wage premium is not taking place in the years preceding naturalization.

Classication of occupation is based on the original categories socio-professionnelles available in the data, and is described in detail in the data section. Medium-and high-skilled occupations referred to here include intermediary oce workers , technical workers, managers and executives.

Note however, that the eects measured could still be specic to those applying for citizenship, or to those whose demand is accepted. I cannot estimate how much the measured eect could be extended if, for instance, naturalization was made easier.

Panel estimates with xed eects allow to control for constant, unobserved individual characteristics inuencing both the probability to naturalize and labor market outcomes. However, another possible source of bias lies in the fact that naturalization reects a longer-term commitment to stay in the host country, so that those willing to naturalize may be accumulating more country-specic human capital, even before naturalization. This can result in higher wage growth for them. This is discussed in section 3.5 below.

The data do not allow to distinguish between these cases; I only observe changes in nationality as reported by an individual's employer, and refer to all such occurrences as naturalizations, after cleaning of the data as detailed below. Note however that children born in France obtain citizenship by declaration when reaching age 18, thus most of these cases are excluded of the analysis as I use data for employed people, mostly older: people between 16 and 18 account for less than 0.5% of the estimation sample.

Note that this variable does not allow to identify immigrants in the commonly admitted denition of the term, i.e. a person born abroad as a foreigner.

In the regressions of table 1, where the indicator variable for the naturalization year is used, observations with an ambiguity for citizenship in the year t + 1 are also eliminated.

First, EU nationals do not face any restriction to stay and work in France, and are not required to hold a permit. Second, a number of professions are open to EU country nationals.

[START_REF] Caliendo | The Anatomy of French Production Hierarchies[END_REF] use the same dataset, and argue that this classication of occupations is hierarchical, in the sense that wage distributions are ranked, and that numbers of workers per layer in a rm decrease when going up. Their category clerks is called white-collar low-skilled here, supervisors are my middle-skilled and senior sta my high-skilled.

The alternative is no change between t and t + 1: individuals whose occupation, employer or location is missing in t + 1 are removed from the estimation sample.

Data cleaning procedures, detailed in section 3, imply that a change in CT Z it can occur at most one time per individual, and always from 0 to 1.

Thus, the dummy naturalized, equal to constant 1 for individuals who ever naturalize, is equal to the sum of the two indicators naturalized with mobility and naturalized without mobility. The case without mobility is the omitted category here.

is present across occupation classes. Results on occupational mobility are consistent with skill mismatch, by some foreign workers are constrained to take jobs below their qualication. But workers in higher-skill jobs also seem to face some type of mismatch, as naturalization creates an opportunity to move to dierent jobs.

Whether these two types of mobility are associated with a wage increase is the question we turn to in the next section.


domain: chim sde

text:
Catherine Berho

Samuel Robert

Christian Garriou

Jean Philippe Ghestem

Thierry Laurioux

Laurence Amalric

Auguste Bruchet

An experimental system representative of groundwater hydraulic conditions to test the applicability of diffusive gradients in thin film (DGT) for groundwater monitoring

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

An experimental system representative of groundwater hydraulic conditions to test the applicability of diffusive gradients in thin film (DGT) for groundwater monitoring

Catherine Berho 1, Samuel Robert 2 , Christian Garriou 2 , Jean -Philippe Ghestem 1 , Thierry Laurioux 1 ; Laurence Amalric The validated common approach of groundwater monitoring is based on spot sampling after purging followed by laboratory analysis but has well known drawbacks (modification of contaminant distribution between the whole aquifer and groundwater sampled by pumping homogenization of the water column which can hide a potential stratification of contaminants ...). Passive sampling techniques present several advantages by comparison to the classical sampling approach (they neither need pumping, nor disturb the groundwater). However, few publications deal with the use of integrative passive samplers in groundwater.

In this context, the aim of this work is to test the applicability of diffusive gradients in thin film (DGT) for metal monitoring in groundwater (Pb, Cd). Indeed, a diffusive boundary layer (DBL)

forming on DGT surface especially in case of low flow conditions influences the uptake of metals. First of all, an experimental system representative of groundwater hydraulic conditions was developed. The system is composed of three open columns with an ascendant water circulation of a natural groundwater spiked with the targeted compounds (Cd, Pb). The flow is respectively in each column of 1, 2 and 4 m/day. DGT with several diffusive gels thicknesses were deployed in triplicates during 7, 14 and 21 days in each column. During the experiments, the concentration of metals in water and the uptake of compounds were followed to verify the linear accumulation with time. The DBL was estimated at 13 & 21 days of duration as well as the time weighted average concentrations (TWA). DBL values higher than those found in literature were found. By taking them into account, TWA concentrations were found closed to concentration of Pb and Cd measured in water samples.

We acknowledge financial support from French National Research Agency (ANR ECOTECH 2011 ORIGAMI project 11 ECOT 003)