S T Éphane Cordier

Carine Lucas
email: carine.lucas@univ-orleans.fr

Jean De Dieu Zabsonr

A TWO TIME-SCALE MODEL FOR TIDAL BED-LOAD TRANSPORT †

Keywords: Shallow-Water Equations, bed-load transport, Exner equation, asymptotic developments, non-dimensional form, limit model, finite volumes scheme. subject classifications. 34E13, 74S10, 65M06

The aim of this article is to derive a simplified sedimentation model thanks to an asymptotic analysis. We consider a two time scale erosion process due to tidal effects and we show that the approximation at the first order can model bed-load transport well. To this end, the simplified model is validated through numerical tests (evolution of a dune submitted to tidal effects in the ocean, run up near the coast) and compared to direct simulations that are very expensive in terms of computation time.

Introduction

Developments in modeling and simulating bed-load transport are crucial to improve the prediction of water flow. Erosion phenomena such as transport or sedimentation can have a great impact on everyday life; one can cite mudslides due to rainfalls for example. Erosion is not only due to rain but it is also related to the oceans. Let us mention, e.g., scientific studies aim at limiting disappearance of sand weakening coastal installations; see [START_REF] Azerad | Shape optimization of geotextile tubes for sandy beach protection[END_REF][START_REF] Bouharguane | Minimization principles for the evolution of a soft sea bed interacting with a shallow sea[END_REF]. Coastal erosion is linked to water flow, and to tides that increase the movements of the sea twice a day.

In this article, we consider models for the evolution of the topography in oceans, i.e. in shallow water submitted to tidal effects. More precisely, we study a Exner type equation for bed-load transport [START_REF] Exner | Uber die wechselwirkung zwischen wasser und geschiebe in flussen[END_REF] coupled with Shallow-Water Equations. Several works have been done on such models; see for example [START_REF] Meyer-Peter | Formulas for bed-load transport[END_REF][START_REF] Van-Rijn | Sediment transport, Part 1: Bed load transport[END_REF] for modeling issues and common empirical laws for the sediment discharge, [START_REF] Hulscher | Formation and Migration of Large-Scale, Rhythmic Sea-Bed Patterns: A Stability Approach[END_REF][START_REF] Roos | Seabed Pattern Dynamics and Offshore Sand Extraction[END_REF][START_REF] Schuttelaars | Evolution and Stability Analysis of Bottom Patterns in Tidal Embayements[END_REF] for stability analyses, or [START_REF] Faye | Singularly perturbed degenerated parabolic equations and application to seabed morphodynamics in tided environment[END_REF] for recent existence results.

The idea of the present work is to perform a multi-scale analysis in time for Shallow-Water Exner Equations and get a simplified system of equations satisfied by the first order approximation of our unknowns. We choose one of the simplest empirical expressions for the sediment discharge in the Exner Equation, namely the Grass model, since our goal is not to study the most complete model but to prove the validity of the proposed approach i.e. that a simplified model derived from multiscale analysis can give qualitatively and quantitatively good approximations. This limit model is compared to the "reference solution", given by a finite volume scheme for the full model (which can be very intricate and computationally expensive); see [START_REF] Castro | Sediment transport models in Shallow Water[END_REF]. The comparison between the two models shows that the solutions of the simplified model are rather accurate approximations of the reference solutions.

More precisely, the outline of the paper is the following: in Section 2, we explain the derivation of the equations. We start from Shallow-Water Equations that model the evolution of the fluid, and the classical Exner Equation for the evolution of the topography with Grass discharge. Then we introduce non-dimensional variables and parameters to get the scaled equations on which we perform the asymptotic analysis. The new simplified model is obtained by combining the first order terms of the asymptotic expansions. In section 3, we explain the numerical methods used for the complete model and we compare the solutions of the two models. The first test case is a dune, initially at rest, whose shape oscillates with the tides. We also consider a beach test, that is a rectangular dune on an inclined plane. In order to validate the model, we study the numerical convergence of the limit model towards the complete model as the small parameter tends to zero. We complete this work with some tests on the numerical diffusion of the two models.

Derivation of the model

We begin our study with the derivation of the model: we consider the Shallow-Water Equations coupled with the Exner Equation for the evolution of the bed. We introduce non-dimensional variables in order to make an asymptotic analysis and obtain an approximate solution of the complete model.

Equations for bed-load transport

The first point is to write equations modelling the transport of sediments, in a shallow domain. Usually, the SWE are coupled with a transport equation on the sediment height. More precisely, we can define the following variables (see Figure 2.1): With these notations, the Shallow-Water Equations (SWE) are given by:

0 sediment water u(t, x) x = (x 1 , x 2 ) ζ(t, x) z h b (t, x) -H
∂ t (ζ -h b ) + div((ζ + H -h b )u) = 0, (2.1a) ∂ t ((ζ + H -h b )u) + div((ζ + H -h b )u ⊗ u)+ g(ζ + H -h b )∇ζ + f (ζ + H -h b )u ⊥ = -ku, (2.1b)
where g is the gravity, f the Coriolis term, k the friction coefficient, and u ⊥ = t (-u 2 u 1 ) if u 1 and u 2 are the two components of the water velocity field u. SWE (2.1) are coupled with an equation that describes the bed-load evolution. For the sediment transport, several empirical formulations of the classical Exner equation [START_REF] Exner | Uber die wechselwirkung zwischen wasser und geschiebe in flussen[END_REF] are given in the literature, depending on the sediment properties (see for example [START_REF] Soulsby | Dynamics of Marine Sands: A Manual for Practical Applications[END_REF] and a review paper in preparation [START_REF] Le | A review of physically based modeling of soil erosion by water[END_REF]). Let us only mention the Van Rijn [START_REF] Van-Rijn | Sediment transport, Part 1: Bed load transport[END_REF] and Meyer-Peter and Müller [START_REF] Meyer-Peter | Formulas for bed-load transport[END_REF] formulations for example. In this paper, for the sake of simplicity as explained in the introduction, we choose one of the simplest expression, namely the Grass model [START_REF] Grass | Sediment transport by waves and currents[END_REF]:

∂ t h b + Adiv(u 3 ) = 0, (2.2)
where A is a coefficient given by the sediment characteristics (usually small).

In the following, our objective is to study the coupling between Equations (2.1) and (2.2).

Choice of the scalings: non-dimensional quantities

As we consider a domain such as an ocean, we have to take into account tidal effects. Then two length scales coexist, namely L (the tidal wave length) and l (the tidal excursion length). If σ denotes the tidal frequency and U the tidal current amplitude, we have l = U/σ. We introduce non-dimensional variables, with a prime, given by:

u = U u ′ , t = t ′ σ , x = lx ′ , h b = Hh ′ b , ζ = U Lσ g ζ ′ .
The scaling on ζ is linked to the typical momentum balance for a tidal wave.

We can introduce the small parameter δ, which is the ratio between l and L (δ ≈ 10 -3 ). This parameter δ can also be written as δ = U/(σL), which means, considering the dispersion relation Lσ = √ gH, that the scaling on ζ reads:

ζ = δHζ ′ , with δ = l L = U σL .
Finally, we define the non-dimensional parameters

A ′ = AU 3 lσH , f ′ = f σ , k ′ = k Hσ
to simplify the writing of the equations.

Non-dimensional equations

We replace the previous relations in Equations (2.1)-(2.2); dropping the primes, we get the following non-dimensional relations:

δ∂ t ζ -∂ t h b + δdiv(ζu) + div(u -h b u) = 0, ∂ t (δζ + 1 -h b )u + div (δζ + 1 -h b )u ⊗ u + 1 δ (δζ + 1 -h b )∇ζ + f (δζ + 1 -h b )u ⊥ = -ku, ∂ t h b + Adiv(u 3 ) = 0.
As A is a small parameter (of order of δ 2 ), we can define a new time scale:

τ = At,
and we assume h b to be a function of τ and x only. Then we can rewrite the nondimensional equations as:

δ∂ t ζ + δA∂ τ ζ -A∂ τ h b + δdiv(ζu) + div(u -h b u) = 0, (2.3a)
∂ t (δζ + 1 -h b )u + A∂ τ (δζ + 1 -h b )u + div (δζ + 1 -h b )u ⊗ u + 1 δ (δζ + 1 -h b )∇ζ + f (δζ + 1 -h b )u ⊥ = -ku, (2.3b)
∂ τ h b + div(u 3 ) = 0. (2.3c)
In order to study these relations, we perform an asymptotic development in powers of δ.

Asymptotic development

We decompose our variables in powers of δ:

ζ = ζ 0 + δζ 1 + δ 2 ζ 2 ..., h b = h 0 b + δh 1 b + δ 2 h 2 b ..., u = u 0 + δu 1 + δ 2 u 2 ....
We replace these relations into Equations (2.3) and we identify the powers of δ. At the first order, we find:

div(u 0 -h 0 b u 0 ) = 0, ∇ζ 0 = 0, ∂ τ h 0 b + div u 0 3 = 0,
and at the second order, we get the evolution of u 0 :

∂ t ζ 0 + div(ζ 0 u 0 ) + div(u 1 -h 1 b u 0 -h 0 b u 1 ) = 0, (1 -h 0 b )∂ t u 0 + div (1 -h 0 b )u 0 ⊗ u 0 + (1 -h 0 b )∇ζ 1 + f (1 -h 0 b )u 0 ⊥ = -ku 0 , ∂ τ h 1 b + 3div u 0 2 u 1 = 0.

Model

The study of the first orders shows that ζ 0 is a function of t only, given by the boundary conditions. The evolutions of u 0 and h

0 b satisfy div(u 0 -h 0 b u 0 ) = 0, (2.4a)
∂ τ h 0 b + div u 0 3 = 0, (2.4b) (1 -h 0 b )∂ t u 0 + div (1 -h 0 b )u 0 ⊗ u 0 + (1 -h 0 b )∇ζ 1 + f (1 -h 0 b )u 0 ⊥ = -ku 0 , (2.4c)
a system that can be solved using finite elements and the augmented Lagrangian method (in order to be able to treat the term in ζ 1 ). Remark 2.1. We could also introduce other space variables, namely X = x/δ and χ = δx. In the first case, writing the equations, we find that the first order does not depend on X, and we get the same system as in Section 2.5 by taking the mean value, in X, of our equations.

In the second case, we obtain a system of the same type as the one of Section 2.5, but instead of ∇ζ 1 we have ∇ζ 1 + ∇ χ ζ 0 , where ∇ χ is the gradient in the coordinates χ.

Numerical test

In order to validate our new model, we compare the results given by a finite volume scheme on the full equations (2.1)-(2.2) and the solution of (2.4) on a one dimensional test case. We consider a dune in the domain and we impose periodic boundary conditions on the velocity to simulate tides.

Finite volume scheme for the full model

The first approach is to get a "reference solution", through the resolution of the full Shallow-Water-Exner equations (2.1)-(2.2). This problem has been studied for example by [START_REF] Castro | A class of computationally fast first order finite volume solvers[END_REF][START_REF] Castro | Sediment transport models in Shallow Water[END_REF] using a finite volume scheme. In order to keep the same notations as the one used in the above references, we do not consider notations of

∂ t h + ∂ x (hu) = 0, ∂ t (hu) + ∂ x (hu 2 ) + g(h + z b )∂ x h = 0, ∂ t z b + A∂ x u 3 = 0. (3.1)

System (3.1) can be written under the form

∂ t W + A(W )∂ x W = B(W )∂ x W , where A(W ) = ∂ W (F (W )) is the Jacobian matrix of F , being W =   h q z b   , F =    q q 2 h + 1 2 gh 2 A q 3 h 3   , B =   0 0 0 0 0 -gh 0 0 0   .
The full Shallow-Water Exner system (3.1) can also be written:

∂ t W + A(W )∂ x W = 0, (3.2)
where A(W ) = A(W ) -B(W ). Due to the definition of F we have the following ex-pression for A(W ):

A(W ) =    0 1 0 -q 2 h 2 + gh 2 q h gh -3A q 3 h 4 3A q 2 h 3 0   .
To simulate this model, we consider the finite volumes scheme developed in [START_REF] Castro | A class of computationally fast first order finite volume solvers[END_REF]. Let W n i be the average of W over the volume V i at time t n . We obtain the following numerical scheme :

W n+1 i = W n i - dt dx D + i+1/2 + D - i+1/2 , with D ± i+1/2 = ± α 0 2 (W n i+1 -W n i ) ± 1 2 + α 1 2 F (W n i+1 ) -F (W n i ) -B i+1/2 (W n i+1 -W n i ) ± α 2 2 A i+1/2 F (W n i+1 ) -F (W n i ) -B i+1/2 (W n i+1 -W n i ) ,
where A i+1/2 is the Roe linearization matrix. The coefficients α i are given by the formulas:

α 0 = |λ 1 |λ 2 λ 3 (λ 2 -λ 1 )(λ 3 -λ 1 ) + |λ 2 |λ 1 λ 3 (λ 1 -λ 2 )(λ 3 -λ 2 ) + |λ 3 |λ 1 λ 2 (λ 3 -λ 1 )(λ 3 -λ 2 )
,

α 1 = -λ 1 |λ 2 | (λ 1 -λ 2 )(λ 3 -λ 2 ) + |λ 3 | (λ 1 -λ 3 )(λ 2 -λ 3 ) -λ 2 |λ 1 | (λ 2 -λ 1 )(λ 3 -λ 1 ) + |λ 3 | (λ 1 -λ 3 )(λ 2 -λ 3 ) -λ 3 |λ 1 | (λ 2 -λ 1 )(λ 3 -λ 1 ) + |λ 2 | (λ 3 -λ 2 )(λ 1 -λ 2 )
, and

α 2 = |λ 1 | (λ 2 -λ 1 )(λ 3 -λ 1 ) + |λ 2 | (λ 1 -λ 2 )(λ 3 -λ 2 ) + |λ 3 | (λ 3 -λ 1 )(λ 3 -λ 2 ) ,
where the coefficients λ i (for i = 0,1,2) are the eigenvalues of the matrix A i+1/2 ; see [START_REF] Castro | Sediment transport models in Shallow Water[END_REF].

Numerical results

We consider the spatial domain [0,20], discretized with 100 points. In this domain, we impose an initial dune, given by

z b (t = 0,x) = b 0 + max 0.1 -0.05(x -10) 2 ,0 , with b 0 = 0.1; see Figure 3.2.
In order to have a constant free surface, we choose a low velocity with periodic condition on the boundaries x = 0 and x = 20, namely:

u(t,x = 0) = u(t,x = 20) = 5.4sin(π t/6), in m/h.
The variable t is the time expressed in hours, such that there are two periods a day (σ ≈ 2.315 × 10 -5 s -1 ). We assume that at the initial time, the velocity is null, u(t = 0,x) = 0, such that the initial conditions are given by Figure 3.2. For these Let us explain the results we obtained. We present the evolution of the bottom at the times t =3, 6, 12, 18, 24, 30, 36, and 48 hours respectively in Figure 3.3 (blue continuous line), solution of System (3.1) with A = 0.001 and 100 points. In Figure 3.4, we used a finer grid and divided the space step by 2 to confirm and improve the results. One can first notice that the dune is moving towards the right or the left, depending on the sign of the velocity. Thanks to the mesh refinement, we can assert that the displacement of the dune cannot be attributed solely to numerical diffusion. At the same time, the dune is spreading.

Let us now compare the solutions of the two systems. One may know that for 100 points, the complete model needs nearly one hour; with 200 points, the computation time is several hours, whereas the limit model takes a few seconds. In Figure 3.3, the red dashed line gives the difference between the complete and the limit model, rescaled by the maximum of the initial topography (i.e. 0.2 m). We first conclude that our new simplified system gives good results on long time and the computation time is much smaller than for the complete model. However, when the top of the dune is not at x = 10 m, i.e. when the dune is slightly shifted, we observe important local errors on the slopes.

To improve the comparison between the two models (full Shallow-Water system with Exner equation and the simplified limit model), we consider the two following functions (of time):

Z(t) = max 0≤x≤L z b (x,t) and N (t) = card i s.t. z b (x i ,t) ≥ Z(t) -b 0 2 + b 0 .
The function Z represents the evolution in time of the maximum of the dune, and the function N characterize the spread of the dune. The results are plotted in Figures 3.5 The first conclusion we can give with these numerical results is that the simplified limit model behaves very well compared to the complete model but has the advantage of a lower computation time.

More numerical results

Beach test

We improve the numerical results with the simulation of a run up in the spirit of [START_REF] Castro | Sediment transport models in Shallow Water[END_REF] but in which we add the effects of tides. In this test, a 15 m long channel has a small slope (0.052%) with a rectangular sand layer of 4.5 cm between 4.5 m and 9 m (see Figure 3.7). This is a way to model the phenomenon of beach erosion.

In Figure 3.8 we plotted the results of the models on this beach test, namely we give the solution of the complete model (3.1) (blue continuous line) and the difference between the two models normalized by the maximum of the initial topography (red dashed line). The error is mainly located on the slopes of the dune and stays quite small.

This shows that the asymptotic model is a good approximation of the complete model for the beach test case also.

Convergence of the asymptotic model

The analytic proof of the convergence of the asymptotic model towards the complete model is beyond the scope of this paper. But we can study the limit of the asymptotic model as δ tends to zero from a numerical point of view. To this end, we compute the norms of the difference between the results of the two models at t = 48 h, for 100 and 200 points, for various values of δ. The configuration is the dune of Section 3.2 and δ 0 = 0.0002 the value corresponding to the conditions pointed out in that part. The results are plotted in Figure 3.9. We see that, as δ tends to zero, the errors are of order 1 in δ, as we assumed when we wrote the asymptotic model. These results show that our assumptions are satisfied from a numerical point of view.

Numerical diffusion

In this part, we focus our attention on the spreading on the dune, in both models. To that end, we consider several space steps: dx = 0.2 m, dx 2 , dx 4 , and dx 8 . Our goal is to quantify the effects of the numerical diffusion.

In Figures 3.10-3.11, we plotted the functions Z and N for the various space steps, for both the complete and the limit models. (The functions N are rescaled to take into account the number of points.) As explained before, the two models have the same behavior, although this is not the point we want to emphasize. These figures and show that the x-coordinate of the culmination of the dune does not depend on the space step (the movement due to tides is well reproduced by the two models). However, in both cases, the height of the culmination point is linked to the value of the space step: the diffusion that makes the dune spread is only numerical diffusion, even if it seems "natural". This means that the diffusion of the topography is not taken into account in the complete system (2.1)-(2.2) (and consequently in the limit model).

Conclusions

In this paper, we performed asymptotic expansions in order to decouple the two time scales that appear in oceans, considering the effect of tides. We obtained a new model and we carried out some experiments. Comparisons with the complete model give good results in one dimension, with the advantage that our new limit model is much faster (a few seconds compared to a few hours) and easier to implement than the complete one. However, the spreading of the dune is only due to the numerical diffusion, which means that, in the Shallow-Water system with Exner equation considering Grass flow, there is no diffusion of the evolution of the topography. This is contrary to the observations one can make, and we can suggest to add diffusive terms in the Exner equation, as in [START_REF] De D. Zabsonré | An Energetically Consistent Viscous Sedimentation Model[END_REF] for example, or [START_REF] Morales De Luna | A duality method for sediment transport based on a modified Meyer-Peter & Müller model[END_REF] for the Meyer-Peter and Müller equation. The numerical validation of these results for the two dimensional case is still in progress.

Fig. 2 . 1 :

 21 Fig. 2.1: Sediment layer and water with free surface

Figure 2 .Fig. 3 . 1 :

 231 Fig. 3.1: Sediment layer and water with free surface for the finite volume scheme

Fig. 3 . 2 :

 32 Fig. 3.2: Initial conditions

  -3.6 (the sawtooth shape of the function N is due to the integer values of N (t) and to the discrete values of the time, every one hour).

  model) at t=12h difference between the models (c) t = 12 h.

  model) at t=30h difference between the models (f) t = 30 h.

Fig. 3 . 3 :

 33 Fig. 3.3: Evolution of the topography with 100 points

  model) at t=30h difference between the models (f) t = 30 h.

Fig. 3 . 4 :

 34 Fig. 3.4: Evolution of the topography with 200 points

Fig. 3 . 5 :

 35 Fig. 3.5: Graphs of the function Z(t)

Fig. 3 . 6 :

 36 Fig. 3.6: Graphs of the function N (t)

Fig. 3 . 7 :

 37 Fig. 3.7: Initial conditions for the beach test

  model) at t=12h difference between the models (c) t = 12 h.

  model) at t=30h difference between the models (f) t = 30 h.

Fig. 3 . 8 :

 38 Fig. 3.8: Evolution of the topography in the beach test case with 100 points

Fig. 3 . 9 :

 39 Fig. 3.9: Errors of the asymptotic model for 100 and 200 points

Fig. 3 . 10 :

 310 Fig. 3.10: Graphs of the functions Z(t)

Fig. 3 . 11 :

 311 Fig. 3.11: Graphs of the functions N (t)

Acknowledgments. As this work started with a French-American collaboration, the second author would like to thanks the "Equipes Associées" program of INRIA (between J. McWilliams's team (UCLA) and Moise INRIA team (Grenoble, France), directed by E. Blayo) which partly funded this work. The third author is partially supported by the AUF, and is very grateful to the MAPMO laboratory for the accommodation he received. The authors would like to thank the anonymous referee for his numerous suggestions

* This work has been partially supported by the project METHODE 566 ANR-07-BLAN-0232 †


Hipólito Simón
email: hsimon@ua.es

General < J7 -Discrimination < J -Labor and Demographic Economics

Keywords: gender wage gap, matched employer-employee data, Juhn-Murphy-Pierce decomposition, segregation

This article examines the origin of the cross-country heterogeneity of the gender wage gap in nine European countries using a unique harmonized international matched employer-employee dataset. Our novel findings suggest that cross-country differences in the intensity of female segregation into low-paying workplaces is a relevant source of international differences in the size of the gap and that international disparities in the characteristics of wage structures are not very influential. On the other hand, the evidence is not fully conclusive with respect to the influence on the variations of the gap of different macroeconomic, social and institutional country-specific features considered previously in the literature.

Introduction

The existence of a significant and persistent gap in earnings between males and females is a welldocumented stylized fact of modern labour markets. Provided that identifying the sources of gender differences in wages is crucial in implementing effective policy decisions so as to reduce them, the origin of the gap has received considerable attention in economic literature (for authoritative reviews, see [START_REF] Altonji | Race and gender in the labor market[END_REF][START_REF] Altonji | Race and gender in the labor market[END_REF]Blau and[START_REF] Blau | Gender Differences in Pay[END_REF].

Most studies on the origin of the gender wage gap apply to individual countries. Although there is a wide variation in results across studies, some general regularities emerge in them. Firstly, differences by gender in productivity-related individual characteristics such as education and experience play only a minor role in explaining the gap, and their influence tends to diminish over time alongside the general improvement of the educational situation and participation rates of females [START_REF] Weichselbaumer | A meta-analysis of the international gender wage gap[END_REF]. Secondly, a larger share of the gap is typically explained by the female segregation into low-paid structures. On this subject, whereas earlier studies highlighted the detrimental effect on female wages arising from female segregation into low-paid occupations and industries (e.g. [START_REF] Groshen | The Structure of the Female/Male Differential: Is It Who You Are, What You Do, or Where You Work?[END_REF][START_REF] Macpherson | Wages and gender composition: Why do women's jobs pay less?[END_REF][START_REF] Macpherson | Wages and gender composition: Why do women's jobs pay less?[END_REF], more recent studies that draw on broad samples of matched employer-employee data reveal that female segregation into low-wage workplaces has a particularly significant negative impact on their relative wages and also, that a high presence of women tends to depress workplace's wages (e.g. [START_REF] Bayard | New evidence on sex segregation and sex differences in wages from matched employee-employer data[END_REF][START_REF] Amuedo-Dorantes | The Role of Segregation and Pay Structure on the Gender Wage Gap: Evidence from Matched Employer-Employee Data for Spain[END_REF][START_REF] Amuedo-Dorantes | The Role of Segregation and Pay Structure on the Gender Wage Gap: Evidence from Matched Employer-Employee Data for Spain[END_REF]. Finally, the size of the gender pay gap seems to be related to the extent of wage inequality, since a more compressed wage structure is likely to diminish the gender pay gap. Therefore, the evolution of wage dispersion over time is a significant determinant of the changes of the gap [START_REF] Richardson | Swimming with the Tide: Solidary Wage Policy and the Gender Earnings Gap[END_REF][START_REF] Blau | Swimming Upstream: Trends in the Gender Wage Differential in the 1980s[END_REF], 2006).

A relevant branch of the gender-related literature consists of cross-country comparative analyses of the origin of international differences in the size of the gender wage gap. Studies with a cross-country perspective are motivated by the striking variation across countries of the gap (see OECD, 2008 for detailed descriptive evidence) and although they are rather scarce, due plausibly to data limitations, they have complemented traditional within-country examinations of gender pay differentials and have led to additional significant progress. In particular, they have emphasised the influence of certain macroeconomic and institutional factors on shaping cross-country differences in the gap. In this vein, the seminal cross-country comparative studies of Blau andKahn (1992, 1996, ) suggest that the size of the gap is related to wage dispersion and accordingly, that wage-setting institutions which are relevant in shaping wage dispersion, such as collective bargaining, have an important impact on cross-country variations of the gender wage gap. Moreover, other studies show that differences across countries in the size of the gap could be related to the generosity of family friendly schemes, such as parental leave provisions or state provision of child-care services [START_REF] Arulampalam | Is There a Glass Ceiling Over Europe? Exploring the Gender Pay Gap Across the Wages Distribution[END_REF][START_REF] Christofides | The Gender Wage Gaps, 'Sticky Floors' and 'Glass Ceilings' of the European Union[END_REF], gender employment gaps [START_REF] Olivetti | Unequal Pay or Unequal Employment? A Cross-Country Analysis of Gender Gaps[END_REF] and cultural beliefs concerning gender [START_REF] Fortin | Gender Role Attitudes and Women's Labour Market Outcomes across OECD countries[END_REF]. This article examines the gender pay gap across a set of representative European countries based on a unique international matched employer-employee dataset, the European Structure of Earnings Survey. This dataset consists of inter-country harmonized microdata, as the survey is conducted in all the countries according to a common methodology. Moreover, it is the only international database that is currently available with matched employer-employee data. This type of data has enabled fundamental progress to be made in the understanding of wage determination in general and of the origin of the gender wage gap in particular [START_REF] Hamermesh | Fun with matched firm-employee data: Progress and road maps[END_REF]Abowd and[START_REF] Abowd | The Analysis of Labor Markets Using Matched Employer-Employee Data[END_REF]. Thus, cross-country comparisons are developed on a strictly comparable basis with a wealth of harmonised information. This enables to extend and enrich previous international comparative studies. They are based on either different national sources of microdata (i.e. [START_REF] Blau | The Gender Earnings Gap: Learning from International Comparisons[END_REF][START_REF] Blau | Wage Structure and Gender Earnings Differentials: an International Comparison[END_REF], 2003) or on international harmonized household-based microdata [START_REF] Arulampalam | Is There a Glass Ceiling Over Europe? Exploring the Gender Pay Gap Across the Wages Distribution[END_REF][START_REF] Olivetti | Unequal Pay or Unequal Employment? A Cross-Country Analysis of Gender Gaps[END_REF][START_REF] Christofides | The Gender Wage Gaps, 'Sticky Floors' and 'Glass Ceilings' of the European Union[END_REF][START_REF] Fortin | Gender Role Attitudes and Women's Labour Market Outcomes across OECD countries[END_REF], a sort of data which involve well-known important restrictions to analysing wages, such as a high risk of measurement error in wages and rather limited information on key wage-determining characteristics of individuals and, particularly, of their jobs and workplaces. [START_REF] Juhn | Accounting for the Slowdown in Black-White Convergence[END_REF] wage decomposition methodology is employed in the empirical analysis in order to ascertain the origin of the gender wage gap and of its international differences. This technique distinguishes between the relative impact that gender-specific factors and wage structure characteristics have on the gap. It should be noted that although it has been previously used in cross-country analysis of the gender wage gap [START_REF] Blau | The Gender Earnings Gap: Learning from International Comparisons[END_REF], its adaptation for use with matched employer-employee data allows us to assess the influence on shaping international differences in the magnitude of the gap of certain additional factors such as the intensity of female sorting into low-wage workplaces. Therefore it permits a more in-depth analysis of the relative influence in the gap of potential relevant sources referred to in the literature, such as female segregation into low-wage structures and the global characteristics of wage structures. The outline of the article is as follows. Section 2 and 3 describe the dataset and the methodology used in the decomposition of the gender wage gap. Section 4 examines the sources of the gap and of international differences in its size, along with the impact that several country-specific macroeconomic, social and institutional factors have on them. Finally, the conclusions are presented in Section 5.

An extension of the

In a nutshell, important differences across European countries in the size of the gap and its determinants are observed. Consistent with previous studies, differences in productivity-related individual characteristics explain just a minor part of the gap in most countries. Conversely, female segregation into low-paying structures usually explains a larger share of the gap, with a marked impact of female segregation into low-wage workplaces in comparison to occupational segregation.

Moreover, a substantial part of the gap remains systematically unexplained, which implies that in every European country a significant average wage differential exists between observationally similar men and women doing the same type of jobs in the same workplaces. On the other hand, crosscountry comparative analyses suggest that international disparities in wage structure characteristics are not major determinants of inter-country differences in the size of the gender wage gap. On the contrary, they seem to be mainly driven by cross-country differences in gender-specific factors and in particular by differences in the intensity of female workplace segregation. Finally, the evidence is not conclusive in terms of the influence that country-specific factors such as female employment rates, family conciliation policies, cultural beliefs about gender or wage-setting institutions have on the variations of the gap across this set of European economies.

Data

The microdata used in this study are drawn from the 2002 wave of the European Structure of Earnings Survey (hereafter ESES). This dataset is a collection of national surveys conducted in all member states of the European Union (as well as in Iceland, Liechtenstein and Norway) according to a standard methodology under the auspices of the Statistical Office of the European Communities.

This study draws on the national data samples for Italy, Spain, Portugal, the Netherlands, Norway, the Czech Republic, Latvia, Slovakia and Lithuania. 1 The ESES provides detailed and comparable information regarding the level and structure of the remuneration of employees, their individual characteristics and the enterprise or local unit to which they belong. It covers workplaces with more than 9 employees in sections C to O of the economic activity classification scheme NACE, except for Norway, Latvia, Italy and Portugal where 1 These are the countries whose national statistics offices allowed researchers to access the data of their national samples of the ESES in the framework of a European research project (European Labour Market Analysis using Firm-level Panel Data and Linked Employer-Employee Data) financed by the European Union under the VI Framework Programme. education; health and social work and other community, social and personal service activities) are not covered and Spain, where sector L is not covered.2 Given that industry coverage in these latter countries does not fully comprise the public sector and that wage differentials in European labour markets tend to be lower in the public sector than in the private sector [START_REF] Arulampalam | Is There a Glass Ceiling Over Europe? Exploring the Gender Pay Gap Across the Wages Distribution[END_REF], excluding the public sector is likely to inflate the size of the raw gender pay gap in these countries.

The ESES consists of cross-section matched employer-employee data with a sample of workers at each workplace. It collects information, usually provided by the management of firms, on demographic information corresponding to workers (earnings, hours worked, sex, age, level of education, tenure in the firm, occupation, type of contract and full-time/part-time indicators) along with detailed information regarding each respondent's workplace (including industry, size and type of financial control, whereas additional features of workplace's labour force composition can be derived from the observations of each workplace). The analysis is restricted to individuals aged 18-64 and to workplaces with at least two observations in the samples. After applying these filters, the national samples are seen to range between 58,049 and 972,729 workers and between 472 and 21,615 workplaces and the number of workers per firm ranges between 8.8 and 831.2 (detailed descriptive statistics are available from the author on request).

The earnings measure used in the empirical analysis is the gross hourly wage. This implies that the aim of the research is to explain international differences in the gender gap of the price of labour rather than in terms of labour incomes. Wages cover remuneration in cash paid by the employer before deductions for tax and employee social security contributions. They comprise all payments different from overtime pay, including commissions, travelling expenses, premium payments for shift, night and weekend work and all bonuses and allowances, regardless of whether or not they are paid regularly in each monthly pay period (thus, they also cover annual bonuses as holiday bonuses, 13 th and 14 th monthly salaries, profit sharing and allowances for leave not taken) and its definition is exactly the same across countries.

Methods

In evaluating the sources of the gender wage gap and its international differences, the extension of the [START_REF] Juhn | Accounting for the Slowdown in Black-White Convergence[END_REF] decomposition suggested by [START_REF] Blau | The Gender Earnings Gap: Learning from International Comparisons[END_REF] is used. It should be noted that it has been specifically adapted to be used with matched employer-employee data, following the hints of [START_REF] Gartner | How collective contracts and works councils reduce the gender wage gap[END_REF]. The empirical analysis departs from the separate estimation for each country of the following wage function:

j ij i ij a ε β X w + + = (1)
where w ij is the natural log of hourly wage of individual i in workplace j; X i is a vector of controls; β is a vector of parameters to be estimated (including an intercept); ε ij is a stochastic error term and a j is an error component corresponding to workplace j and invariant for all the individuals working in the same workplace. 3 Controls include individual and job characteristics (the highest level of education reached by the individual, age and its squared term, the time spent with the current employer and its squared term, dummies for 27 major occupational groups and indicators for a permanent contract and a fulltime job) and, in an alternative specification of the equation, also workplace characteristics (indicators for industry -55 dummies-; the type of financial control -a dummy for fully publicly owned firms-; size -five dummies-and a set of characteristics of the workplace workforce -namely, the ratio to all employees in the workplace of women, low-and high-educated workers, defined as those workers with lower than upper-secondary and with tertiary education, respectively, and the average age and tenure). In order to ensure cross-country comparability of the results, the specification of the wage equation is exactly the same for all countries.

Equation ( 1) is estimated for the pool of workers (i.e. males and females) in each country.

Although choosing the wage structure of the majority group as the reference structure with which to develop wage decompositions is largely standard practice in the literature, there are several advantages to using a pooled approach obtained from a matrix combination of both the female and the male prices as the estimate of the wage structure that would exist in the absence of discrimination. Firstly, pooling the wage structures for all workers allows all the available information to be used in order to estimate market wage returns and constitutes a more natural approximation to the labour market's non-discriminatory wage structure than simply adopting the structure of the main group or using other alternatives [START_REF] Oaxaca | On discrimination and the decomposition of wage differentials[END_REF][START_REF] Oaxaca | On discrimination and the decomposition of wage differentials[END_REF][START_REF] Neumark | Employer´s discriminatory behaviour and the estimation of wage discrimination[END_REF]. Secondly, there are some methodological and computational advantages, since it renders the use of percentile 3 Given that workplace specific effects also capture unobserved individual effects common to all employees in a workplace and that it is not possible to identify this effect in ESES cross-section microdata, they are relegated to the residual. Existing evidence for several countries suggests that unobserved individual effects tend in general to be weakly correlated with workplace specific effects [START_REF] Abowd | The Relative Importance of Employer and Employee Effects on Compensation: A Comparison of France and the United States[END_REF][START_REF] Lane | Inequality and the Labour Market: Employers[END_REF]. Identification of the workplace effects is guaranteed, given that there is more than one observation per workplace in the dataset. Since the result of the Hausman's contrast for all the countries indicates that workplace specific effects are correlated with the rest of the explanatory variables in equation ( 1), it is estimated by fixed effects (which is equivalent to estimating by ordinary least squares with a set of workplace dummies). Relying on the properties of the ordinary least squares estimator, after the estimation of equation ( 1) with the pooled data of country A and having obtained the values of A β ˆ, σ A y η A , the average wage of the subgroup of workers s (s=males or females) in country A can be expressed as:

A s A A s A A A s A s λ η θ σ β X w + + = ˆ where ) 1 , 0 ( Ã θ , ) 1 , 0 ( Ã λ (2)
where the superscript A is for country A (note that subscripts i and j have been omitted in the equation for ease of presentation); A s w stands for the mean natural log of the hourly wage of given group s; A s X is a vector of the average of the set of explanatory variables for group s; A s β ˆ is the vector of coefficients estimated with equation ( 1) and the pooled data of country A; σ A is the standard deviation of wage residuals of the pool of workers; A s θ is the average standardized residual of group s; η A is the standard deviation of workplace effects of the pool of males and females and A s λ is the average standardized workplace effect of group s.

Using the pooled wage structure as the market price references in the decomposition, the wage gap between males and females in country A can be written as follows:

η λ σ θ β X η λ λ σ θ θ β X X w w D A A A A A A A f A m A A f A m A A f A m A f A a A ∆ ∆ ∆ ) ( ) ( ) ( + + = + + = = - - - - (3)
where the subscript m is for males and f for females and a ∆ prefix denotes the average difference between males and females in the subsequent variable.

In brief, equation ( 3 On the other hand, the difference in the magnitude of the gender wage gap between two countries (A and B) may be expressed, after applying the decomposition in equation ( 3) twice, as the following decomposition equation:

) ( ∆ ) ∆ ∆ ( ( ∆ ) ∆ ∆ ( ) ( ∆ ) ∆ ∆ ( B A B A B A B A B A B A B A B A B A B A η η λ η λ λ σ σ θ σ θ θ β β X β X X D D - - ) - - - - - + + + + + = (4)
According to the accounting scheme of cross-country differences in the gender wage gap provided by equation ( 4), international discrepancies in the magnitude of the gap can be explained by inter-country differences in six factors. The first term of the decomposition captures the effect in the gap of cross-country differences in the relative observed characteristics of males and females. The second term reflects the contribution of differences in the market prices of observed characteristics.

The third term measures the impact of inter-country differences on the relative positions of males and females within the residual wage distribution (after controlling for measured characteristics and workplace effects). The fourth term isolates the impact of differences in wage residual dispersion with the relative position of the average worker of each group in the residual distribution remaining constant. 5 The fifth term captures the impact of cross-country differences in the extent of female workplace segregation. Finally, the sixth term measures the effect of differences in the dispersion of workplace wage differentials. Note that the first and second decomposition terms in equation ( 4) can be aggregated to assess the overall effect of observed characteristics in generating international differences in the gender wage gap. Similarly, the third and fourth terms capture the overall influence of unobserved factors and the fifth and sixth terms assess the joint effect of workplace-related factors. Alternatively, the components of the decomposition methodology can be further grouped into those terms that capture the role of inter-country deviations attributable to differences in worker-specific factors (the first, third and fifth terms) and those that measure the overall effect of inter-country differences in the underlying wage structure (the second, fourth and sixth terms), respectively.

Results

Descriptive evidence

The first panel of The second panel of Table 1 provides summary results of the within-country decompositions of the gender wage gap according to equation (3). It comprises the dispersion of residuals and workplace effects and the average position of men and women in both distributions. In short, this evidence reveals that unobserved elements and workplace-related factors are, without exception, unfavourable for female wages in all the economies. Yet, their impact is quite different across countries and, as a consequence, they constitute potential relevant sources of international differences in the size of the gender wage gap.

Therefore, the average wage residual is systematically positive for males and negative for females and, consequently, the average female position in the residual distribution is always well below the median (on average, females are in percentile 44 of the distribution) and the average male position is above it (percentile 59). Yet, some international differences can be found with regard to the importance of this phenomenon (the mean female wage residual ranges from -0.238 to -0.076) and also the magnitude of residual wage inequality. In the same vein, in all the countries females are systematically segregated into low-paying workplaces (the average male workplace effect is always positive whereas the average female 6 These gaps should be exponentiated in order to express the estimates as percentage mark-ups.

7 This information may be accessed on the website of the European Commission (http://ec.europa.eu). workplace effect is largely negative). Moreover, the intensity of segregation varies significantly across countries (the average female workplace effect ranges from -0.051 to -0.325, with an average value of -0.179), and international differences in inequality workplace effects, which determine the specific wage penalty on female wages of this type of segregation, are also observed (the average standard deviation of workplace effects ranges between 0.126 and 0.568, with an average of 0.294).

Decomposition results

Table 2 contains the results of the separate within-country decompositions of the gender wage gap according to the three terms shown in equation ( 3). As can be observed, differences in measured characteristics of males and females account in general for a minor part of the gap (on average, 0.046 log points or 22.7% of the total gender wage gap of 0.202 points). The specific impact of gender differences in measured qualifications is not usually very important (overall, differences in education, age and tenure explain only 6.9% of the total gap) whereas, in turn, job characteristics are a more significant source of the gap (16.3%). The bulk of this last effect is explained by differences by gender in occupational distribution (12.4%), which implies that, with respect to the impact of observed characteristics, female occupational segregation is by far the most relevant origin of the gap. It must be noted, nevertheless, that in some cases, average results reveal a remarkable heterogeneity across countries. Thus, for example, the impact on the gap of gender differences in productivity-related individual characteristics such as education and age is quite significant in the Netherlands (where they explain 26.4% of the total gap) and is, indeed, beneficial for female wages in Latvia (-0.012) and Lithuania (-0.036), where females are more highly educated than men and they have longer tenure and total work experience (as proxied by age). In the same vein, females are actually sorted into high-paying occupations in Lithuania. Yet, with these few exceptions, empirical findings by and large confirm previous available evidence that differences by gender in productivity-related characteristics are in general a minor source of the gap in earnings and that occupational segregation is more significant.

Unobserved factors tend to be a relevant source of the gender wage gap. Thus, the second term of the breakdown accounts on average for 35.2% of the total average gap and the within-workplace differential between males and females ranges from 0.047 to 0.108 log points, with an average across countries of 0.071 points. Interestingly, this result reveals put differently, that in all the countries a significant within-workplace wage differential exists between observationally similar men and women doing the same type of jobs.

Overall, gender differences in workplace distribution are comparatively the most important origin of the gender pay gap in all the countries (although a significant cross-country heterogeneity is also observed in this case). Hence, the third term of the breakdown has an average effect of 0.085 log In order to ascertain the specific attributes of low-wage workplaces in which European women are over-represented, Table 3 contains the results of the within-country decompositions of the gender wage gap with an alternative specification of the model of wage determination, in which workplace effects have been substituted by a set of workplace characteristics. These attributes account for 0.090 points of the gap, which compares to 0.085 points corresponding to workplace effects with the previous specification of the wage equation. Hence they almost entirely capture the effect on the gap of workplace effects. As can be observed, the factors with the greatest detrimental effect on female relative wages are female sorting into low-paying industries and, especially, into workplaces with a high presence of female employees. The estimated coefficient of the female share is negative and significant at conventional levels in every country and this factor has an average explanatory power of 0.068 log points (or 33.3% of the total gap) and is highly relevant in every country (it actually ranges from 0.034 to 0.118 points). Therefore, previous findings in the literature indicating that a disproportionate location of females in certain labour structures tends to lower wages are clearly confirmed as regards workplace segregation. The evidence also suggests that the phenomenon is systematic and particularly relevant.

Table 4 displays the summary outcomes of the between-country decomposition of the international differences in the size of the gender wage gap according to equation ( 4). Specifically, it contains the average results of all the possible pairwise decompositions of cross-country differences in the gender wage gap. For each pair of countries the comparison where the difference in the magnitude of the wage gap is positive has been considered (the total amount of comparisons is 36 and full results of pairwise country comparisons can be obtained from the author on request). Hence, the aim of the empirical analysis is to examine why comparatively higher gender wage gaps prevail in some countries.

As can be observed in the first line of Table 4, the total average cross-country difference in the magnitude of the gender wage gap is relatively high (0.091 log points). In short, inter-country comparisons reveal, firstly, that although both differences in endowments and in the market returns of observed characteristics are significant sources that explain international differences in the size of the gap, cross-country differences in relative endowments are clearly more relevant (their explanatory power is of 0.030 points) than differences in returns (0.013 points). The global impact of unobserved factors is relatively low (0.017 points or 18.6% of the average difference in the gap) which implies, interestingly, that the bulk of international differences in the magnitude of the gender wage gap are identified in practice. Moreover, it is mainly due to differences in the female relative position in the residual wage distribution (differences in the residual gap explain 0.015 points), given that cross-country differences in residual wage inequality have an almost negligible influence (0.002 points). In turn, differences in the impact of workplace effects are also important to explain cross-country differences in the size of the gap (0.031). This is due to the effect of differences in the extent of female workplace segregation (0.041),

given that international disparities in the dispersion of workplace wage differentials have an opposite influence as inter-firm wage differentials tend to be lower in countries with higher gender gaps (-0.010).

By grouping the components of the inter-country decomposition methodology into those attributable to worker-specific factors and those related to the wage structure we gain an additional insight into the origin of international differences in the size of the gender wage gap. Gender-specific components play a very important role in explaining differences in the gender wage gap between countries, since they explain 0.086 points (or 94.1%) of a total average difference of 0.091 points. From a disaggregate perspective, this is due to the fact that in countries with higher gender wage gaps the relative endowments of observed characteristics have a comparatively higher detrimental effect on female wages (with an average effect of 0.030), differences by gender in the residual gap are also relatively more disadvantageous for females (0.015) and, particularly, female segregation into low-paying workplaces is considerably more intense (0.041). With respect to the global impact of female segregation into low-paying structures, it is noteworthy that the joint effect of differences in occupational and workplace segregation is considerably large (0.046 points and 50% of the total gap) and that the impact of workplace segregation (0.041) is much higher than that of occupational segregation (0.005).

On the contrary, cross-country differences in wage structures seem to play on the whole a comparatively minor role in shaping international differences in the gender wage gap. Thus, although female wages in countries with higher wage gaps tend to be disfavoured by global wage structure characteristics, this factor explains just 0.005 points (or 5.5%) of the total average difference of 0.091 points. This low impact is due to the fact that the effect of the comparatively more unfavourable returns to observed characteristics (0.013 points) and a higher residual wage inequality (0.002) are counteracted by usually lower inter-firm wage differentials (-0.010). Nevertheless, overall this evidence suggests that in contrast with the findings of earlier studies that wage structure characteristics are prominent in explaining cross-country differences in the magnitude of the sex wage gap, this conclusion cannot be generalized.

Country-specific features and the size of the gender wage gap

The final part of the empirical analysis explores the influence of certain country-specific features (namely female employment rates, family conciliation policies, cultural beliefs about gender and wage- 13 setting institutions such as collective bargaining) whose potential influence in cross-country variations in the size of the gender wage gap has been previously referred to in the literature. Firstly, it has been hypothesized that gender wage and employment gaps could be negatively correlated across countries if non-randomness of female selection into work implies that in countries with lower female labour force participation women with a relatively low return to paid jobs would choose not to participate, thus narrowing the average wage gap in these countries [START_REF] Olivetti | Unequal Pay or Unequal Employment? A Cross-Country Analysis of Gender Gaps[END_REF]. Secondly, the generosity of family friendly schemes such as parental leave provisions or state provision of child-care services are likely to influence the behavior of men and women differently and hence affect gender wage gaps. The expected impact of these policies in unclear a priori as they could, inter alia, motivate women to participate in the labour force, but also have unintended effects on the labour market position of women if they imply longer absences of work of women or attract comparatively less productive women into the workforce. Yet, the empirical evidence suggests that countries with more generous work-family policies tend to have a lower gender wage gap [START_REF] Arulampalam | Is There a Glass Ceiling Over Europe? Exploring the Gender Pay Gap Across the Wages Distribution[END_REF]. Thirdly, given that women's attitudes toward work are important determinants of human capital investment and labour supply [START_REF] Vella | Gender Roles and Human Capital Investment: The Relationship between Traditional Attitudes and Female Labour Market Performance[END_REF], the gender wage gap could be in practice lower in countries with more genderegalitarian cultures [START_REF] Fortin | Gender Role Attitudes and Women's Labour Market Outcomes across OECD countries[END_REF]. Finally, it has been hypothesized that wage-setting institutions could well have important indirect gender effects through their impact on wage structure given that, as women are usually concentrated in the lower part of the wage structure, the more dispersed the structure prevailing in a country the greater the penalty for female wages. Hence, collective bargaining and minimum wages could affect the gender wage gap insofar as countries with higher minimum wages and with more centralized or coordinated bargaining tend to have lower wage dispersion and, plausibly, lower gender wage gaps (Blau andKahn, 1992, 2003).

In order to explore the influence of these factors, Table 5 contains information on a set of country-specific macroeconomic, social and institutional features for each country and Figure 1 plots their relation with the gender wage gap. 8 Given the relatively low number of countries covered by the research, following [START_REF] Arulampalam | Is There a Glass Ceiling Over Europe? Exploring the Gender Pay Gap Across the Wages Distribution[END_REF] and [START_REF] Olivetti | Unequal Pay or Unequal Employment? A Cross-Country Analysis of Gender Gaps[END_REF], our aim is not to provide a conclusive test of the impact of the set of factors on the gender pay gap but simply to provide correlations between summary measures of potentially important factors and observed gender pay gaps.

8 Although detailed information on its calculation can be found in Table 5, we should note that family conciliation policies are proxied through the recreation of the OECD work-family reconciliation index (a summary measure of the policies prevailing in a country on work-family issues) carried out by [START_REF] Christofides | The Gender Wage Gaps, 'Sticky Floors' and 'Glass Ceilings' of the European Union[END_REF] for all the EU members. Alternatively, gender role attitudes have been measured, following [START_REF] Fortin | Gender Role Attitudes and Women's Labour Market Outcomes across OECD countries[END_REF], with the information of the 1999-2001 wave of the World Value Survey. In particular, perceptions of the man as main breadwinner, as well as anti-egalitarian views or discriminatory attitudes against working women are captured through the agreement to the statement 'When jobs are scarce, men should have more right to a job than women' and perceptions with respect to women's traditional role is measured as agreement to the statement 'Being a housewife is just as fulfilling as working for pay'. Overall, the empirical evidence for this sample of countries is not fully conclusive with respect to the influence on the international heterogeneity of the gap of cross-country differences in the macroeconomic, social and institutional elements previously highlighted in the literature. Gender wage and employment gaps are, contrary to expectations, positively corelated and their unconditional correlation (0.28) is not statistically significant. In a similar way, the correlation of the gender gap is not statistically significant either with the generosity of work-family policies (0.08) or with any of the proxies of the social gender beliefs (-0.18 and 0.14, respectively). Finally, the evidence does not corroborate a positive association between wage inequality and the magnitude of the gender gap, given that the bivariate correlation across countries between the size of the gender wage gap and wage dispersion is actually negative (-0.51), although not significant at conventional levels. 9 Consequently, the gender wage gap is not significantly correlated across countries either with the minimum wage or with the collective bargaining coverage rate (with bivariate correlations of -0.09 and 0.40 not being significant in any case at conventional levels). 10

Conclusions

This research examines the origin of international differences in the gender wage gap in a number of representative European economies on the basis of microdata drawn from the European Structure of Earnings Survey. This survey constitutes a unique harmonized international matched employer-employee dataset with linked information on both worker and workplace characteristics.

Consequently, its use provides a novel comparative evidence that largely complements previous findings in the gender-related literature and a sounder empirical base for assessing the sources of the gender wage gap in earnings and its heterogeneity across countries and consequent policy options.

This examination is particularly appealing because, despite long-standing equal pay and equal opportunity legislation, a significant gender gap in pay is generally observed in the European Union, with a remarkable heterogeneity across its members (Eurostat, 2005 andEuropean Commission, 2006).

The empirical evidence confirms that in general, differences in individual productivity-related characteristics play a minor role in the explanation of the gender pay gap and reveals that in all European countries significant average within-workplace wage differentials exist between observationally similar men and women doing the same job. From a policy perspective, these findings suggest that policies should partly focus on differential treatment within the labour market 9 Interestingly, this same result holds for all the EU countries according to ESES 2002data (European Commission, 2006). 10 A thorough analysis of international differences in wage inequality and the influence of wage-setting institutions in European economies using the ESES data can be found in [START_REF] Simón | International Differences in Wage Inequality: A New Glance with European Matched Employer-Employee Data[END_REF]. A novel finding is that female segregation into low-wage structures, and in particular into low-wage workplaces, contributes significantly to both the gender pay gap in all European economies and to international differences in its size. Although it should be taken into account that some degree of gender segregation could be plausibly optimal for both men and women if they differ in their preferences regarding non-labour activities and non-pecuniary job attributes or in their socialization patterns (Blau and Kahn, 1998), this evidence supports potential attempts to enforce an equal distribution of men and women across occupations and workplaces through equal treatment legislation, affirmative action or other means. Furthermore, as segregation of females into workplaces with a high presence of female employees has been identified as a factor with a particularly detrimental effect on their relative wages, particular attention should be given to lower wages in labour structures which tend to be dominated by females and to policy initiatives aimed at improving the remuneration of female-dominated jobs, such as the development and application of gender-neutral systems of job evaluation.

On the other hand, international disparities in wage structures, and in particular in the extent of wage inequality, do not seem to be major determinants of inter-country differences in the size of the gender wage gap in Europe. This result contradicts the findings of previous comparative studies and reveals that the generalization of their conclusions is not straightforward. Moreover, it suggests that policy initiatives adopting a mainstreaming or multi-dimensional approach that includes potential changes of institutional factors such as wage formation systems might not be fundamental to reducing the gender pay gap.

To conclude, the influence of certain country-specific factors previously referred to in the literature as potential sources of cross-country variations in the size of the gap is also explored. Yet, overall the evidence for the countries covered by the research is far from conclusive in terms of the influence on the gap of cross-country differences in factors such as female employment rates, family conciliation policies, cultural beliefs about gender or wage-setting institutions. Nevertheless, it must be noted that the limited number of countries could significantly hinder the empirical analysis, warranting further research in these issues.

F

  M, N and O (respectively, public administration, defence and compulsory social security;

  [START_REF] Juhn | Accounting for the Slowdown in Black-White Convergence[END_REF] decomposition unnecessary, which can lead to problems of identification in the decomposition[START_REF] Suen | Decomposing Wage Residuals: Unmeasured Skill or Statistical Artifact[END_REF] 4 .

  ) provides a within-country decomposition of the gender wage gap. It quantifies the extent to which average wage differences between males and females in a country are related to (a) differences in observed characteristics, (b) the influence of unobserved elements and (c) the influence of workplace-related factors. More specifically, the first term on the right-hand side of the equation corresponds to the portion of the wage differential attributable to differences between market prices ( A β ˆ), which coincides with the 'explained' component of the standard Oaxaca-Blinder decomposition. The second term measures the influence of the unobserved factors in the model. This component comprises the effect of unobserved ability, motivation and discrimination, and corresponds to the impact of differences by gender on the average standardized residual ) ( money value per unit difference in the standardized residual (σ A ), which determines the specific wage penalty suffered by the disadvantaged group. Finally, the third term estimates the influence of workplace-related factors. This term is taken as a product of the difference in the average standardized workplace effect of males and females ) ( -, which measures the intensity of female segregation into comparatively low-wage workplaces, and the dispersion of wage differentials across workplaces (η A ), which determines the extent of the wage penalty of females resulting from this segregation.

  issues of differential access to education and other productive endowments (for a thorough review of potential policy responses to the gender pay gap, see EuropeanCommission, 2006).

  Figure 1Relation between the gender wage gap and country-specific fetures.

  Table1documents the gender wage gap for the nine European countries (the final column reports the unweighted average values). Consistent with previous evidence, a high level of international heterogeneity may be observed in the size of the wage gap, which ranges from 0.067 log points in Lithuania to 0.313 points in Slovakia.

6

Interestingly, the countries embraced by this research cover almost the full range of heterogeneity in the gender wage gap in Europe given that, according to equivalent estimates for the European Union members with the 2002 wave of the European Structure of Earnings Survey, the hourly gender wage gap varies from 0.052 log points (Slovenia) to 0.329 (Slovakia).

7

  1% of the total average gap), ranging from 0.025 to 0.16 log points. It should be noted that the negative impact that female sorting into low-wage labour structures has on female wages is still more clean-cut when occupational and workplace segregation are aggregated, since 54.4% of the total average gap is explained by this factor.

	points (42.
	F o
	r
	P
	e e r
	R e v i e w
	11

Table 4

 4 Between-country decomposition of differences in the gender wage gap. The table contains average values calculated from all the pairwise comparisons of the countries in the sample where the difference in the gap is positive, with the wage structure of country A and country B weights as the base for the breakdown.

	o
	r
	P
	e e r
	R e v i e w

16

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

The national samples of Norway, Latvia, Lithuania, the Netherlands and Slovakia cover workplaces with less than 10 employees. In order to work with similar types of workplaces in all the countries, they have been dropped from the samples.

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

A recent assessment of the merits and shortcomings of the[START_REF] Juhn | Accounting for the Slowdown in Black-White Convergence[END_REF] decomposition can be found in[START_REF] Yun | Wage Differentials, Discrimination and Inequality: A Cautionary Note on the Juhn, Murphy and Pierce Decomposition Method[END_REF]. According to this author, the decomposition relies on a few bold assumptions difficult to verify.

If inter-country differences in residual inequality were interpreted as differences in the market premium for unobserved skills, this component would represent the effect of differences in the returns to unobservable skills. However, this is quite a strong interpretation of residual inequality as it may also capture, inter alia, the effect of measurement error, equation misspecification and heterogeneity in unmeasured characteristics.

Acknowledgements

This work benefits from funding support of the project European Labour Market Analysis using Firm-level Panel Data and Linked Employer-Employee Data financed by the European Union under the VI Framework Programme. I am grateful to Eurostat and the National Statistical Offices of Spain, the Netherlands, Norway, the Czech Republic, Latvia, Slovakia, Portugal, Italy and Lithuania for data access to their national samples of the European Structure of Earnings Survey 2002. In order to fulfil data protection and confidentiality restrictions, the research was conducted through online remote access (LISSY System) to the microdata. I wish to thank Tanvi Desai for excellent technical support with the LISSY remote system and David Marsden, Francis Kramarz, Alex Bryson and other participants in the project for their helpful comments.

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

 EIRO (2005). For Portugal, Statutory minimum wage/Median gross wage. In Norway and Italy there not exists a national statutory minimun wage and collective bargaining is the regulatory mechanism of low-wages. c [START_REF] Christofides | The Gender Wage Gaps, 'Sticky Floors' and 'Glass Ceilings' of the European Union[END_REF]. The composite index is the sum of indicators on policies about work-family issues (such as parental leaves and child-care policies) and is scaled in order to have a zero mean and standad deviation equal to unity. d The employment rate gap is the difference between the employment rate (calculated by dividing the number of persons aged 15 to 64 in employment by the total population of the same age group) of males and females. The indicator is based on the EU Labour Force Survey. e Agreement (as measured by the proportion of respondents of the total population) to the statement in the 1999-2001 wave of the World Value Survey.


Joergen ; Kjaer
email: joergen.kjaer@fli.bund.de

Friedrich

Scholz

GLAWATZ, H J B Kjaer

Dr Joergen B Kjaer

Reducing stress during welfare inspection: validation of a non-intrusive version of the 1 LayWel plumage scoring system for laying hens 2 3

Keywords: Behaviour, Welfare, Feather pecking, Laying hens, Physiology, Stress

. 50

, (2) impose as little disturbance to the birds as possible, and (3) be time-60 effective, enabling the user to score a large number of birds under commercial conditions in a

version (RLS) of the LayWel plumage scoring system in domestic laying hens with reference 21 to complete, intrusive scoring (CLS) and to investigate the effect of these two scoring 22 methods on corticosterone metabolite concentrations. 23 2. A total of 312 medium-heavy laying hens from 4 commercial hybrids kept in 24 floor pens 24 were scored by two experienced teams. Another 150 hens from two hybrids kept in 6 pens 25 were used for estimating scoring treatment effects on corticosterone metabolites in droppings. 26 3. Plumage scores were in general higher using the RLS method compared to the CLS 27 method. The agreement between teams for plumage scores (CLS) were on a high (total score) 28 to an excellent (single body part except breast and cloaca) level. 29 4. Birds subjected to CLS tended to have higher concentrations of corticosterone metabolites 30 in droppings 2 h after scoring compared with birds in the control treatment (not scored). Birds 31 subjected to RLS had intermediate concentrations. 32 5. It was concluded that a reduced version of the LayWel scoring system is a valid and 33 reliable scoring method which tends to induce less stress to the subjects than the original 34 Animal welfare inspection of laying hen flocks often includes the evaluation of plumage 38 condition which is considered to be an indirect measure of the amount of feather pecking in 39 the flock [START_REF] Hughes | Feather pecking and cannibalism in domestic fowls[END_REF]. Such scoring systems are important since recording the incidence of 40 feather pecking in a flock by direct observation is difficult and very time consuming. Several 41 methods of plumage scoring have been used, however, for practical reasons, subjective 42 scoring is by far the most common method. The methods are classified as (i) application of a 43 general score for the plumage of the whole body [START_REF] Hughes | The influence of strain and environment upon 281 feather pecking and cannibalism in fowl[END_REF][START_REF] Hill | Feather loss in layers[END_REF] and44 (2) application of a specific score for individual parts of the body [START_REF] Tauson | Evaluation of procedures for 307 scoring the integument of laying hens -Independent scoring of plumage condition[END_REF]; procedures which can raise plasma corticosterone concentrations within minutes (Kannan and 63 Mench, 1996). In addition, capturing a representative sample in floor or free range systems 64 can be difficult and there are potential risks of sampling errors. CLS fulfils the requirements 65 of the first criterion, but not the second and third. We therefore developed a reduced version 66 of the LayWel scoring system (RLS) by introducing two major changes: (1) scoring only 4 67 body parts (neck, back, wings and tail) and (2) scoring birds on the ground without catching 68 and handling birds at any point. To our knowledge, no results from objective recording of 69 physiological stress variables after a combination of catching, handling and plumage scoring 70 have yet been published. We therefore assessed adrenocortical activity non-invasively (by 71 quantifying corticosterone metabolites in the droppings) after scoring, comparing values 72 obtained with these two scoring methods with concentrations of un-scored controls. 73 Thus, the objectives of the present study were to (1) validate the reduced, non-74 intrusive version of the LayWel plumage scoring system in domestic laying hens (Gallus 75 gallus domesticus) with reference to the complete, intrusive scoring, and (2) to investigate the 76 effect of these two scoring methods on corticosterone metabolite concentrations. 77

MATERIALS AND METHODS 79

Animals, housing and management 80

A total of 1100 non-beak-trimmed chickens of 4 hybrid strains (ISA Warren (IW), Lohmann 81 Brown (LB), Lohmann Tradition (LT) and Tetra SL (TS)) were reared on litter floor and 82 housed at 16 weeks in 44 (11 per breed) partly (2/3) slatted floor pens (1.15 m wide x 4.10 m 83 long) at a stocking density of 6 hens per m 2 (25 hens per pen) and with a communal nest at the 84 rear of the pen. Layer mash (200 g CP/kg, 11.2 MJ ME/kg feed) and water were supplied ad 85 libitum. A 14L:10D light programme was applied with an approximate light intensity of 15 86

Data collection 90

Plumage scoring 91

Plumage condition of 312 hens was scored at the age of 73 weeks by two teams, each 92 consisting of two scorers and one assistant. Both teams scored the same 13 hens from each of 93 22 randomly chosen pens (6 per breed of LB and LT, 5 pens per breed of ISA and TB). The 94 practical scoring procedure consisted of the following steps: 95

(1) All hens were shepherded gently to one half of the pen and kept there by dividing it with a 96 catching frame made of steel and wire netting. 97

(2) Hens were separated by an assistant and individually guided through an opening to the 98 other half of the pen, while the scorers were standing nearby (2-3 m) scoring (blind to the 99 other scoring team) and recording the scores on paper (RLS method, see below). 100

(3) The assistant then caught, marked and crated the hen that had just been scored. Blue dye 101 marks on the legs enabled the second team to identify and score the same birds previously 102 scored by the first team, in order to produce independent scores by both methods on each bird. 103

The second team thus produced a CLS score blind to the RLS score given by the first team. 104 (4) After scoring, birds were immediately released back into the pen, thus avoiding the risk of 105 recapture. 106

The Complete LayWel Plumage Scoring System (CLS) is described in the 107 Introduction. Supplementary material with colour illustrations is available at the LayWel 108 homepage (LayWel, 2005) and also in Tauson et al. (2007). In the present experiment, only 109 that part of the integument representing plumage quality was used and validated and this 110 system will be called the 'complete LayWel plumage scoring system' (CLS). 111 The Reduced LayWel Plumage Scoring System (RLS) introduced two major changes: 112

(1) scoring only 4 body parts, neck, back, wings and tail, and (2) scoring birds on the ground 113 without catching and handling birds at all. The scorer stood outside the pen during the 114 scoring, thus minimising disturbance. 115

No scoring was carried out in the control treatment (CON) and no humans stood in 116 front of the pen. Only normal animal care, as practised in the other pens in the house, was 117 permitted. 118 119

Measurement of corticosterone metabolites 120

Three pens of LB and three pens of LT hens, not previously scored for plumage condition, 121 were used to investigate the effect of scoring method and genotype on stress hormone 122 metabolites. One of three scoring methods was applied to each genotype: CLS, RLS or CON. 123 In CLS, all birds of a pen were caught and crated before scoring 30 min later. Birds were 124 scored while handled and released into the pen again. In RLS, the scorer went to the front of 125 the pen, opened the door and scored the birds individually from a distance; scoring time was 126 approximately 5 min per pen. In CON, there was no scoring or crating and no humans stood 127 in front of the pen. Excreta samples (consisting of faeces and urates together) were taken from 128 all hens in a pen beginning 120 min after initiation of the treatment. Excreta sampling lasted 129 approximately 20 min per pen. Only samples of adequate size (>0.1 g) from 86 out of a total 130 of 133 sampled birds were analysed. Samples were frozen at -21ºC until later analysis for 131 3,11-dione glucocorticoid metabolites, as described by [START_REF] Rettenbacher | 294 Measurement of corticosterone metabolites in chicken droppings[END_REF] using a 132 cortisone enzyme immunoassay previously validated for chicken excreta (Rettenbacher et al., 133 2009)

Plumage scoring 137

For each combination of method (CLS, RLS) and scoring team (A, B), a total feather score 138 for each hen was calculated by summing the scores for each body region and then calculating 139 the average score per pen. This score had a minimum of 4 points (1 p per body part × 4 body 140 parts) and a maximum of 16 points (4 x 4) for the RLS method, summing scores for neck, 141 back, wings and tail. For the CLS method, two sums were calculated; a partial sum used for 142 comparing methods was calculated exactly like for the RLS method, summing neck, back, 143 wings and tail. Further, a complete sum was calculated for testing repeatability of teams 144 within this method, summing neck, back, tail, wings, breast and cloaca, thus making the 145 maximum possible sum 24 points per hen. 146

Pen average plumage score was the statistical unit. Method (CLS, RLS), team (A, B), 147 the interaction between method and team, and genotype (LT, LB, TS, IW) were included as 148 fixed factors into a mixed model procedure in SAS (SAS Inst. Inc., Cary, Il, USA). Method 149 and team were included as repeated measures [START_REF] Littell | SAS 292 System for Mixed Models[END_REF], and normal distribution of 150 residuals was accepted after visual inspection. 151 152

Reliability of methods and teams 153

The between-method and between-team reliability were estimated using several measures of 154 agreement, namely kappa, weighted kappa and prevalence-adjusted bias-adjusted kappa 155 (PABAK), since there is controversy as to the best statistic. The kappa statistic alone is 156 appropriate if the marginal totals for the 2 x 2 table are relatively balanced, but if the 157 prevalence of a given response is very high or low, the value of kappa may indicate poor 158 agreement even when the observed proportion of agreement is quite high. Therefore we also 159 present the prevalence-adjusted bias-adjusted kappa (PABAK) to more fully characterise the 160 extent of the agreement between the two methods and teams respectively [START_REF] Byrt | Bias, prevalence and kappa[END_REF]. 161 The procedure FREQ of SAS was used to calculate kappa, asymptotic standard error, 162 standardised test statistic, the P value for testing the two-sided hypothesis Pr > |T|, and 163 weighted kappa. A custom-written SAS-program was used to calculate PABAK, following 164 [START_REF] Cunningham | More than Just the Kappa Coefficient: A Program to Fully 264 Characterize Inter-Rater Reliability between Two Raters[END_REF] and using the formula PABAK = ([k + p]-1)/(k-1), where k is the number 165 of categories and p the proportion of agreement. According to [START_REF] Fleiss | Statistical methods for rates and proportions, 268 3rd edition[END_REF], a PABAK 166 score larger than 0.40 can be interpreted as good agreement and a score larger than 0.75 as 167 excellent agreement. 168 169

Hormone data 170

Glucocorticoid metabolite concentrations, with pen mean as statistical units, were subjected to 171 one-way analysis of variance using the GLM procedure of SAS. Post hoc inspection of the 172 data revealed no effects of hybrid and the model included treatment only (CLS, RLS, CON). 173

RESULTS 175

Plumage scoring 176

Effects of method, team and genotype 177

Plumage scores were significantly higher for the wings and tail with the RLS method and for 178 the neck and tail by team A. Total scores were subsequently significantly higher for the RLS 179 method and team A (see Table 1). Significant interactions were found between method and 180 team for neck, wings and tail score (Table 1). Only neck score showed a significant main 181 effect of genotype, with LB and TS having slightly lower scores even though pair-wise 182 differences were not significant (Table 1

Agreement between methods and teams 187

In general, kappa and weighted kappa values between methods and teams for the total 188 plumage score ranged from 0.25 to 0.34 and all were significantly larger than zero (Table 2). 189 PABAK values for total scores were higher (0.35 to 0.55). Scoring the single body parts gave 190 excellent PABAK scores ranging from 0.75 to 0.97, with a few (cloaca and breast) being 191 somewhat lower (0.73 and 0.40 respectively) ( The results showed that it is possible to obtain good precision by scoring birds at a distance 204 compared with catching them and scoring while handling. Furthermore, we found that 205 adrenocortical activity tended to be highest when birds were scored after catching and 206 handling, intermediate when scored at a distance, and lowest when not scored at all. 207 RLS scored significantly higher on all body parts than CLS. The same finding (RLS 208 scoring lower damage than CLS) was reported by [START_REF] Bright | A non-intrusive method of assessing 262 plumage condition in commercial flocks of laying hens[END_REF]. It makes sense that 209 more damage is recorded when (1) birds are closely inspected (handled) and (2) when the 210 number of body parts scored increase. In addition, teams scored significantly differently. This 211 Agreement between teams using the CLS method, based mainly on PABAK scores, 214 were high for total plumage scores and excellent for single body regions, except for the breast 215 and cloaca. These findings are comparable to those found when validating the original version 216 of the LayWel scoring system [START_REF] Tauson | Evaluation of procedures for 307 scoring the integument of laying hens -Independent scoring of plumage condition[END_REF] and other plumage scoring systems 217 [START_REF] Adams | Effects of flock size, age at 252 housing, and mating experience on two strains of egg-type chickens in colony cages[END_REF][START_REF] Bright | A non-intrusive method of assessing 262 plumage condition in commercial flocks of laying hens[END_REF]. Interestingly, the somewhat lower agreement 218 between teams within CLS for the body parts breast and cloaca indicates that these body parts 219 are more difficult to score and special attention should be given here during the introduction 220 and training phase for scoring teams. Agreement was very high for the back score, which is 221 one of the most important areas for estimating the extent of feather pecking in the flock. 222

Our data support and extend those of [START_REF] Bright | A non-intrusive method of assessing 262 plumage condition in commercial flocks of laying hens[END_REF], who compared handling vs. 223 scoring at a distance using a scoring method [START_REF] Bilcík | Changes in feather condition in relation to feather 255 pecking and aggressive behaviour in laying hens[END_REF] only slightly different 224 to the one used in the present study. The two methods (handling vs. distance) used by Bright 225 et al. (2006) were found to be significantly correlated. However, there was a potential risk of 226 recapture in the investigation of [START_REF] Bright | A non-intrusive method of assessing 262 plumage condition in commercial flocks of laying hens[END_REF], thus possibly inflating the correlation. In 227 the present study this problem was overcome by the experimental design. 228

To our knowledge, this is the first study to investigate the potential of plumage scoring 229 to elicit physiological stress responses. The differences (45-65 ng/g) in corticosterone 230 metabolite concentrations between controls and treated birds were smaller than those reported 231 by [START_REF] Janczak | Effects of stress in 283 hens on the behaviour of their offspring[END_REF], who found elevations of between 100 to 250 ng/g faecal 232 corticosteroid metabolites when unpredictable feeding schedules were applied to hens. 233 Baseline levels were very similar in the present experiment to those of Janzak et al. (2006), 234 even though, among other things, genotypes differed (White Leghorns vs. medium-heavy 235 strains). This is in accordance with findings of [START_REF] Fraisse | Corticosterone and fear behaviour in white and 270 brown caged laying hens[END_REF] [START_REF] Riber | Effect of brooders on feather pecking 300 and cannibalism in domestic fowl (Gallus gallus domesticus)[END_REF]. 240

In conclusion, a reduced version of the LayWel scoring system is a valid and reliable 241 scoring method which tends to induce less stress to the subjects than the original procedure. 242

The scores cannot, however, be expected to equal those obtained with the complete method.

  The objectives of the present study were to validate a reduced, non-intrusive 20

  time, and without stressing the birds. Capture and handling are stressful 62

  hens were part of an experiment investigating the design of 'on farm' performance 87 tests of laying hen hybrids for organic egg production. 88 89

  known risk and the effect is normally balanced and included in the statistical models 212 used. 213

F

  . Data were expressed as ng hormone equivalent per g excreta.

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	134 135	O n l
	136	Statistical analysis	y

Table 2

 2

	). Kappa values for these body parts

Table 1 .

 1 Plumage score (least squares means) for methods (CLS = complete LayWel scoring; RLS = *, ** or *** indicates a significant effect with P <0.05, P <0.01 or P <0.001 respectively 3272 After Tukey-Kramer adjustment for multiple tests, no pair-wise differences between genotypes were significant 328

	316
	317	reduced LayWel scoring), teams and genotypes ( IW = ISA Warren, LB = Lohmann Brown, LT =
	318			Lohmann Tradition and TS = Tetra SL)
	319
	320	Body part	Method	Team	Genotype	P values 1
	321		CLS RLS A	B IW	LB	LT	TS	Meth. Team M*T Genotype
	322	Neck	2.28 2.29 2.36 2.21 2.35 2.22 2.36 2.21 ns	**	*	* 2
	323	Back	3.68 3.77 3.71 3.74 3.62 3.68 3.76 3.84 ns	ns	ns	ns
	324	Wings	3.58 3.78 3.71 3.65 3.74 3.62 3.71 3.65 *** ns	*	ns
	325	Tail	3.62 3.84 3.76 3.70 3.65 3.71 3.86 3.71 *** *	**	ns
	326	Total (CLSP) 13.2 13.7 13.5 13.3 13.4 13.2 13.7 13.4 *** *	ns	ns

1

Page 15 of 17 E-mail: br.poultsci@bbsrc.ac.uk URL: http://mc.manuscriptcentral.com/cbps British Poultry Science

Table 2 .

 2 Measures of agreement between methods (CLS = Complete LayWel Scoring; RLS = Reduced LayWel Scoring) within teams (A and B) 329and between-teams within methods. SE(kappa), Z and P<|Z| are the asymptotic standard error, the standardised test statistic and the P value of 330 the two sided test of the simple kappa, respectively

	331
	332
	333	Comparison	Variable	Neck	Breast Back Wings Tail Cloaca	Total 1
	334
	335	Method CLS vs. RLS
	336	Within team A
	337	Kappa		0.59	-	0.62 0.51 0.23 -	0.28
	338	SE(kappa)	0.05	-	0.05 0.05 0.05 -	0.04
	339	Z		11	-	13	10	5	-	9
	340	P < |Z|		***	-	*** *** *** -	***
	341	Weighted Kappa	0.63	-	0.70 0.54 0.26 -	0.52
	342	PABAK	0.84	-	0.90 0.84 0.75 -	0.47
	343	Within team B
	344	Kappa		0.69	-	0.74 0.45 0.32 -	0.34
	345
	346	SE(kappa)	0.06	-	0.05 0.05 0.05 -	0.04
	347	Z		13	-	16	9	6	-	11
	348	P < |Z|		***	-	*** *** *** -	***
	349	Weighted Kappa	0.73	-	0.79 0.53 0.40 -	0.61
	350	PABAK	0.94	-	0.95 0.78 0.77 -	0.53
	351
	352	Team A vs. B
	353	Within method CLS
	354	Kappa		0.60 0.18 0.78 0.72 0.64 0.38	0.25
	355	SE(kappa)	0.05 0.04 0.05 0.05 0.05 0.06	0.03
	356	Z		11	5	15	13	12	6	11
	357	P < |Z|		*** *	*** *** *** ***	***
	358	Weighted Kappa	0.64 0.41 0.83 0.76 0.69 0.42	0.61
	359	PABAK	0.87 0.40 0.96 0.90 0.87 0.73	0.35
	360

ACKNOWLEDGMENTS 245

The authors thank Brigitte Müller and Anna-Lea Kopmann for valuable technical assistance. 246 247