H Benoit-Cattin

F Bellet

J Montagnat

C Odet

MAGNETIC RESONANCE IMAGING (MRI) SIMULATION ON A GRID COMPUTING ARCHITECTURE

. The results presented show that simulation of 3D MRI data is achieved with a reasonable cost which gives new perspectives to MRI simulations usage.

INTRODUCTION

The simulation of Magnetic Resonance Imaging (MRI) is an important counterpart to MRI acquisitions. Simulation is naturally suited to acquire theoretical understanding of the complex MR technology. It is used as an educational tool in medical and technical environments [START_REF] Torheim | A simulator for teaching MR image contrast behavior[END_REF][START_REF] Rundle | Magnetic resonance imaging simulator: A teaching tool for radiology[END_REF]. By offering an analysis independent of the multiple parameters involved in the MR technology, MRI simulation permits the investigation of artifact causes and effects [START_REF] Brenner | Removal of artifacts in steady-state multipulse sequences[END_REF][START_REF] Olsson | A computer simulation program for MR imaging: Application to RF and static magnetic field imperfections[END_REF]. Likewise simulation may help in the development and optimization of MR sequences [START_REF] Brenner | Optimization of ultrafast multiple sequences for dynamic MR sequences[END_REF].

With the increased interest in computer-aided MRI image analysis methods (segmentation, data fusion, quantization ...), there is a greater need for objective methods of algorithm evaluation. Validation of in vivo MRI studies is complicated by a lack of reference data (gold standard) and the difficulty of constructing anatomical realistic physical phantoms. In this context, an MRI simulator provides an interesting assessment tool [START_REF] -S. Kwan | An extensible MRI simulator for post-processing evaluation[END_REF] since it generates 3D realistic images from medical virtual objects perfectly known.

In 1984, Bittoun et al. built one of the first 1D MRI simulator by numerically solving the Bloch equations [START_REF] Bloch | Nuclear induction[END_REF] at each point in an object [START_REF] Bittoun | A computer algorithm for the simulation of any nuclear magnetic resonance (NMR) imaging method[END_REF]. The same technique was later applied to 2D and 3D objects by Summers et al. [START_REF] Summers | A computer simulation of nuclear magnetic resonance imaging[END_REF] and Olsson et al. [START_REF] Olsson | A computer simulation program for MR imaging: Application to RF and static magnetic field imperfections[END_REF]. Brenner et al. have proposed a distributed implementation of these computationally intensive simulations [START_REF] Brenner | Distributed large-scale simulation of magnetic resonance imaging[END_REF]. In the domain of brain imaging, Kwan et al. [START_REF] -S. Kwan | An extensible MRI simulator for post-processing evaluation[END_REF][START_REF] Kwan | MRI simulation based evaluation of image processing and classification methods[END_REF] have limited the computation time by using templates of the main brain tissues. Nevertheless, MRI simulation is still under investigation in order to simulate high resolution MR images including MRI artifacts (Magnetic susceptibility, chemical shift, diffusion, …) that may impact the quantitative measurements required for several MRI applications.

In this context, we develop, in collaboration with the CNRS LRMN-MIB 1 lab and with CEMAGREF/TEA 2 research unit, a 3D MRI simulator named SIMRI that is designed to simulate realistic high resolution 3D MR images. Since simulation of the MR physics is computationally very expensive [START_REF] Brenner | Distributed large-scale simulation of magnetic resonance imaging[END_REF], parallel implementation is mandatory to achieve performances compatible with the target applications. By offering a virtually unlimited computing power, grid technologies appear to be promising.

In this paper, we focus on the grid implementation of this simulator. Parts II gives the main components of the simulation process. Part III details the "gridification" of the computation kernel and presents the main results.

MRI SIMULATION

2.1

Simulator overview MR imaging [START_REF] Liang | Principles of magnetic resonance imaging. A signal Processing perspective[END_REF] involves the nuclear spin system of an object to be imaged, the magnetic fields generated by the imager, the resonance and relaxation phenomena arising from the interaction nuclei / magnetic fields, and the signal detection and reconstruction. All these components are taken into account by the SIMRI simulator (Figure 1). From a virtual object and a MRI sequence, the magnetisation computation kernel computes the RF signals named k-space. The final MR image is reconstructed from the k-space with generally a 3D fast Fourier transform [START_REF] Liang | Principles of magnetic resonance imaging. A signal Processing perspective[END_REF].

2.2

Virtual object description The virtual 3D object is a discrete description of a real object spin system [START_REF] Liang | Principles of magnetic resonance imaging. A signal Processing perspective[END_REF]. Each voxel of the virtual object contains a set of physical values necessary to computes with the Bloch equations the local spin magnetization. These values are the proton density noted ρ and the two relaxation constants T 1 and T 2 . Basically, a virtual object describes the nuclear spin system of one isochromat, the water hydrogen atom. Note that SIMRI is able to deal with many isochromats in order to simulate chemical shift artifact [START_REF] Liang | Principles of magnetic resonance imaging. A signal Processing perspective[END_REF] (Figure 2) or partial volume effect. In this case, each voxel contains the ρ, T 1 , T 2 values of each isochromat.

A local main field homogeneity is also attached to each virtual object voxel. This value is used to simulate inhomogeneous main field and/or susceptibility artifact.

A virtual 3D object of size S= X.Y.Z voxels is then described by (3p+1).S values where p is the number of isochromats modeling to each object point.

MRI Sequence

During an MRI experience, an object is placed in a static magnetic field named B 0 and is excited by electro-magnetic events of two types: Radio Frequency (RF) pulse referred as B 1 field and magnetic fields gradients. Excitation steps are followed by an RF acquisition step. It corresponds to the MRI system antennas acquisition of the magnetization state of the object which is stored as a complex signal in the kspace [START_REF] Liang | Principles of magnetic resonance imaging. A signal Processing perspective[END_REF]. The time chaining (Figure 3) of the magnetic events with RF signal acquisitions is named MRI sequence. It defines the way of filling the k-space and determines the final image characteristics.

It must be noted that a MRI sequence in the simulator has the same components and the same time schedule than in a real system.

RF acquisition

) (t M r ) ( 1 t M r ) ( 2 t M r Magnetic event k-space filling

Magnetization kernel

The magnetization computation kernel called during the simulation of an MRI sequence is based on the solving of the 3D Bloch equation [START_REF] Bloch | Nuclear induction[END_REF]. It is a linear differential equation describing the time evolution of the spin magnetization and it is given by :

          - - × = 1 0 2 2 / ) ( / / ) .( T M M T M T M B M dt M d z y x r r r γ (1)
where

T z y x M M M M ) , , ( = r
is the spin magnetization vector, M 0 is the spin magnetization equilibrium value which depends of the proton density ρ, (T 1 , T 2 ) are the relaxation constants and γ is the gyromagnetic constant of the considered isochromat (42.58 MHz/T for the Hydrogen proton). The magnetic field B is modeled as follows :

) ( ). ). ( ( 1 0 t B z r t G B z B B r r r r r r r + + ∆ + = (2)
where B 0 is the main static magnetic field, B r ∆ are the The simulation kernel implements a discrete time solution [START_REF] Bittoun | A computer algorithm for the simulation of any nuclear magnetic resonance (NMR) imaging method[END_REF] of the Bloch equation with the means of rotation matrices and exponential scaling which depend of the magnetic events of the MRI sequence. The magnetization vector evolution is computed from its previous time value according to the following equation:

) , ( . . ). ( ). ( ) , ( t r M R R Rot Rot t t r M RF relax i g r r r r θ θ = ∆ + (3)
where Rot(α) is a rotation matrix defined by:

          - = 1 0 0 0 cos sin 0 sin cos ) ( α α α α α Rot (4)
where Ø g is linked to the applied gradient

) (t G r by: ∫ ∆ + = t t t g d G r τ τ γ θ ) ( . . r r (5)
where Ø i is linked to the field inhomogeneities by:

t r B i ∆ ∆ =
). ( . r γ θ [START_REF] Olsson | A computer simulation program for MR imaging: Application to RF and static magnetic field imperfections[END_REF] where R relax describes the relaxation effect by: and where R RF represents the rotating effect of an RF pulse of phase angle φ leading to a flip angle α defined by: To design an MRI sequence, the magnetization computation kernel (based on equation 3) offers three functions which are application of RF pulse, application of gradient, and waiting which corresponds to the spin magnetization relaxation.

                = ∆ - ∆ - ∆ - ) ( ) ( ) (
          - + - - - + = α α φ α φ α φ α φ φ α φ φ α φ α φ φ α φ
One can notice in equation 3 that the magnetization vector at a given localization depends only on the previous magnetization vector at the same position. This property will be used by the gridification of the simulation kernel.

The last functionality offered by the kernel is the RF signal acquisition (Figure 3) which corresponds to the acquisition by two antennas in the x,y plane of the magnetization state of the object after a given excitation. The RF signal is a one dimensional discrete complex signal that will fill in respect with the excitation sequence one line of the k-space volume.

One point k of the RF signal is obtained by summation of the local magnetization over all the virtual object (Eq. 9). The next point is obtained after an evolution of the local magnetization respecting equation 3 with a time step ∆t equal to the sample period of the signal. This linearity property will be exploited by the grid architecture.

∑ ∑ + = n n n n y t M j x t M k s r r r r ). ( ). ( ] [ (9)
From equation 3 and equation 9, it appears that the simulation of one magnetization evolution is proportional to the virtual object dimension (X.Y.Z), while the simulation of the whole k-space acquisition is proportional to the object size and to the MRI image size ( N.M.P). The whole simulation time of a 3D sequence (T s ) is then given by: ] ) . . ).[( . . .(

ex s N P N M Z Y X c T + = (10)
where c is a constant and N ex is the number of magnetic events simulated before an acquisition.

In a MRI sequence, N ex is negligible comparing to the MRI image size. So, as an example, multiplying by two all the dimensions of the virtual object and the MR image leads to a simulation time multiplication by 16 in two dimensions and by 64 in three dimensions.

If the simulation of small images (128x128 pixels) is done within a minute on a Pentium IV PC, equation 10 shows that high resolution MRI 3D simulation is not practicable on such a computer. Therefore, we turn toward Grid technologies that promise a virtually unlimited computing power.

GRID IMPLEMENTATION AND RESULTS

The whole code of the SIMRI simulator is written in ANSI C language. One module concerns virtual objects manipulation, one set of modules implements MRI sequences, one module deals with image reconstruction and the final set of modules is related to the magnetization computation kernel.

Profiling the execution of a SIMRI simulation indicates the percentage of time spent in each part of the simulation code. It appears clearly that most of the time (more than 90 %) is spent in the computation kernel specifically on the rotational and exponential scaling needed by the Bloch equation resolution. Consequently, we focused our parallelisation efforts on the kernel code in order to have a grid implementation of the simulator. This modification has to be almost transparent for MRI sequence developers .The gridification of the kernel must be done using the MPI [START_REF]MPICH[END_REF] version of GLOBUS [START_REF] Globus | [END_REF] since the middleware targeted for this application is the European DataGrid project [START_REF]European DataGrid project[END_REF] built on top of GLOBUS.

3.1

Gridification of the magnetization computation kernel Because all the spin magnetization vectors are independents (Equation 3) and because the signal acquisition process is linear (Equation 9), many solutions for parallelisation can be considered.

One solution consists in distributing a minimal task which is to compute the new magnetization sate of a single spin vector. In this case, the granularity is maximized but the time of node communication will be predominant compared to the computation time. The second approach consists in distributing the magnetization computation of a subset of spin vectors. This subset can be fixed to a given size or adapted to the number of active nodes. We have selected this last solution and since each computation node has a set of magnetization vectors, this node will compute the contribution of these vectors to the RF signal generated during an acquisition step.

The data and process distribution to the grid nodes is given in Figure 4. All the computation nodes have the MRI sequence knowledge and they receive from the master node a part of the virtual object. They compute the magnetization evolution of the corresponding spin vector subset. At the end of each acquisition step, the master node collects and add all the RF signal contributions and stores the RF signal in the k-space. At the end of the MRI sequence, the master node applies the reconstruction algorithm to generate the MRI simulated image.

This solution is scalable and follows a simple parallelisation scheme of type "divide & conquer" with a regular problem of space division. Two types of activities are defined: computation of subset for N-1 nodes and results collect for one node. The time dedicated to the node communication is minimized since each node received only one task. Nevertheless, this solution drawback is a low granularity introducing loss of efficiency on heterogeneous grid. Indeed, all the computation nodes have the same amount of data to process and then the lowest node will give the timing.

Results

The results presented here have been obtained on a 8 nodes cluster. Each node is a Pentium III-1Ghz with 1Go of RAM. We run the MPICH-G2 [START_REF]MPICH[END_REF] version of MPI associated to Globus 2.2 [START_REF] Globus | [END_REF] for the grid access control. First of all, we have compared the efficiency of using our grid compared to a single machine. When the virtual object size is over 2 10 , the average efficiency of each grid node is over 87 % meaning that the simulation time is divided by 7 at least. Since one node out of eight is just collecting results and reconstructing the image, this means that the seven computation nodes have an efficiency close to 100 %.

This very good efficiency is due to the homogeneity of our grid and to the kernel gridification chosen which minimizes the number and the size of the exchanged messages as shown in figure 5. For a 256 2 simulation, during an acquisition step, messages exchange and nodes synchronization takes 0.13 s compared to 2.5 s of computation time which corresponds to 5.2 % of the computation time. Table 1 shows that when the size of the virtual object increases this percentage decreases until a limit of 1.5 %. This limit is due to one node of our grid which is systematically late compared to the others. The grid implementation of our simulator have been tested on 2D and 3D MRI Spin echo sequences applied on synthetic virtual objects of different sizes (Figure 67). Simulation time results are given in Tables 2 and3. One can note that after a given size (128 2 and 64 3 ) the time factor induced by the dimension change follows the rule of equation 10. Before these size, the communication and synchronization time is too important compared to the process time (Table 1 These simulation results obtained are very encouraging since it shows that with a small cluster, MRI simulation of high resolution (1024²) 2D objects is possible within three days. Concerning 3D images, it is not realistic to simulate on such a small set of processors over 64 3 cubic MRI images. Nevertheless, it is possible to simulate within a week 3D multislice images (16 slices of 512x512 pixels). The simulation of high resolution 3D images should be tractable on full scale grids like the ones actually in development [START_REF]European DataGrid project[END_REF]

CONCLUSION

In this paper, we present a grid implementation of a 3D MRI simulator based on Block equations. The gridification is done in the magnetization computation kernel of the simulator and makes it transparent at the sequence level used by MRI sequence developers. The gridification strategy makes the simulator very efficient on an homogeneous grid. Results obtained on an 8 nodes cluster show that high resolution MRI simulation is possible at a reasonable cost. This is very encouraging for the different researches using MRI simulation like artifact analysis and correction or MRI post-processing [START_REF] Kwan | MRI simulation based evaluation of image processing and classification methods[END_REF].

Further works under development include analysis of MRI simulation performance on a larger grid and tests of different strategies for gridifying the computation kernel. Evolutions of the MRI simulation model is also under consideration in order to simulate more complex physical phenomena.

Figure 6 : Example of a simulated MRI image( 512x512 pixels) using a ρ weighted spin echo sequence. The virtual object is composed by an elliptic zone (T1=350 ms, T2=75ms, ρ=60), a square zone (T1=2500 ms, T2=200 ms, ρ=100) and a circular zone (T1=500 ms, T2=90 ms ρ=70).

ACKNOWLEDGEMENT

This work is in the scope of the scientific topics of the PRC-GdR ISIS research group of the French National Center for Scientific Research CNRS. This work is partly supported by the IST European Data-Grid Project [START_REF]European DataGrid project[END_REF] and the French ministry for research ACI-GRID project [START_REF] Medigrid | French Research Ministry[END_REF]. This work has been also funded by the INSA Lyon. We want to thank our partners in the SIMRI project, H. Saint-Jalmes and O. Beuf from the CNRS LRMN-MIB lab, G. Collewet from the CEMAGREF / TEA Research Unit and S. Balac from the CNRS MAPLY lab. The SIMRI project has been initiated thanks to the work done by G. Soufflet and H. Saint-Jalmes on the initial 1D MRI simulator of J. Bittoun.

Figure 1 :

 1 Figure 1 : SIMRI Simulator overview.

Figure 2 :

 2 Figure 2 : 256² simulation of the chemical shift artifact using a two isochromats (water and fat) virtual object. The white and black part at the left and the right of the central circle correspond to the artifact.

Figure 3 :

 3 Figure 3 : MRI sequence time chaining reproduced by the simulator computation kernel.

Figure 4 :

 4 Figure 4 : Data and Process distribution to the grid nodes.

Figure 5 :

 5 Figure 5 : Nodes activity reported by XMPI during a 256 2 2D spin echo simulation using MPI instead of MPICH. Horizontal bars correspond to the 8 nodes activity between 0 and 16.94 seconds. Vertical white bars correspond to MPI message exchange at the end of RF signal acquisition.

Figure 7 :

 7 Figure 7 : 3D visualization of a simulated MRI image (64x64x64 voxels) using a T1 weighted 3D spin echo. The virtual object is composed by an elliptic zone (T1=500ms, T2=90 ms, ρ=70 ) and a spherical zone (T1=350 ms, T2=375 ms, ρ=60).

Table 2 :

 2 ).

	Object size	32²	64²	128²	256²	512²	1024²
	Time	0.9 s	3.4 s	43.1 s	12 m 201 m 3277 m
	Time factor	-	3.8	12.7	16.7	16.8	16.3

2D MRI simulation computation time on a 2D spin echo sequence function of the object size. Virtual object and simulated image have the same size.

  .

	Object Size	16 3	32 3	64 3	128 3
	Time	4.9 s	3.5 m 210 m 1626 m
	Time factor	-	42.9	60	7.7
	Table 3 : 3D MRI simulation computation time on a 3D
	spin echo sequence. Virtual object and simulated image
	have the same size except for the 128 3 object where the
	simulated image is 64 3 explaining a time factor of 7.7
			instead of 64.


Ben Chiraz
email: chiraz.benali@supco-amiens.fr

Ali

Cédric Lesage
email: lesage@hec.fr

Ownership concentration and audit fees: do auditors matter most when investors are protected least?

Keywords: audit fees, controlling shareholder, minority expropriation, agency conflict

, 2000). Our results show 1) a negative relation between audit fees and managerial shareholding, which is stronger for common law than for civil law countries; 2) a curvilinear (concave) relation between audit fees and controlling shareholding for civil law countries; 3) no Type II conflict in the common law countries. These results illustrate the mixed effects of the legal environment and of each agency conflict on audit fees.

Ownership concentration and audit fees: do auditor matter most when investors are protected least?1

Introduction

Previous literature evidenced that civil law countries present weak investor protection compared to common law countries which gives shareholders incentives to hold large part of capital to better control managers (La [START_REF] Porta | Corporate ownership around the world[END_REF][START_REF] Porta | Investor protection and corporate governance[END_REF]. Consequently, ownership is more concentrated in civil law countries and the agency conflict between managers and shareholders (called type I agency conflict) is reduced [START_REF] Shleifer | A survey of corporate governance[END_REF][START_REF] Porta | Law and finance[END_REF][START_REF] Porta | Corporate ownership around the world[END_REF][START_REF] Denis | International corporate governance[END_REF][START_REF] Gillan | Corporate governance, corporate ownership, and the role of institutional investors: A global perspective[END_REF]. However, this situation gives controlling shareholders the possibility to profit from private benefits of control which raises a new agency conflict between controlling shareholders and minority shareholders (called type II agency conflict). Indeed, (La Porta et al. 2000, p. 4) assert that "Investor protection turns out to be crucial because, in many countries, expropriation of minority shareholders and creditors by the controlling shareholders is extensive".

Corporate governance is, to a large extent, a set of mechanisms through which outside investors protect themselves against expropriation by the insiders2 . We investigate a complementary firm-level corporate governance to better protect minority shareholders: auditing. Auditors' role is to increase trust on corporate information by reducing the possibility of manipulation of accounting numbers. Traditional audit fees model [START_REF] Simunic | The pricing of audit services: Theory and evidence[END_REF] explains that the amount of audit fees is a function of (1) the effort of the auditor during the engagement and (2) the risk incurred by the auditor after the disclosure of his/her audit report (risk premium). Consequently, agency conflicts should influence the risk premium [START_REF] Lafond | Managerial ownership and accounting conservatism[END_REF] and thus the audit pricing.

Most of prior research focuses on the impact of the type I agency conflict on audit pricing because they have been mainly made in common law countries, particularly in the USA and the UK where ownership is dispersed. These studies find a negative relation between management ownership and audit fees and conclude that audit plays a governance role to mitigate type I agency problems [START_REF] Agrawal | The dividend policies of all-equity firms: A direct test of the free cash flow theory[END_REF][START_REF] Gul | Free cash flow, debt monitoring, and audit pricing: Further evidence on the role of director equity ownership[END_REF][START_REF] Nikkinen | Does agency theory provide a general framework for audit pricing[END_REF]. To our best knowledge, only one study [START_REF] Fan | Do external auditors perform a corporate governance role in emerging markets? Evidence from east asia[END_REF] focuses on type II agency conflict across countries while this conflict is predominant in the world (La [START_REF] Porta | Investor protection and corporate governance[END_REF]. Indeed, controlling shareholders have the possibility to expropriate minority shareholders and profit from private benefits of control, therefore type II agency conflict is likely to influence audit pricing.

Moreover, [START_REF] Niemi | Audit effort and fees under concentrated client ownership: Evidence from four international audit firms[END_REF] and [START_REF] Hay | Audit fees: A meta-analysis of the effect of supply and demand attributes[END_REF] underline that very few studies examined the relation between ownership and audit fees and these studies present mixed results about the direction and the significance of the relation between ownership concentration and fee levels.

We suggest two alternative perspectives to explain these ambiguous results.

First, previous studies define ownership concentration as the insiders' ownership with the exception of only two studies [START_REF] Peel | The relationship between governance structure and audit fees pre-cadbury: Some empirical findings[END_REF][START_REF] Fan | Do external auditors perform a corporate governance role in emerging markets? Evidence from east asia[END_REF]. Therefore, previous research does not distinguish between both types of conflicts, which could potentially lead to conflicting effects on audit fees. In this study, we examine the impact of both agency conflicts separately.

Second, based on the results of La [START_REF] Porta | Investor protection and corporate governance[END_REF], we suggest that the legal system should play an important role in influencing audit fees risk premium related to agency conflicts (type I vs. type II agency conflicts). We then suggest that in weak investor protection countries, the relationship between audit fees and minority expropriation should be curvilinear (concave) while the few studies which isolate this conflict assumed its linearity. Namely, it is likely that a type II conflict first increases with the percentage of controlling shareholders ownership (entrenchment effect). Then, when controlling shareholders hold a very large part of capital, their interests could be expected to be aligned with the interests of minority shareholders, therefore mitigating type II agency problems and decreasing audit fees (alignment effect).

We use regression analyses on non financial listed companies over 17 countries (10 code law and 7 common law countries) on 2006-2008. We then focus on four countries (Germany and Franc for code law and UK and the USA for common law countries). First, the results of this study show a negative relation between management ownership and audit fees stronger in common law countries than in code law countries. We assume that type I agency conflict is less severe in firms where the manager hold large percentage of cash flow rights because he is more invested in the company, which leads to less effort from auditors and decreases the scope of the audit engagement. These results support the incentive alignment effect that suggests that management ownership contributes to align the manager interests with those of the investors. Therefore, auditors charge lower fees for firms where manager hold large shareholding than they do for firms where ownership and control is separated.

Second, we find different results depending on the country investor protection level for the relation between ownership concentration and audit fees. In lower investor protection environment (civil law countries), we find a significant quadratic relation between the controlling shareholders capital rights and audit fees. Audit fees first increase with the controlling shareholders ownership: audit could be seen here as a substitution mechanism to mitigate internal corporate governance weaknesses. Then, beyond a threshold of around 20-25%, the relation becomes negative. We assert that very high ownership concentration does not harm the interests of minority shareholders: cash flows resulting from the detention of shares are superior to the private benefits of control, which contribute to align the interests of controlling shareholders with the interests of minority. These results are consistent with the [START_REF] Williamson | Organization form, residual claimants, and corporate control[END_REF] substitution hypothesis.

In high investor protection countries (common law countries), our results show that controlling shareholding level does not influence audit fees. We therefore conclude that the type II agency conflict is non relevant in high investor protection (for instance the USA) and that auditors do not ask for a risk premium. Our results are coherent with the results of La [START_REF] Porta | Investor protection and corporate governance[END_REF] on investor legal system. In common law countries, the main agency conflict is the one opposing shareholders and managers.

We contribute to the existing literature in several ways. First, this is the first study that examines the influence of agency conflicts (type I and type II) on audit pricing in relation to investor protection and legal systems. Also, [START_REF] Niemi | Audit effort and fees under concentrated client ownership: Evidence from four international audit firms[END_REF] and [START_REF] Hay | Audit fees: A meta-analysis of the effect of supply and demand attributes[END_REF] notice the absence in audit research of studies on ownership structure, particularly the influence of non managerial ownership concentration on audit fees. Our study aims to fulfill this need in demonstrating that the relation between ownership concentration and fee levels depend on the investor protection legal system assuming two levels of investor protection (high: common law countries, weak: civil law countries). Then, in civil law countries, the relation is likely to be curvilinear: the behavior of shareholders depends of the level of ownership concentration.

This study therefore contributes to the research on corporate governance mechanisms in putting in evidence the effect of type II agency conflict (La [START_REF] Porta | Law and finance[END_REF]).

The paper is organized as follows. The next section (section 2) provides the theoretical framework and section 3 develops our hypotheses. Section 4 presents the research design and section 5 provides the sample selection procedures and descriptive statistics. Regressions results are disclosed in section 6 and discussed in section 7. Finally we summarize the main findings and limits of our study.

Investor protection and corporate governance

Ownership concentration as a substitute governance mechanism in low investor protection countries

La [START_REF] Porta | Law and finance[END_REF] first evidenced that the investor protection regulations and its enforcement vary across countries and legal families. They show that civil laws give investors weaker legal rights than common laws, the weakest protection being given by French-civil law countries (with German-civil-law and Scandinavian countries fallen between the other two). Then they wonder whether the poor protection countries have other substitute mechanisms of corporate governance. First, they check whether the quality of law enforcement substitutes or compensates for the quality of laws. Their results reject this hypothesis: the quality of the enforcement is the highest in the Scandinavian and Germancivil-law countries, next highest in common law countries, then again the lowest in Frenchcivil-law countries. If it does not exist at the country level, a substitute mechanism of corporate governance may be set by shareholders themselves. They therefore investigate a firm-level substitution mechanism: ownership concentration. They posit two main reasons for which ownership in weaker investor protection countries should be weaker. First, "large, or even dominant shareholders who monitor the managers might need to own more capital, ceteris paribus, to exercise their control rights and thus to avoid being expropriated by the managers" (La [START_REF] Porta | Law and finance[END_REF]Porta et al. , p. 1145)), which is especially true when legal protection is weak.. Second, small investors may not be willing to buy shares at high prices, because of the risk of expropriation: therefore, as firms are not likely to issue shares at low prices, this effect increases indirectly the ownership concentration.

La Porta et al 's (1998) results suggest that highly concentrated ownership may substitute at the firm level for weak investor protection stated at the country level. La [START_REF] Porta | Investor protection and corporate governance[END_REF] privilege the legal approach of corporate governance, which "holds that the key mechanism is the protection of outside investors (whether shareholders or creditors) through the legal system, meaning both laws and their enforcement". They suggest that the better investor protection stated in common law countries can be originated in both the judicial tradition and the political history [START_REF] Roe | Legal origins, politics, and modern stock markets[END_REF].

We posit that within the country level investor protection regulations, internal corporate governance mechanisms at the firm level remain pivotal to investor protection to compensate agency problems. La [START_REF] Porta | Law and finance[END_REF][START_REF] Porta | Investor protection and corporate governance[END_REF] themselves studied the ownership concentration. In relation to this stream, we want to investigate one specific corporate governance mechanism: auditing.

Auditing: a firm level substitute for investor protection

Since the role of auditing is to enforce the application of proper accounting polices (Francis and Dechun 2008, p. 157), auditing is part of the corporate governance system [START_REF] Francis | The role of accounting and auditing in corporate governance and the development of financial markets around the world[END_REF], whose cost has to be beard by the shareholders as one key component of monitoring costs [START_REF] Jensen | Theory of the firm: Managerial behavior, agency costs and ownership structure[END_REF]. It is therefore expected that the auditors will spend more time, relative to regular inspection of accounts, to inspect managers' activities if the agency problem is greater, which may lead to higher audit fees.

A large body of audit research has focused on the determinants of audit fees [START_REF] Hay | Audit fees: A meta-analysis of the effect of supply and demand attributes[END_REF] since the original seminal Simunic's work (1980). This author has developed an audit fees model which has become a landmark in audit research. Its starting point is that auditors are jointly liable together with the managers of the financial information quality vis-à-vis the financial statement users. Consequently, [START_REF] Simunic | The pricing of audit services: Theory and evidence[END_REF] develops an audit fees model that includes two components: audit effort and risk premium.

AUDFEE = p*q + E(L)
Where AUDFEE is the amount of audit fees, p: hourly pricing, q: number of auditing hours, E(L): risk premium, assessing the probability of expected losses.

The first component (p*q) represents the audit effort needed, which depends of the difficulty of the audit engagement. The determinants are mainly the size of the client and its organization complexity that is largely related to the industrial sector, internationalization degree, etc. The second element represents a premium related to the expected risk of paying post auditing losses in case of unveiled audit failure. [START_REF] Lyon | The importance of business risk in setting audit fees: Evidence from cases of client misconduct[END_REF] argue that much of the prior literature on auditor's risk focuses on litigation risk, which is the risks of incurring liability payments and of damaged reputation for the quality of its services [START_REF] Palmrose | Audit fees and auditor size: Further evidence[END_REF][START_REF] Francis | A test of audit pricing in the small-client segment of the u.S. Audit market[END_REF][START_REF] Simunic | The impact of litigation risk on audit pricing: A review of the economics and the evidence[END_REF][START_REF] Willenborg | Empirical analysis of the economic demand for auditing in the initial public offerings market[END_REF][START_REF] Venkataraman | Litigation risk,audit quality, and audit fees: Evidence from initial public offerings[END_REF][START_REF] Feldmann | Financial restatements, audit fees, and the moderating effect of cfo turnover[END_REF]. All these studies evidence the importance of risk premium component in the audit fees levels due to the positive relationship between audit fees and litigation risk.

Recently, research has also studied the impact of different legal environments on the audit fees risk premium. [START_REF] Francis | The role of accounting and auditing in corporate governance and the development of financial markets around the world[END_REF] evidence the effectiveness of auditing as an enforcement mechanism in limiting managerial opportunism across different investor protection regulation systems. [START_REF] Francis | The joint effect of investor protection and big 4 audits on earnings quality around the world[END_REF] show that auditor incentives change as investor protection regimes become stricter, and there is a greater likelihood that client misreporting is detected and auditors are punished. [START_REF] Choi | Cross-listing audit fee premiums: Theory and evidence[END_REF] argue that legal environments play a crucial role in determining the auditor's legal liability and show that auditors charge higher fees for firms that are cross-listed in countries with stronger legal regimes.

We extend this stream of research by focusing on the impact of differentiated agency conflicts across investor protection systems. [START_REF] Hay | Evidence on the impact of internal control and corporate governance on audit fees[END_REF] posit that previous studies generally suggest a substitution effect between internal corporate governance control and external auditing, hence better internal control is associated with lower audit fees. However, the evidence about this issue is mixed [START_REF] Hay | Evidence on the impact of internal control and corporate governance on audit fees[END_REF]. In their literature review on audit fees, [START_REF] Hay | Audit fees: A meta-analysis of the effect of supply and demand attributes[END_REF] advocated for further investigation on this topic as given the observed contradictory results.

Hypotheses development

According to La [START_REF] Porta | Law and finance[END_REF], the observed difference in ownership concentration between common law versus civil law countries should result from the difference in investor protection law. One consequence of this finding should be that agency conflicts are not similar in both systems. In common law countries, the consequence of a lower ownership concentration is that agency conflicts between shareholders and managers are more likely to exist (La [START_REF] Porta | Investor protection and corporate governance[END_REF], as shareholders have less monitoring and controlling power through their ownership. By contrast, firms in civil law countries are more likely to be owned and controlled by larger shareholders, which decreases the likelihood of having an agency conflict between them and the managers [START_REF] Shleifer | A survey of corporate governance[END_REF][START_REF] Porta | Investor protection and corporate valuation[END_REF], but increases the likelihood of agency conflicts between controlling shareholders and minority shareholders [START_REF] Shleifer | A survey of corporate governance[END_REF]. The next two sections will consequently develop both kinds of agency conflict and their respective impact on audit fees.

Low ownership concentration: a type 1 agency cost in high investor

protection law countries [START_REF] Jensen | Theory of the firm: Managerial behavior, agency costs and ownership structure[END_REF] distinguish between "insiders" (management and controlling shareholders) and "outsiders". The former control the firm, are part of their management or nominate their members because they hold exclusive voting rights while the latter do not have voting rights in excess to their cash flow rights. As strong investor protection countries are characterized by a low ownership concentration, it can therefore be hypothesized that the dominant agency conflict in these countries should be the conflict between the shareholders and the managers. According to [START_REF] Jensen | Theory of the firm: Managerial behavior, agency costs and ownership structure[END_REF], managerial ownership contributes to reduce type I agency conflicts (manager vs. shareholders), in aligning the interests of managers with those of the shareholders. It is considered as a complementary motivation for managers to incite themselves to better control the firm and then achieve better performance [START_REF] Jensen | The distribution of power among corporate managers, shareholders, and directors[END_REF][START_REF] Hart | Property rights and the nature of the firm[END_REF]. Consequently, in organizational structures characterized by high managerial ownership, the separation between ownership and control is lower and information asymmetry is weaker than in other organizations, which should result in a weaker demand of assurance (less monitoring cost). As a consequence, it can be hypothesized that monitoring costs, including audit fees, are higher for firms with lower manager ownerships, as argued by [START_REF] Agrawal | The dividend policies of all-equity firms: A direct test of the free cash flow theory[END_REF], [START_REF] Gul | Free cash flow, debt monitoring, and audit pricing: Further evidence on the role of director equity ownership[END_REF]. Indeed, DeFond (1992) posits that the extent of agency conflicts determines the degree of auditing needed to make management credible to current and potential investors.

Therefore, the higher the extent of the agency conflicts are, the higher the demand for audit quality should be.

Several studies have established relations between auditor choice or audit fees on the one hand and management ownership on the other hand. [START_REF] Agrawal | The dividend policies of all-equity firms: A direct test of the free cash flow theory[END_REF], [START_REF] Gul | Free cash flow, debt monitoring, and audit pricing: Further evidence on the role of director equity ownership[END_REF], [START_REF] Nikkinen | Does agency theory provide a general framework for audit pricing[END_REF] found a negative association between audit fees and management ownership. Other research shows that the probability to choose a big audit firms (audit quality) increase in firms where the information asymmetry is high between owners and managers [START_REF] Francis | Auditor changes: A joint test of theory relating to agency costs and auditor differentiation[END_REF][START_REF] Beatty | Auditor reputation and the pricing of initial public offerings[END_REF][START_REF] Defond | The association between changes in client firm agency costs and auditor switching[END_REF].

One of the main raisons explaining the decrease in demand of audit quality is that ownermanagers are more invested in daily operational duties. They are consequently more likely to better manage the company asset that non owner-managers. Abdel-khalik (1993, p. 49) suggests that "the voluntary demand for audit (positive) assurance emanates from the needs of owner/managers of privately owned companies to compensate for the loss of control associated with increasing organizational complexity". The amount of audit fees is increasing with the organizational complexity. Consequently, firms that are owned by their managers are likely to have weaker audit fees.

Another reason is related to managers' behavior toward the risk. [START_REF] Jensen | Agency costs of free cash flow, corporate finance, and takeovers[END_REF] shows that managers who invest their own money in the company are more risk adverse in their decisions than other managers with a more diversified portfolio. [START_REF] Lafond | Managerial ownership and accounting conservatism[END_REF] show that the decrease of managerial ownership increases the agency conflict between managers and shareholders, which increases the demand for a more conservative financial statement approach. Using a sample of 648 Australian firms, [START_REF] Gul | Discretionary accounting accruals, managers' incentives, and audit fees[END_REF] show that there is a positive association between discretionary accruals and audit fees, and that managerial ownership negatively affects the positive relationship between discretionary accruals and audit fees.

Finally, firms that are managed by a manager/owner are characterized by a weaker level of information asymmetry, a weaker level of organizational complexity and a weaker audit risk, which results in a decrease in audit demand. Moreover, as given the lower ownership concentration in strong investor protection countries, agency conflict between shareholders and managers should be more accurate. Therefore, we state hypothesis H1 as follows:

H1: Audit fees are more significantly negatively related to managerial ownership in strong investor protection countries than in weak investor protection countries.

High ownership concentration: a type 2 agency cost in weak investor protection countries

Several studies [START_REF] Shleifer | A survey of corporate governance[END_REF][START_REF] Porta | Law and finance[END_REF][START_REF] Porta | Corporate ownership around the world[END_REF][START_REF] Denis | International corporate governance[END_REF][START_REF] Gillan | Corporate governance, corporate ownership, and the role of institutional investors: A global perspective[END_REF] show that in the majority of countries, the ownership is concentrated and minority interests are not well protected, particularly in civil law countries [START_REF] Porta | Law and finance[END_REF]. In this context, high ownership concentration, as evidenced by La Porta et al 's (1998) to substitute for a weak investor protection regulation, raises a new concern: minority investor expropriation (La [START_REF] Porta | Law and finance[END_REF]Porta et al. , p. 1151;;La Porta et al. 2000, p. 4). In a weak investor protection country, controlling shareholders and minority shareholders have both the right to the same dividend per share [START_REF] Denis | International corporate governance[END_REF].

However, the former has private benefits of control and can increase his wealth in consuming additional perquisites to the detriment of outsider shareholders. Consequently, when controlling shareholders have an effective control of the firm via a high percentage of ownership, they have incentives to expropriate minority shareholders3 [START_REF] Shleifer | A survey of corporate governance[END_REF], which leads to higher agency conflict between controlling and minority shareholders, called type II agency costs.

Thus, the legal system of investor protection may influence the role of statutory auditors in substituting for agency conflicts between both kinds of shareholders. Hence, auditors should ask for a higher risk premium for auditing financial statements of firms with high type II agency conflict.

Previous studies having studied the impact of a type II agency conflict on audit fees provide mixed results. [START_REF] Fan | Do external auditors perform a corporate governance role in emerging markets? Evidence from east asia[END_REF] study audit fees determinants in Asia, where family ownership is high and investors are less protected. They test whether auditors ask for an additional premium to their clients when agency conflicts are high. The authors find a positive relation between audit fees and ownership concentration and explain that auditors assume a higher risk to audit those firms. However their study did not differentiate between managerial and controlling shareholding. [START_REF] Chan | Determinants of audit fees for quoted UK companies[END_REF] posits that, in the absence of regulation, the propensity of firms to demand timely independent audits is a function of the extent of the divorce between ownership and control assuming that a high insider ownership contribute to mitigate agency conflict between manager and shareholders. Using an initial sample of 985 UK listed companies that they divided in two sub-samples (big firms vs non big firms), [START_REF] Chan | Determinants of audit fees for quoted UK companies[END_REF] show that insider (managerial and major shareholder ) ownership is negatively associated to audit fee of the whole sample and the sub-sample of big firms and is non significant for the small firms sub-sample. [START_REF] Niemi | Audit effort and fees under concentrated client ownership: Evidence from four international audit firms[END_REF] tests the model of [START_REF] Chan | Determinants of audit fees for quoted UK companies[END_REF] on Finnish firms and finds a non significant relation between audit fees and the measure of the combined managerial and non-managerial ownership concentration (i.e. insiders). In France, [START_REF] Piot | Agency costs and audit quality: Evidence from france[END_REF] finds a non significant relation between insider ownership and the choice of big audit firm (audit quality). Finally, [START_REF] Hay | Audit fees: A meta-analysis of the effect of supply and demand attributes[END_REF] summarize the large body of audit fees determinants research using a meta-analysis and conclude that the results on the relation between ownership structure (insiders) and audit fees are mixed and that they should be interpreted carefully because of the small number of studies. [START_REF] Niemi | Audit effort and fees under concentrated client ownership: Evidence from four international audit firms[END_REF] explains these result by the fact that managerial and non-managerial ownership concentration should have opposite effects on audit fees. After having distinguished between firms that are controlled by the management, by a foreign holding or by the state, he finds (1) a significantly negative relation between audit fees and management control of the firm; (2) a positive relation between audit fees and state control and foreign holding control.

We already stated a separate hypothesis for managerial ownership. We now focus on the major shareholder ownership by assuming a differentiated impact on audit fees depending on the investor protection regime.

We hypothesize a curvilinear relationship between ownership concentration and audit fees in weak investor protection countries. To the best of our knowledge, the existence of such a curvilinear relation has never been established before 4 . When controlling shareholders have effective control of the firm via a high percentage of cash flow rights, they have incentives to expropriate minority shareholders, which leads to higher type II agency costs. Then, auditors demand a high risk premium to audit those firms. Consequently, we suggest a positive relation between the controlling shareholders' ownership and audit fees. But when controlling shareholders ownership exceeds a certain level, controlling shareholders have no incentive to behave on the detriment of the company interest (and therefore, the minority shareholders interests). Holding high level of capital leads them to support all the consequences of their decisions in terms of wealth: private benefits of control become lower than the potential value firm losses that they have to expect (due to decisions that harm minority and company interests). Hence, controlling shareholders will manage the firm to maximize its value by better controlling the manager or participating in its management. In this context, controlling shareholders are the guarantee for a good firm interests' protection and have therefore no incentive to expropriate minority shareholders. Consequently, type II agency conflict is lower and auditors demand lower audit fees since the risk premium is reduced. Hence, for very high level of controlling shareholding, we assume a negative relation between fee levels and controlling shareholders cash flow rights. For instance, [START_REF] Francis | Assessing france's joint audit requirement: Are two heads better than one?[END_REF] in the French context find a negative relation between audit quality measured by the choice of two big four auditors and the major shareholder ownership5 when the percentage of his cash flow rights exceed 25%.

We therefore state the following hypothesis:

H2.1: Audit fees are first positively then negatively associated (concave relation) with the ownership concentration in low investor protection countries

However, firms in well protected environment should not suffer from type II agency conflict (controlling vs minority shareholders) and the prevalent agency costs are those due to type I agency conflict (managers vs shareholders). For instance, [START_REF] Peel | The relationship between governance structure and audit fees pre-cadbury: Some empirical findings[END_REF] did not find a significant relationship between audit fees and major shareholding in UK listed firms.

We therefore state the following hypothesis: H2.2: Audit fees are not related to ownership concentration in high investor protection countries.

Research design

We use the following regression model to test our hypotheses:

LOGAUDFEE = β 0 + β 1 CSHCAP + β 2 CSHCAP2 + β 3 DCAP + δ k FSCONTROL+ χ j CSCONTROL + Fixed effects+ ε ∑ = 7 1 k ∑ = 3 1 j
Where LOGAUDFEE is defined by the natural logarithm of audit fees (in KUSD), FSCONTROL denotes firm-specific variables and CSCONTROL denotes country-specific variables. All variables are defined in Table1.

The test variable for H1 is DCAP and represents the managerial ownership. The coefficient on DCAP (β 3 ) thus captures the audit fee discount in case of managerial ownership. As H1.1 states a general negative relationship between managerial shareholding and audit fees, we therefore expect β 3 to be negative on all countries. However, as H1.2 states a more significantly negative relationship between managerial shareholding and audit fees in stronger than in weaker investor protection countries, we therefore expect β 3 to be more significantly different from 0 in common law countries than in code law countries.

The test variables for H2 are SHCAP and SHCAP2. SHCAP is computed as the sum of the shareholders owning more than 5% of the firm shares. Both H3 hypotheses are based on a quadratic relationship between the controlling shareholders ownership and the audit fees. Due to inherent collinearity issues between the linear and the quadratic terms, we use a transformation of the variable SHCAP and mean center it in the following manner: CSHCAP= SHCAP -mean (SHCAP), which allows us also to construct CSHCAP2= (CSHCAP) 2 .

The expected sign on β 2 depends on the hypotheses. As H2.1 states a curvilinear (positive then negative) relationship between controlling shareholders' cash flow rights and audit fees for lower investor protection countries, then we expect β 1 and β 2 to be negative for these countries. On the contrary, as H2.2 states the absence of relationship between controlling shareholders' cash flow rights and audit fees for higher investor protection countries, then we expect the couple (β 1 , β 2 ) to be non significant for these countries.

Our audit fees model includes two types of firm specific control variables, which control for:

(1) audit costs (size and complexity); (2) the risk of loss that an audit could face in the future [START_REF] Simunic | The pricing of audit services: Theory and evidence[END_REF][START_REF] Francis | The effect of audit firm size on audit prices : A study of the australian market[END_REF][START_REF] Hay | Audit fees: A meta-analysis of the effect of supply and demand attributes[END_REF]. The audit cost is estimated by LOGSALES which proxies for client size, and two variables which proxy for client complexity: INVREC, INTPCT. Similar to [START_REF] Simunic | The pricing of audit services: Theory and evidence[END_REF] and [START_REF] Choi | Cross-listing audit fee premiums: Theory and evidence[END_REF], we include LOSS and LEV to measure the client-specific litigation risk potentially borne by the auditors. Finally, we include the audit firm size (BIG) to capture the Big4 premium [START_REF] Francis | The effect of audit firm size on audit prices : A study of the australian market[END_REF]. As client size, client complexity and client-specific risks should be positively correlated to audit fees, we expect all the coefficients from δ 1 to δ 6 to be positive.

We include three country-level control variables in the cross-country regressions. First [START_REF] Wingate | An examination of cultural influence on audit environment[END_REF] reports anecdotal evidence based on assessments of a leading underwriter of auditor indemnity insurance. Then we expect GDP (Gross domestic product) to have a positive association, as audit fees are likely to be higher in rich countries than in poor countries. Third the demand for audit services is likely to be higher in countries with more foreign direct investments (FDI) than in countries with less. Finally, model includes also fixed year effects and country effects and an error term (ε).

Low and high investor protection countries is implemented through LAW, coding for common (LAW=1) and code (LAW=0) countries, to check the impact of the regime on audit fees, as common law countries are supposed to demand higher audit fees because of a higher likelihood and higher financial sanctions of being liable for any unveiled audit failure [START_REF] Francis | The joint effect of investor protection and big 4 audits on earnings quality around the world[END_REF]. We therefore create code and common law subsample.

Sample and descriptive statistics

Our sample is initially composed of all firms for which audit fee data are provided by Worldscope over the period 2006-2008. We exclude firm-year observations with missing values for the independent variables, and we drop. We dropped two countries (Canada and India) for which ownership data are irrelevant and countries with less than 50 observations. We also dropped financial institutions (Standard Industrial Classification [SIC] 6000-6999). We finally dropped extreme outliers at the country-level and we also removed outliers that have a Cook's distance value greater than 4/(sample size) for each regression at the country level. We finally obtain 8 647 firm-year observations (hereafter named firm observations for ease of notation). et al. (1998, p. 1147-1148) on the sole 3 largest shareholders amongst the 10 largest listed firms of the country. It has also been noticed that block ownership plays an increasingly important role in U.S. capital markets [START_REF] Brockman | Block ownership, trading activity, and market liquidity[END_REF]. [START_REF] Dlugosz | Large blocks of stock: Prevalence, size, and measurement[END_REF] find that block ownership increased from 21.7% of outstanding shares in 1996 to 25% in 2001 in their sample of over 1,900 relatively large firms.

Same similarities hold for France (0.44 vs 0.34) and Germany (0.45 vs 0.48), but UK exhibits a much larger difference (0.33 vs 0.19 in La [START_REF] Porta | Law and finance[END_REF]. These differences could be explained by our much larger sample, which therefore includes smaller firms exhibiting larger shareholding. When compared to a larger sample, our data exhibit a smaller difference (for instance 0.27 obtained on 259 UK quoted firms by [START_REF] Peel | The relationship between governance structure and audit fees pre-cadbury: Some empirical findings[END_REF]).

Control variables are widely ranged for all countries, which illustrates the diversity of the selected firms within our sample. Our sample includes 17 countries (7 common law and 10 code law countries).

Table 3 also discloses t-values for mean differences between code law and common law countries for all variables. We observe that code law countries exhibits lower audit fees (diff. LOGAUDFEE=-0.105, p<0.01), a higher ownership concentration (diff. SHCAP=0.111, p<0.01) and a lower managerial ownership (diff. -0.04, p<0.01). These results are consistent with the premises of our hypotheses. This matrix shows that the independent variable (LOGAUDFEE) is negatively and significantly correlated at 1% to the ownership concentration (SHCAP) and managerial shareholding (DCAP) and the occurrence of a loss (LOSS). LOGAUDFEE is also positively and significantly correlated at 1% to sales (LOGSALES), leverage (LEV), audit quality (BIG), international sales (INTPCT) and the legal regime (LAW). The direction of correlations is consistent with our hypotheses. However, we must run the multivariate analysis before reaching any conclusion on the relations.

The magnitudes of the pairwise correlations among firm specific variable do not exceed 0.4, with the highest significant correlation being between INVREC and INTPCT (coeff.=0.305,p<0.01) and LOGSALES and BIG (coeff.=0.299,p<0.01). We therefore may have no correlation concerns. However, Table 4 reports high correlation between country specific variables. We therefore also perform regression without the four country-level control variables.

Regression results

All tables presented here report the ordinary least squares (OLS) estimates for the models discussed above. P-values are computed using robust standard errors, adjusted for heteroscedasticity and clustering at the firm level. All the regressions are estimated after removing outliers with a Cook's distance greater than 4/sample size within each country or group of countries. This design is similar to [START_REF] Choi | Cross-listing audit fee premiums: Theory and evidence[END_REF]. We include a year-effects in all regressions, and the cross countries regression include either country-level control variables or country-effects. 5 here*** Due to the inherent colinearity concerns regarding the use of the term and the quadratic term in the same regression, we transform SHCAP into its mean-centered CSHCAP, defined as: CSHCAP = SHCAP -mean (SHCAP), and thus create CSHCAP2 = CSHCAP 2 .

Model "Code law countries" shows that DCAP has no significant correlation with LOGAUDFEE. On the contrary, we observe that model "Common law countries" shows a negative and highly significant correlation to LOGAUDFEE (coeff.: -0,453, p<0,01). Therefore we validate H1: Audit fees are more significantly negatively related to managerial ownership in strong investor protection countries than in weak investor protection countries.

Model "Code law countries" shows that CSHCAP (coeff.: -0,423, p<0,01) and CSHCAP2 (coeff. : -0.689, p<0,01) are both negatively and highly significantly correlated to LOGAUDFEE. This result suggests the existence of a curvilinear (concave) relation between audit fees and ownership concentration.

In addition, Table 6 shows that the Wald test rejects the null hypothesis H 0 : (β 1, β 2 ) = 0 for model "Code law countries" and do not reject it for "common law countries". It also reports that both couples (β 1, β 2 ) estimates for both countries are not identical.

Therefore we validate both H2 hypotheses: H2.1: Audit fees are first positively then negatively associated (concave relation) with the ownership concentration in low investor protection countries. H2.2: Audit fees are not related to ownership concentration in high investor protection countries.

We now present some robustness checks.

Robustness analyses

First, we change the proxy for some independent variables. For instance we substituted the natural logarithm of total assets to proxy for size, instead of LOGSALES. We also measured SHCAP by the total sum of major shareholders or by the first three major shareholders (La [START_REF] Porta | Law and finance[END_REF]Porta et al. , p. 1146)), instead of the sum of >5% ownership. Results are qualitatively similar.

Then, we ran a country-level analysis on four countries (Germany, France, UK and USA).

These countries have been selected as given their economic significance, and their diversity regarding investor protection. France and Germany present institutional characteristics which are interesting when one wants to study the impact of type II conflict on audit fees. First, the generally assumed ownership concentration of the French and German listed firms is likely to raise the type II agency conflict (La [START_REF] Porta | Corporate ownership around the world[END_REF][START_REF] Faccio | The ultimate ownership of western european corporations[END_REF]. Then, France and Germany have been identified by La [START_REF] Porta | Law and finance[END_REF] as representative countries of two country families. According to La [START_REF] Porta | Law and finance[END_REF], French civil law countries provide the weakest investor protection, common law countries provide the highest, with German civil law countries being intermediate. La [START_REF] Porta | Law and finance[END_REF] do not distinguish among common law countries. However other studies evidence that within common law countries, that investor protection is higher in the US than in the UK. Wingate [START_REF] Wingate | An examination of cultural influence on audit environment[END_REF], for instance assess the level of protection as 15 for the USA and 10 for UK (and 6.22 for France and Germany), on a 15 point scale.. Table 7 reports regression results for the four countries. **** Insert Table 7 here *** Regarding DCAP, France reports a non significant estimate and Germany reports a negative and significant at 5% estimate (coeff.: -0,703, p<0,05). For both common law countries, DCPA estimates are negative and very significant (UK: coeff.: -0,728, p<0,01; US: coeff.: -0,455, p<0,01). Therefore "H1: Audit fees are more significantly negatively related to managerial ownership in strong investor protection countries than in weak investor protection countries" is confirmed for France (weak investor protection) and the USA and UK (strong investor protection) but not for Germany.

Table 7 shows that ownership concentration estimates for code law countries are consistent with hypotheses 2.1: France exhibits a negative and significant SHCAP estimates (coeff.: -0,416, p<0,05) and SHCAP2 estimates (coeff.: -1.342, p<0,05) and Germany exhibits a negative and significant SHCAP estimates (coeff.: -0,535, p<0,01) and SHCAP2 estimates (coeff.: -1.151, p<0,05). *** Insert Table 8 here*** Table 8 shows that the joint test (β 1, β 2 ) = 0 is significant for both code law countries (France: Chi2=7.15, p<0.01; Germany: Chi2=9.85, p<0.01). Therefore H2.1: "Audit fees are first positively then negatively associated (concave relation) with the ownership concentration in low investor protection countries" is confirmed.

Table 8 also reports non significant Chi2 statistics for the USA and significant for UK (Chi2=3.06, p<0.05). Therefore, H2.2: "Audit fees are not related to ownership concentration in high investor protection countries" is confirmed for the USA, but not for UK.

Discussion

Results presented above provide an interesting perspective on the determination of audit fees as well as on the agency conflicts. Our results globally confirm the idea that audit fees include a risk premium [START_REF] Simunic | The pricing of audit services: Theory and evidence[END_REF]) associated to agency conflicts. Our choice of disentangling managerial from controlling shareholding enables us to clearly evidence their mixed effects on audit fees, as suggested by [START_REF] Niemi | Audit effort and fees under concentrated client ownership: Evidence from four international audit firms[END_REF].

Managerial ownership is suggested as a governance mechanism to align interests of managers to shareholders' [START_REF] Jensen | Theory of the firm: Managerial behavior, agency costs and ownership structure[END_REF]. However, managerial ownership can also create management entrenchment at higher level of managerial ownership (Holderness, 2003;Stulz, 1988): the entrenchment/alignment balance has been showed to depend of corporate governance system across countries. In our sample, we namely observe different country relationships between managerial shareholding and audit fees. In code law countries, which provide a low investor protection, there is no relationship. This result is exemplified by France case. In common law countries, which provide a higher investor protection, we found a strong negative relationship, confirmed by the analysis of the US and UK cases. It therefore seems that the alignment hypothesis is mainly evidenced for higher investor protection countries. This result could be explained by the existence of a more efficient market discipline in higher protection countries such as managerial labor market (Fama, 1980), takeover activities (Fama and Jensen, 1983), expert board of directors (Fama and Jensen, 1983), etc.

Regarding the ownership concentration, our descriptive results first confirm that code law countries exhibit a higher major shareholding concentration. We show that the USA is an outlier regarding the diffused ownership: while Germany and France exhibit similar ownership concentration (with a mean around 0.45), the USA reports a much lower mean (0.26), with the UK in the middle range (mean=0.33). Demsetz (1983) and Demsetz and Lehn (1985) argue that ownership structure is designed by each firm so as to be at the optimal level in which profits are maximized, given a specific institutional context. One consequence, according to [START_REF] Shleifer | A survey of corporate governance[END_REF], is that concentrated ownership is likely to be found mostly in countries with weak shareholder protection: with concentrated shares, controlling shareholders are better motivated to provide good monitoring and have enough power to challenge poor managers than diffused shareholders. Our results partially evidence this theoretical position. Concentrated ownership may create agency problem between controlling shareholders and minority shareholders, leading to a risk of minority expropriation, as identified by La [START_REF] Porta | Law and finance[END_REF] on lower investor protection countries. Controlling shareholders may exercise their power to influence managers for their own benefits without sharing to minority shareholders and firms. Opposition between both effects (entrenchment effect versus alignment effect) has also been mobilized about minority expropriation risk by controlling shareholders [START_REF] Morck | Management ownership and market valuation[END_REF][START_REF] Claessens | Disentangling the incentive and entrenchment effects of large shareholdings[END_REF][START_REF] Fan | Do external auditors perform a corporate governance role in emerging markets? Evidence from east asia[END_REF][START_REF] Attig | Effects of large shareholding on information asymmetry and stock liquidity[END_REF][START_REF] Ali | Corporate disclosures by family firms[END_REF] For lower investor protection countries (France and Germany), our results demonstrate a curvilinear (concave) relation between audit fees and the ownership concentration of controlling shareholders. Moreover, Figure 1 exhibits a very similar behavior in both countries. Therefore, for lower investor protection countries, audit fees first include a risk premium related to the minority expropriation risk. Around the turn-over point (around 25%), the effect decreases up to zero, then reverses: as the proportion of cash flow held by controlling shareholders becomes high, auditors estimate that the expropriation risk decreases when ownership concentration increases: advantages drawn from private benefits of control seems to become gradually lower that the probable loss incurred by controlling shareholders.

Therefore, in firms where the concentration of capital held by controlling shareholders is high, auditors assess that the type II agency conflict is low, which generates a lower risk premium.

We therefore validate an entrenchment (resp. alignment) effect on lower (resp. higher) levels of concentrated ownership, for lower investor protection levels.

For higher investor protection countries, our results show that the type II agency conflict is not significantly evidenced. In the UK, the quadratic (resp. linear) term is significant (resp. not significant) and positive, which means the absence of any risk premium related to a type II agency conflict: the positive and significant linear term evidences mainly an alignment effect only on the range of data. In the USA, neither the linear nor the quadratic terms are significant. We can therefore conclude to the absence of any significant risk premium related to a type II agency conflict in higher investor protection countries: a more efficient market discipline and a higher litigation risk may explain these results.

Conclusion

In this paper, we study the influence of ownership concentration levels on audit fees in code law and common law countries by disentangling managerial and controlling shareholding effects. Overall, our results confirm that audit fees include a risk premium related to type I and type II agency conflicts, the latter only for low investor protection countries. We confirm these results in two typical code law (France, Germany) countries and two common law countries (UK, USA). Our study contributes to research on governance mechanisms by evidencing the differential effect of the type II agency conflict in a common versus civil law country (La [START_REF] Porta | Law and finance[END_REF]. We show that the effect of agency conflicts on audit fees is complex, and depends on the institutional context. Globally speaking, our study supports the substitution hypothesis of governance mechanisms [START_REF] Williamson | Organization form, residual claimants, and corporate control[END_REF]). However, this study suffers from some limits. First of all, our data must be extended to include more country variables to cope with more various investor protection levels than embodied in code vs common law legal regimes. Then, variables related to ownership are direct and not ultimate ownership. Despite these limits, our study aims at improving our understanding of the complex relationships between audit fees and ownership structure, by studying the non managerial ownership, which remains very rare [START_REF] Niemi | Audit effort and fees under concentrated client ownership: Evidence from four international audit firms[END_REF][START_REF] Hay | Audit fees: A meta-analysis of the effect of supply and demand attributes[END_REF]). Future research is needed to evaluate the generality of the results in other institutional contexts of investors' protection.

Table 1: Empirical definitions of variables

Variable

Empirical definition Data source Dependent variable and test variables for Firm i in Country j in Year t LOGAUDFEE ijt = natural log of audit fee in thousands of U.S dollars Worldscope SHCAP ij = the ratio of controlling shareholders cash flow rights on total cash-flow rights (a) Worldscope DCAP ij = the ratio of managers' shareholders cash flow rights on total cash-flow rights (a) Worldscope With: LOGAUDFEE: natural log of audit fee in thousands of U.S dollars; SHCAP: the ratio of controlling shareholders cash flow rights on total cash-flow rights; DCAP: the ratio of managers' shareholders cash flow rights on total cash-flow rights; LOGSALES: natural log of sales in thousands of U.S dollars; BIG: 1 if a firm uses one the big 4 auditors, and 0 otherwise; LEV: the ratio of year-end total debt to total assets; INVEC: the sum of inventories and receivables divided by total sales; INTPCT: foreign sales divided by total sales; LAW: 0 if a code law country, and 1 if a common law country; WINGATE: indicator of auditor's litigation risk [START_REF] Wingate | An examination of cultural influence on audit environment[END_REF]; GDP=gross domestic product per capita in thousands of US dollars; FDI=foreign direct investment (inward) scaled by GDP. 7.

Firm

  . Once again, our results demonstrate a differentiated effect of concentrated ownership on audit fees across legal regimes: code law countries exhibit a curvilinear relationship while common law countries exhibit no relationships. As given the difficulty in interpreting a log-quadratic specification, we graphically represent this relation. **** Insert Figure 1 ***

  10, ** p<0.05, *** p<0.01 (bivariate tests)

Figure

  Figure 1: Audit fees and ownership

  Table 2 explains the sample selection process.

**** Insert Table

2

here ***

Table 3

 3 presents descriptive the mean values on dependent and independent variables. *** Insert Table3here *** Data disclosed in this table are consistent with previous literature on similar samples. For instance, variable SHCAP (Capital rights of the controlling shareholders) disclose an average of 0.26 for the USA, which is consistent with the concentration of 0.20 observed by La Porta

*

Table 4

 4 discloses the correlation matrix of the dependent variable (audit fees) and the whole set of independent variables.

**** Insert Table

4

here ***

Table 5

 5

	presents our main tests.

**** Insert Table

Table 6

 6 *** Insert Table 6 here *** Table 6 rejects the null hypothesis: both DCAP estimates are not equal (Chi2=16.93, p<0.05).

	reports coefficient comparisons across models, by using Wald tests (Baum 2006),
	with the null hypothesis of coefficient equality.

*

  -Specific control variables for Firm i in Country j in Year t LOGSALES ijt = natural log of sales in thousands of U.S dollars Worldscope BIG4 ijt = 1 if a firm uses one the big 4 auditors, and 0 otherwise Worldscope LEV ijt = the ratio of year-end total debt to total assets Worldscope INVEC ijt = the sum of inventories and receivables divided by total sales Worldscope INTPCT ijt = foreign sales divided by total salesWorldscope Worldscope provides us only with current data on ownership structure. We found that, in average, the last update was done in the year 2007. Following[START_REF] Fan | Do external auditors perform a corporate governance role in emerging markets? Evidence from east asia[END_REF], we assume that controlling and management ownership are stable over the studied period.

	Country-Specific control variables for Country j
	WINGATE j = indicator of auditor's litigation risk	Wingate (1997)
	GDP jt = gross domestic product per capita in thousands of US dollars	International Monetary Fund
	FDI jt = foreign direct investment (inward) scaled by GDP	United Nation Conference on Trade & Devt
	Criteria for low/high investor protection countries
	LAW J = 1 if a common country, and 0 if a code law country	La Porta et al.(1998)
	(a)

Table 2 : Sample selection

 2 For still unknown reasons, Worldscope provides both countries obviously abnormally low shareholding data. (b) OTC US market requirements are lower for auditors, and missing data on listing markets may create noisy effects on audit fees. (c) Those countries are not included because of an insufficient number of data.

	Nb. of observations with no missing values on audit fees in non East-Asian countries for 2006-2008 27 961
	less: nb. of observations from India and Canada (a)	(3 747)
	less: missing values on shareholding	(3 722)
	less: missing values on other independent variables	(29)
	less: nb. of observations from financial institutions (SIC: 6000-6999)	(5 908)
	less: nb. of observations from US OTC market or missing data on listing market (b)	(2 607)
	less: countries with less than 50 observations (c)	(93)
	less: extreme outliers (±3 times interquartile range, country level)	(2328)
	less: Cook's residual (>4/N, country level)	(2120)
	Total Data	8 647
	(a)

Table 3 : Descriptive statistics

 3

		Countries	N	LAW LOGAUDFEE SHCAP	DCAP	LOSS	LEV	LOGSALES BIG INVREC INTPCT GDP FDI WINGATE
					(mean)	(mean)	(mean)	(mean)	(mean)	(mean)	(mean) (mean)	(mean) (mean) (mean) index
	Australia	AUS	463	1	6.541	0.355	0.078	13.104	0.868	0.078	0.260	0.269	0.350 42.190 31.699 10.00
	Switzerland	CHE	65	0	8.232	0.175	0.053	15.185	1.000	0.108	0.206	0.322	0.614 60.634 74.215	6.22
	Germany	DEU	539	0	6.828	0.43	0.036	13.912	0.764	0.141	0.205	0.330	0.467 40.197 19.952	6.22
	Denmark	DNK	50	0	8.199	0.311	0.002	14.661	0.940	0.060	0.238	0.340	0.616 56.381 40.477	4.82
	Spain	ESP	150	0	7.075	0.397	0.106	14.353	0.920	0.053	0.300	0.433	0.369 31.784 39.332	4.82
	Finland	FIN	135	0	6.985	0.288	0.076	14.083	0.926	0.096	0.245	0.319	0.561 46.125 34.595	3.61
	France	FRA	446	0	7.552	0.441	0.088	14.302	0.543	0.085	0.245	0.385	0.457 41.543 35.424	6.22
	U.K.	GBR	1 217	1	7.146	0.332	0.078	13.477	0.850	0.104	0.218	0.286	0.434 43.329 43.406 10.00
	Ireland	IRL	71	1	7.252	0.319	0.069	14.210	0.944	0.099	0.267	0.213	0.525 57.486 70.723	6.22
	Italy	ITA	22	0	6.335	0.298	0.121	13.623	0.864	0.182	0.316	0.644	0.434 35.457 16.087	6.22
	The Nederland	NLD	55	0	9.062	0.322	0.011	15.996	1.000	0.127	0.238	0.329	0.694 47.045 82.272	6.22
	Norway	NOR	52	0	7.806	0.442	0.049	14.486	1.000	0.154	0.311	0.318	0.724 83.538 28.928	6.22
	New-Zealand	NZL	36	1	6.685	0.488	0.119	13.431	1.000	0.028	0.362	0.272	0.569 28.509 51.992 10.00
	Portugal	PRT	34	0	6.997	0.597	0.055	14.421	0.706	0.059	0.408	0.411	0.533 20.920 45.971	3.61
	Sweden	SWE	53	1	8.364	0.263	0.04	15.522	1.000	0.038	0.260	0.335	0.668 48.343 58.107	4.82
	USA	USA	5 129	1	7.58	0.263	0.11	13.881	0.864	0.184	0.230	0.248	0.277 46.336 14.935 15.00
	South Africa	ZAF	130	1	7.476	0.447	0.038	14.470	0.908	0.023	0.179	0.299	0.295 5.687 38.810	4.82

Table 4 : Correlation matrix

 4

		LOGAUDFEE SHCAP	DCAP LOGSALES	BIG	LOSS	LEV	INVREC INTPCT WINGATE	GDP	FDI	LAW
	LOGAUDFEE	1
	SHCAP	-0.174***	1
	DCAP	-0.238*** -0.024**	1
	LOGSALE	0.777*** -0.161*** -0.263***	1
	BIG	0.317*** -0.033*** -0.156***	0.299***	1
	LOSS	-0.063*** 0.106*** 0.057***	-0.225*** -0.027**	1
	LEV	0.146*** 0.0556*** -0.036***	0.155*** 0.081*** 0.049***	1
	INVREC	-0.009 0.048*** -0.064***	-0.101*** -0.109***	0.013 -0.067***	1
	INTPCT	0.284***	0.009 -0.116***	0.176*** 0.060***	-0.014 -0.077*** 0.305***	1
	WINGATE	0.

This title has been inspired fromLang et al.'s (2004) title paper: Concentrated control, analyst following, and valuation: Do analysts matter most when investors are protected least? Journal of Accounting Research 42 (3): 589-623.

We refer to both managers and controlling shareholders as the "insiders".

Expropriation can take a variety of forms. In some instances, the insiders simply steal the profits. In other instances, they sell the output, the assets, or the additional securities in the firm they control to another firm they own at below market prices. Such transfer pricing, asset stripping, and investor dilution, though often legal, have largely the same effect as theft. In still other instances, expropriation takes the form of diversion of corporate opportunities from the firm, installing possibly unqualified family members in managerial positions, or overpaying executives. "Tunneling" allows controlling shareholders to transfer firm assets and benefits out of the reach of both creditors and minority shareholders[START_REF] Johnson | Tunneling[END_REF].

We found however studies in corporate governance showing that the behavior of the controlling shareholders is not the same depending on the level of ownership. For instance, Morck et al.[START_REF] Morck | Management ownership and market valuation[END_REF] show a curvilinear relation between firm value measured by the Tobin's Q and the proportion of capital hold by insiders. Based on a sample of 371 Fortune

firms, the authors evidence a significant non-monotonic relationship. Tobin's Q first increases with insiders' ownership beyond a level of 5%, then declines when insider ownership exceeds 25%. Using a sample of more than 400 of the largest public Canadian closely-held firms, from 1995 to 1999,[START_REF] Bozec | Large shareholder entrenchment and performance: Empirical evidence from canada[END_REF] find a non-monotonic relation between performance and the percentage of cash flow of the major shareholders. They suggest that (1) when the ownership is concentrated in the hand of outside shareholders, the latter exerts a control on managers because of large blocks of shares that give them an economic incentive and enough resources to do it; (2) however, these block shareholders are motivated to represent their interests that don't always fit with those of minority shareholders resulting in a minority expropriation.

The authors use a dichotomous variable that takes 1 when the major shareholder ownership exceeds 25% of cash flow rights.

the Fondation HEC (Project F0802) and of the INTACCT program (European Union, Contract No. MRTN-CT-2006-035850). He is a member of GREGHEC, CNRS Unit, UMR 2959. The authors are pleased to thank W. Alissa, V. Capkun and G. Hilary for their useful

With: CSHCAP (variable SHCAP mean-centered, SHCAP=percentage of controlling shareholders cash flow rights); CSHCAP2 (square of CENTSHCAP).LOGAUDFEE: natural log of audit fee in thousands of U.S dollars; DCAP: the ratio of managers' shareholders cash flow rights on total cash-flow rights; LOGSALES: natural log of sales in thousands of U.S dollars; BIG: 1 if a firm uses one the big 4 auditors, and 0 otherwise; LEV: the ratio of year-end total debt to total assets; INVEC: the sum of inventories and receivables divided by total sales; INTPCT: foreign sales divided by total sales.