Geoffrey Pagnoux

Siegfried Fouvry

Michaël Peigney

Benoit Delattre

Guillaume Mermaz-Rollet

Mechanical behavior of DLC coatings under various scratch conditions

Keywords: DLC, scratch, coating failure, FE model, wear 1

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

INTRODUCTION

DLC coatings are widely used for their great tribomechanical properties such as their low wear rate and their low coefficient of friction compared to non-coated solutions [START_REF] Donnet | Tribology of diamond-like carbon films: Fundamentals and applications[END_REF]. Many studies pointed DLC wear mechanisms depend on the atmosphere, on their thickness, their microstructure (hydrogenated or not, doped or not, mono or multi-layered), their interface quality with the substrate and the imposed loading. When applied to an industrial system with complex and various loading, several wear mechanisms can become coupled and a predictive wear model must be seen as a long-term goal.

In lubricated conditions, recent studies highlight the DLC sensibility to particles in the lubricant [START_REF] Haque | The role of abrasive particle size on the wear of diamond-like carbon coatings[END_REF]. In a previous work, the analysis of a cam-tappet system with DLC-coated tappets leads to a complete wear scenario where coating delamination starts around scratch networks and inside tribochemical areas [START_REF] Pagnoux | Usures et endommagements des revêtements DLC sur systèmes camepoussoir[END_REF]. Scratches may come from particles in the lubricant or asperities on the initial surface of the uncoated counterpart. They are particularly numerous on delaminated tappets, but they do not all lead to delamination. It is then assumed there is a specific scratch severity promoting untimely delamination.

To better understand the link between local scratches and generalized coating failure, simplified tests with controlled scratches need to be conducted. Scratches are performed by a standard scratch tester. Those have been used for many years to assess coating-to-substrate quality, though they do not systematically match the actual scratch conditions. In this study, two DLC coatings have been scratched under various and calibrated conditions and the observed failures are compared to both worn coated tappets and a numerical model.

SCRATCH MECHANICS

A scratch test consists in moving at a constant speed a tip on a surface while applying an increasing normal load. Standard scratch tests are performed using a Rockwell C diamond indenter with a 200µm tip radius and a normal load going from 0 to several tenth of Newton. In the case of a coated surface, at a certain critical load the coating will start to fail. The critical loads can be very precisely detected by means of an acoustic sensor attached to the load arm but can also be confirmed and collated with observations from a built-in optical microscope. The critical load data is used to qualify and compare the adhesive or cohesive properties of different film -substrate combinations. In this study, the critical load corresponds to the first observable massive spallation. Multiple failure modes can be observed [START_REF] Bull | Failure modes in scratch adhesion testing[END_REF]. It usually starts from substrate plasticity and a slight residual groove. At a certain point, angular or parallel cracks can be seen at the edge of the groove. Those cracks can also be fully developed beyond the indenter and form conformal or Hertz cracks. With increasing load, a ploughing effect can be seen ahead of the moving tip and several spallation mechanisms appear, from localized chipping to gross spallation. The system response to a scratch test depends on a lot of intrinsic and extrinsic parameters [START_REF] Bull | An overview of the potential of quantitative coating adhesion measurement by scratch testing[END_REF]. Holmberg et al. developed a systematic numerical approach to analyze the scratch mechanics, focusing on local stress fields and first crack location [START_REF] Holmberg | Tribological analysis of fracture conditions in thin surface coatings by 3D FEM modelling and stress simulations[END_REF]. The effect of contact geometry was studied by Xie [START_REF] Xie | Effect of contact geometry on the failure modes of thin coatings in the scratch adhesion test[END_REF] who pointed out the tip radius highly influences the failure mode.

EXPERIMENTAL DETAILS

Sample description

Scratch tests

Scratches have been performed using a CSM scratch tester and a Rockwell C diamond indenter with a spherical tip and a 120° cone angle. In a previous work, a simplified numerical model has been created to estimate the load transmitted by asperities [START_REF] Pagnoux | A model for single asperity perturbation on lubricated sliding contacts with DLC-coated solids[END_REF]. As a result, a scratch map has been defined to represent the contact conditions of a coated cam-tappet system from an automotive engine which encounters asperities.

The tip radius (10, 20, 50, 100 and 200µm) and scratch length (1 to 5mm) have been chosen to cover the range of observed ones on cam-tappet systems, while the normal load is raised until failure or until the maximum load given by the scratch map. The tip speed has been set to 1 and 100mm/min. Before tests, the specimens where cleaned with acetone.

OBSERVATIONS

In the following section, the main results from DLC 1 tests will be highlighted. For 10µm and 20µm tip radius tests, either nothing or only a slight residual groove coming from substrate plasticity is observed. This means the main stress field generated (up to a maximal contact pressure of 20GPa) is restricted to the coating and do not exceed the yield limit of the substrate, so a quasi-full elastic recovery arises after the tip transit. With the 50µm tip radius tests come the first observable cracks, which can be classified as tensile to Hertz cracks (fig. 1). However, at the maximum imposed normal load, no critical failure can be observed.

There are multiple mechanisms of failure with 100µm tip radius tests (fig. 2). The coating exhibits substrate plasticity between 0 and 2.5N. Surface angular cracks located at the groove edge start to appear at 2.5N and become more numerous up to 5.8N. They also become longer by propagating toward the groove center with a slight curvature. At 5.8N, the first critical failure is observed with the creation of large circular spalls alternatively located from one side of the wear track to another. The entire coating is removed as the remaining material is the substrate. Spalling occurs until the end of the scratch.

200µm scratch tests (fig. 3) are quite similar to 100µm ones. Angular cracks appear at 12.1N and propagate to the groove center with a slight curvature at low load, then straight to the center with higher ones. Chipping occurs at 17.8N, followed closely by critical failures from 18.2N to the end of the scratch. The spalls from 200µm tests seem to have a thinner profile than those of 100µm, but a comparative analysis indicates all spalls have actually the same average dimensions.

There is no major difference between scratches at 1 and 100mm/min, meaning there is no viscous effect acting at such speed. Despite the sliding speeds are widely inferior to those acting in the actual cam-tappet systems (up to several m/s), the present scratches exhibit similar failure mode, although spalling is rarely observed on coated tappets. This is relevant with the scratch map, in which most of the calculated load transmitted by asperities does not exceed the observed critical load.

The same scratches have been performed on samples coated with DLC 2. While both DLC are hydrogenated DLC and have the same thickness, they behave differently. DLC 2 exhibits similar failure modes but with higher critical loads. Thus, DLC 2 has a better fracture resistance, although it does not have an adhesive layer. This confirms the high dependence of the coating mechanical behavior to its intermediate layers.

NUMERICAL ANALYSIS AND DISCUSSION

In this numerical analysis, we focus on one substrate, one coating (DLC 1) and several scratch conditions. The substrate is chosen elastic perfectly plastic, without hardening. The coating is assumed homogeneous, isotropic and fully elastic. The surface and interface are perfectly smooth and the indenter is chosen has a perfectly rigid sphere. No residual stress is taken into account, as they were not measured on the scratched samples. The material parameters are taken from table 1, and the coefficient of friction has been set to 0.15, according to the average data measured during tests. The boundaries are at least 5 to 10 times away from the contact area. Due to theoretical symmetry from both side of the scratch track, only half of the geometry was modeled. There is a minimum of 10 elements in the contact half-length and at least 7 elements in the coating thickness. All elements are three-dimensional tetrahedral elements, for a total of around 2e 5 elements (fig. 5).

The loading is chosen as a 3 phase loading. The tip is firstly put into contact with the surface then a constant normal force is imposed as well as a longitudinal displacement. The last step consists in removing the indenter by applying an imposed normal and longitudinal displacement. The scratch length is chosen so that a steady state is reach at the end of the loading step. The full scratch test is not represented as it would require too many elements. As a result, the model can only be representative of an instant of the scratch test. The numerical model has been run for every scratch configuration. The chosen constant load was either the identified critical load or the maximal load, depending on whether or not a critical failure has been observed during scratch. The first result to highlight is the correlation between the observed cracks critical failure (dashed line on figure 6 (a-c), top) and the direction perpendicular to the direction of the maximal principal stress on the surface (figure 6 (a-c), bottom). This means, as expected, the coating behaves as a brittle material and the first crack initiates on the surface, driven by the principal stress directions, and propagates toward the interface. Those results are similar to the mechanism of crack initiation developed in [START_REF] Holmberg | Tribological analysis of fracture conditions in thin surface coatings by 3D FEM modelling and stress simulations[END_REF]. It can also be pointed out that the maximum stress value from which angular cracks start to appear are similar from one test to the other, and equals approximately XXX MPa at 0.8, 2.5 and 12N, respectively. The critical failure is characterized here by massive spall creation up to the interface. This means the system dissipates the stored energy accumulated in the coating by cracking in the surface as well as in the interface, via through thickness cracking. At the interface for instance, failure can be due to an excess of shear or normal traction. Another common loading mode is the excess of compressive stress ahead of the indenter that causes buckling of the coating. Each mechanism tends to dissipate energy so, as a global approach, one can analyses the recoverable energy density in the coating, at its surface and in the interface. However, the entire recoverable energy does not contribute to crack initiation and propagation. By assuming a virtual surface crack front initiated perpendicularly to the direction of the maximal principal stress ( , fig. 7), the surface energy density required for it to propagate can be seen as part of the total available energy density. It can be expressed as in eq. ( 1), where refers to the projection of the direction of the maximal principal stress on the surface and equals , except .

This means compressive stresses are not included in the calculated energy density, as they do not contribute to initiate nor propagate the considered virtual crack.

( ). (1)
At the interface and based on the work of Pradeilles-Duval [START_REF] Pradeilles-Duval | Mechanical transformations and discontinuities along a moving surface[END_REF], the calculated energy density corresponds to the jump of energy density across the interface minus the normal part of it, as it is the only part which does not participate in any mode of failure. The energy is expressed as in eq. ( 2), where refers to the normal at the interface (fig. 7), |[ ]| to the jump of value across the interface, < > to the mean value at the interface, and is the total energy density.

|[ ]| |[ ]|. (2)
The stress state complexity before critical failure implies the used numerical model cannot be as representative of the system as it is at lower loads, especially considering it does not take into account the energy released by previous existing cracks. However, there is an acceptable correlation between the calculated energy densities and the failure modes. On surface, for 50µm scratch test, the recoverable energy concentrates at the indenter side and is split in two behind it (fig. 8 tests, there is a massive overlap between the area of maximal energy density at the surface and at the interface. Thus, the following failure's kinetics is proposed: first cracks are developed on surface, behind the tip and at the groove edge and propagate toward the interface. This propagation depends on the direction of the maximal principal stress. Cracks are likely to bifurcate toward the area of highest energy density, facilitated by the overlap between areas of maximal energy density. Consequently, they turn into the initial defects required for the coating to buckle, due to excessive compression at the front-side and front of the tip. This kinetics is consistent with the nano-scratch failure behavior proposed in [START_REF] Huang | Elasto-plastic deformation and fracture mechanism of a diamond-like carbon film deposited on a Ti-6Al-4V substrate in nano-scratch test[END_REF]. Furthermore, it has been shown a bigger tip radius leads to an increase of the compressive stress and a decrease of the bending one [START_REF] Xie | Effect of contact geometry on the failure modes of thin coatings in the scratch adhesion test[END_REF]. This effect, combined with the decrease of the critical buckling stress with the radius of the loaded region [START_REF] Evans | Modelling oxide spallation[END_REF], drastically enhances the probability of coating spallation.

The numerical model was also used to simulate the same scratch conditions but with a partially worn coating (i.e. with a reduced thickness). Results shown higher stress levels (and energy density) for the worn coatings. This upholds the scratch severity increases with wear, and that scratches made by asperities after a long-term test may be more severe than those realized during a running-in period. After the indenter removal, the recoverable energy stored in the coating is of the same order than the one existing during scratch, particularly at the groove edge. Therefore, in the cam-tappet system, the initial scratches created by asperities are more likely going to evolve into generalized coating delamination when coupled with tribochemical wear.

CONCLUSION

Two different hydrogenated DLC coatings have been scratched under various conditions by varying the tip radius, the normal load and the sliding speed. The wear mechanisms include substrate plasticity, cracks and spallation. The more severe scratches are those with the bigger tip radius. This is due to the ploughing effect arising at bigger loads, which promote compressive stress and buckling-like failure mode ahead of the indenter. Observations demonstrate the mechanical behavior of each constitutive layer of the coating has to be evaluated to correctly catch the actual coating behavior under fracture. Before critical failure, the numerical model confirms the coating behaves as a brittle material and first cracks appears at the surface, behind the contact area and at the groove edge, driven by the maximal principal stress. The analysis of the maximal energy density areas at the surface and at the interface allows suggesting a failure's kinematics explaining the origin of the initial defect required for the coating to buckle. The numerical model also highlights that for a given scratch, a worn (i.e. thinner) coating is more sensitive than an unworn one by storing a higher recoverable energy after the indenter removal. This is in agreement with observations on complex environments like coated cam-tappet systems, where generalized delamination initiates around scratch networks and inside tribochemically worn area.

7

Figure 1 -Figure 4 -

 14 Figure 1 -R = 50µm, Fn = 0.03 -2.0N, L = 2mm, v = 1mm/min

Figure 5 -

 5 Figure 5 -Illustration of the FE model

Figure 6 -

 6 Figure 6 -Surface cracks before failure (top) and first principal stress at the critical load (bottom)

Figure 7 -

 7 Figure 7 -Virtual surface crack and normal vector illustration

  Figure 8 -Surface ( top) and interface ( bottom) energy density

ACKNOWLEDGEMENTS

The authors would like to acknowledge the support of HEF Group for providing the DLC-coated samples.

8


M Fares
email: mfares@toulouse.inra.fr

Luis Orozco

Tournament Mechanism in Wine-Grape Contracts: Evidence from a French Wine Cooperative

Keywords: JEL classification: L14, D82, Q13) supply contracts, quality, tournament, cooperative

. In our case, the cooperative promotes competition between growers by offering a promotion, while, at the same time, organizing the contest by creating homogenous groups of growers using a menu of contracts and monitoring through regular visits to the vineyard. Using a database of 1219 contracts, we test the effect of: (i) the cooperative's tournament compensation scheme; (ii) the menu of contracts and monitoring mechanism. The results of our econometric estimations provide some confirmation of both effects. (

Introduction

Growers' vineyard practices are one of the main determinants of grape quality1 . But wineries face a classical agency relationship with its growers. That is, the cooperative's (winery) interest is for growers to deliver quality grapes. However, two problems arise: first, wineries are unable to observe the grower's effort level (moral hazard). Their remuneration is based only on proxies, i.e. observable indicators, of the grape quality once delivered to the winery. Second, the growers have different ability and productivity (adverse selection).

In this paper, we study a wine cooperative in the South West of France that implements an incentive compensation system to induce growers to provide the maximum effort towards quality.

To do so, it sets a differentiated payment system and a system of promotions. Compensation is not based on the absolute quality of their grape, but instead on a relative performance scheme, where the individual output is compared to that of their peers. This compensation scheme is similar to that in tournaments [START_REF] Lazear | Rank-Order Tournaments as Optimum Labor Contracts[END_REF][START_REF] Green | A comparison of tournaments and contracts[END_REF][START_REF] Knoeber | A Real Game of Chicken: Contracts, Tournaments, and the Production of Broilers[END_REF].

In our case, the cooperative promotes competition between growers, first by promising the possibility for a grower to be "promoted" to a higher quality contract, and second by providing a price differential within each quality contract, an additional incentive for growers to search for higher prices. At the same time, the cooperative needs to face the adverse selection problem by organizing the competition between different homogenous groups. For this, the cooperative proposes a menu of contracts and monitors the production process.

Our empirical results from a database of 1219 contracts confirm that the tournament mechanism aims to: (i) provide some incentives in presence of a common shock that may affect all the growers; (ii) reduce the heterogeneity among the growers embedded in the same contest depending on the contract chosen. This paper is organized as follows. Section 2 provides a short overview of the theoretical approaches when agency problems are at stake in the production of quality grapes and tournament theory. Section 3 describes the wine cooperative's contract stages and the organization of our database. Results are presented in Section 4. The last section brings some concluding remarks.

Quality incentives and contracts

While explicit contracts in the wine grape production have been largely used between independent growers and wineries [START_REF] Gaucher | Incitation à la qualité dans la relation vignoblenégoce[END_REF][START_REF] Goodhue | Contracts and Quality in the California Winegrape Industry[END_REF][START_REF] Fraser | Microeconometric analysis of wine grape supply contracts in Australia[END_REF][START_REF] Fares | Brokers as Experts in the French Wine Industry[END_REF], in this paper we focus on cooperative organizations where the growers are both suppliers of the grapes and members of the cooperative. The cooperative faces a classical agency relationship with its growers [START_REF] Alchian | Production, Information Costs, and Economic Organization[END_REF][START_REF] Jensen | Theory of the Firm : Managerial Behavior , Agency Costs and Ownership Structure[END_REF][START_REF] Pennerstorfer | Product quality in the agri-food chain: do cooperatives offer high-quality wine?[END_REF]. In the case of cooperative-grower, or principal-agent, "one party

[grower] has an informational advantage over another [cooperative] that can be exploited to the benefit of the advantaged party" [START_REF] Jensen | Theory of the Firm : Managerial Behavior , Agency Costs and Ownership Structure[END_REF]. The first kind of asymmetric information is the adverse selection problem, where the grower is supposed to know his characteristics, skills and competencies (his type) but the cooperative cannot observe them without cost. To overcome the problem of adverse selection, the cooperative offers a "menu of contracts". If the menu is well-designed, the grower may reveal his type by choosing the contract that maximizes his utility. The second kind of problem is the moral hazard problem, where the cooperative cannot observe the effort in grape quality undertaken by the grower once the contract is signed. Therefore, the contract offered by the cooperative has also to give incentives to effort.

An optimal compensation scheme based on the observable output is defined. When the grower has some risk aversion, this optimal compensation scheme is confronted with the "incentive versus insurance" trade-off [START_REF] Sappington | Incentives in principal-agent relationships[END_REF]. In this case, a piece rate mechanism (with a fixed base pay) can be optimal.

In practice, the vineyard contract relationship departs from this simple model since the output (quality) itself is costly to monitor [START_REF] Gaucher | Incitation à la qualité dans la relation vignoblenégoce[END_REF]. First, there are no easy ways to control (thus, enforce) the grower's vineyard practices. Even if the cooperative's technicians visit the vineyard during the year and provide extension services, the actual work in the vineyard is not observed. Second, there is no easy ex post evaluation of the output (grape quality), although there are tests based on pre-established parameters, such as sugar contents [START_REF] Alston | Too Much of a Good Thing? Causes and Consequences of Increases in Sugar Content of California Wine Grapes[END_REF], or the sanitary and physiochemical proprieties of grapes that could indeed provide some indication [START_REF] Montaigne | Quelles perspectives pour les contrats en raisin entre production et négoce?[END_REF]. However, they do not directly reflect the grower's effort level. Finally, there is no "mechanical" relationship between the application of specific vineyard practices and the qualitative end result of grapes. Elements related to the pedoclimatic environment of land blocks or yearly meteorological conditions could influence the output attributes [START_REF] Ashenfelter | Predicting the Quality and Prices of Bordeaux Wine[END_REF][START_REF] Ashenfelter | Using hedonic models of solar radiation and weather to assess the economic effect of climate change: the case of Mosel valley vineyards[END_REF].

In cases where monitoring is either unreliable or costly, tournaments could be a desirable incentive scheme [START_REF] Lazear | Rank-Order Tournaments as Optimum Labor Contracts[END_REF]. This compensation system remunerates individual performance not on the absolute value of their output, but on the position their output ranks compared to that of their peers. In what follows, we characterize the efficient solution of a compensation scheme piece rate (2.1), before analyzing the specificities of a differentiated compensation scheme, where agents can be heterogeneous (2.2).

Agency problems and piece rate compensation scheme

The timing of the relationship between the cooperative and the grower is defined as follows. In the first period, the cooperative offers a menu of contracts and the grower chooses the contract that maximizes his expected utility. In the second period, given the contract chosen, the grower i undertakes an investment or effort level e i that increases his performance, i.e. the quality q i of the grape produced (output). Developing investment or exerting effort is costly to the grower and

𝐶 𝑒 ! = 𝜃 ! 𝑒 !
! /2 denotes the cost of investment or effort, with 𝜃 ! the grower ability or productive parameter. Quality may also be impacted by a common shock (𝜂) and an idiosyncratic shock (𝜀 ! ).

The shocks follow an i.i.d. normal distribution with mean zero, and the common shock has a variance 𝜎 ! ! while the idiosyncratic shock has a variance 𝜎 ! ! . The quality production function can be written as follows

𝑞 ! = 𝑒 ! + 𝜂 + 𝜀 ! [1]
The cooperative cannot observe the grower's effort and thus cannot assert the extent to which the quality produced (or some of its proxies) is due to effort or to shocks, either common or idiosyncratic.

In the case where a piece rate contract can be used to remunerate growers [START_REF] Lazear | Rank-Order Tournaments as Optimum Labor Contracts[END_REF][START_REF] Gibbons | Piece-Rate Incentive Schemes[END_REF], the growers are paid based on output (quality). Because output is dependent on effort 𝑒 ! , a piece rate contract should encourage greater effort and penalties could be applied if the observed output is insufficient. Following [START_REF] Lazear | Rank-Order Tournaments as Optimum Labor Contracts[END_REF], we suppose for ease of exposition that growers are risk neutral and free entry in a competitive output market set the value of the product at V per unit. Let r i be the piece rate, then the grower net income

𝑟 ! 𝑞 ! -𝐶(𝑒 ! ).
A risk-neutral grower chooses e i to maximize his utility

q i 𝐸 𝑟 ! 𝑞 ! -𝐶 𝑒 ! = [𝑟 ! 𝑒 ! -𝐶 𝑒 ! ] [2]
The first order condition of this program is 𝑟 ! = 𝑒 ! /𝜃 ! , i.e. the piece rate equates the marginal cost of effort. Since the cooperative is also supposed to be risk neutral, its expected profit is

𝐸 𝑉𝑞 ! -𝑟 ! 𝑞 ! = (𝑉 -𝑟 ! )𝑒 ! .
Because the free entry assumption implies 𝑟 ! = 𝑉, substituting in [2] and deriving gives

𝐶 ! 𝑒 ! = 𝑉 [3]
That is, the marginal cost of effort equals its social return. The optimal effort level is then

𝑒 ! * = 𝜃 ! 𝑉.
This result suggests that piece rate is an efficient compensation scheme. However, since it is costly and difficult for the cooperative to directly measure the grower absolute level of each grower's output2 , it can be more efficient to observe the relative position of each grower by ranking the different output levels [START_REF] Prendergast | The provision of incentives in firms[END_REF].

Tournaments and relative compensation schemes

The wine cooperative's differentiated payment system studied in this paper is like a tournament.

Tournaments remunerate individual performance, not on their absolute value, but on the position of their output ranking compared to that of their peers. The literature on tournament [START_REF] Lazear | Rank-Order Tournaments as Optimum Labor Contracts[END_REF][START_REF] Green | A comparison of tournaments and contracts[END_REF][START_REF] Knoeber | A Real Game of Chicken: Contracts, Tournaments, and the Production of Broilers[END_REF] shows the cases where the principal promotes competition between agents because monitoring of output itself is either unreliable or costly. In our case, the cooperative creates incentives to work harder first by promising the possibility for a grower to be "promoted" to a higher quality contract and, second, by providing a price differential within each quality contract that provides an additional incentive for growers to work harder for a better quality.

Promotions are used to sort workers based on their talents and reward them accordingly [START_REF] Rosen | Authority, Control, and the Distribution of Earnings[END_REF]. In a tournament system, the winning prize is a promotion, which should be an incentive for the agents to improve their effort level [START_REF] Prendergast | The provision of incentives in firms[END_REF]. [START_REF] Lazear | Rank-Order Tournaments as Optimum Labor Contracts[END_REF] were the first to study this type of payment system. In the presence of high monitoring costs, with regards to effort and final output, this type of payment system is preferred because it would be less expensive to observe the relative position of agents with regard to each other than to measure their individual production levels. [START_REF] Green | A comparison of tournaments and contracts[END_REF] and [START_REF] Nalebuff | Prizes and incentives: Towards a General Theory of Compensation and Competition[END_REF] deepened the analysis by considering that tournaments are particularly preferred when the agents are confronted with a common shock (random variable that might represent economic conditions that affect all of the agents). As stated in [START_REF] Tsoulouhas | Tournaments with Ex-post Hetrogeneous Agents[END_REF] and [START_REF] Tsoulouhas | Hybrid Cardinal Tournaments[END_REF], when agent production activities are subject to common shock individual performance is not a sufficient statistic for individual effort. The performance levels obtained by the rest of the agents convey an informative signal about the common shock and, thus the effort choice of any given agent. Therefore, tournaments constitute a move closer to the first best solution because the principal uses the available information more efficiently. By removing common uncertainty from the responsibility of agents, and by charging a premium for this insurance, the principal increases his profit without hurting the agents.

To give an intuition of the main result of the tournament mechanism, we follow the [START_REF] Lazear | Rank-Order Tournaments as Optimum Labor Contracts[END_REF] simple model where the two agents (growers) are rewarded for their performance with one of two prizes, 𝑡 ! 𝑜𝑟 𝑡 ! , where 𝑡 ! > 𝑡 ! . The higher prize 𝑡 ! goes to the grower with the better performance, while the lower prize goes to the poorer performing grower.

The probability of a grower i wining the higher prize depends positively upon his own effort (𝑒 ! ).

Let P be the probability of winning the tournament3 , the expected payoff to grower i is

P e i ( ) t 1 -C e i ( ) " # $ % + 1-P e i ( )
( ) t 2 -C e i ( ) " # $ % = P e i ( ) t 1 -t 2 ( ) + t 2 -C e i ( ) [4]
Assuming risk neutrality and holding the opponent's action constant, grower i will choose 𝑒 ! to maximize [4]. By deriving the grower payoff with respect to 𝑒 ! , the first order condition is

𝑃 ! (𝑒 ! ) 𝑡 ! -𝑡 ! = 𝐶′(𝑒 ! ).
In a symmetric Nash equilibrium, where grower j reasons similarly to grower i, the effort level implemented is

𝑒 = (𝑡 ! -𝑡 ! ) !! ! [5]
This implies that effort depends positively upon: (i) the marginal effect of effort on the probability of winning (P'); and (ii) the prize differential (𝑡 ! -𝑡 ! ). This latter implies that effort is unaffected by changes in the absolute level of prizes that leave this differential constant4 . This price differential mechanism of the tournament provides protection to growers against common shocks. Indeed, if these shocks are systematically applied, universally boosting or decreasing production signals do not change the rankings between growers, and thus their expected payoff.

This tournament mechanism can achieve the efficient solution (𝑒 = 𝑒 * ) by choosing a prize differential such that

𝑡 ! -𝑡 ! = [ ! ! ! ] [6]
This result shows that tournament mechanism can also achieve an efficient outcome when the growers are risk-neutral. When they are risk averse, this efficiency result cannot be obtained with piece rates and tournaments due to the trade-off between incentives and insurance. When there are no common shocks and only idiosyncratic shocks, the piece rates do provide an improvement over tournaments. In contrast, relative pay in tournaments may yield greater effort than pieces rates when a common shock is sufficiently large [START_REF] Tsoulouhas | Tournaments with Ex-post Hetrogeneous Agents[END_REF].

The empirical papers on tournaments that studied the North American broiler production industry, confirm the theoretical predictions [START_REF] Knoeber | A Real Game of Chicken: Contracts, Tournaments, and the Production of Broilers[END_REF][START_REF] Knoeber | Testing the Theory of Tournaments: An Empirical Analysis of Broiler Production[END_REF]. They

find that: (i) the extent of this payment depends on the grower's relative performance with regard to others (measured by the grower's settlement cost compared to an average); (ii) changes in the level of prizes that do not change the prize differentials motivate no change in chicken production (and thus, farmer effort). [START_REF] Ehrenberg | Do Tournaments Have Incentive Effects?[END_REF] provide also interesting empirical confirmation of tournament's effect on the effort of competitors through their analysis of professional golfers. [START_REF] Main | Top Executive Pay: Tournament or Teamwork[END_REF] show that promotion from corporate vice-president to president generates a pay increase, which is positively correlated to the number of vice-presidents competing for the position. That is, the executive pay is the prize of a tournament rather than compensation for value added. [START_REF] Eriksson | Executive compensation and tournament theory: empirical tests on Danish data[END_REF] presents similar findings by regressing firm performance (log (profit/sales)) by pay differentials (the gap between CEO and VP pay), controlling for industry and firm-size. His pay differential yields a statistically significant coefficient, which gives some evidence of the main prediction of the theory.

Organizing the contest between heterogeneous growers

In the previous simple models the growers were supposed homogenous. In practice, growers may be heterogeneous and thus each one will respond differently in the tournament to the prize differential and/or promotion. That is, growers with high cost of effort may choose zero effort because of their competitive disadvantage; or they can take excessive risks in hope of leaping ahead of the frontrunner. Therefore, when agents are heterogeneous relative performance evaluation via tournaments exposes agents to uncertainty about the average agent ability. The rationale is that, unlike piece rates, tournaments filter away common uncertainty from the responsibility of agents who pay a premium for this insurance. Since tournaments expose agents to the idiosyncratic shocks of other agents, so that tournaments become less desirable when the variance of the distribution of ability types (heterogeneity) is large [START_REF] Tsoulouhas | Regulating broiler contracts: tournaments versus fixed performance standards[END_REF][START_REF] Tsoulouhas | Tournaments with Ex-post Hetrogeneous Agents[END_REF].

This problem of adverse selection in tournaments has been documented first by [START_REF] Lazear | Rank-Order Tournaments as Optimum Labor Contracts[END_REF] who show that without a specific mechanism, agents would not self-select since it is more interesting for all agents to be in the high ability group. Consider the simple case of two different types of growers, who know their type (ability) but the cooperative does not. There are two leagues: league 𝜃 ! wich yields the most efficient outcome given the high ability people and league 𝜃 ! , which yields the highest outcome given low ability growers. The problem is that league 𝜃 ! is strictly prefered since it generates a strictly higher payoff. This leads to the lower type 𝜃 ! contaminating league 𝜃 ! which results in a mixed "league" bag of growers of different abilities. That is, growers have no incentive to sort themselves in the two leagues according to their abilities. As shown above, this "league composition risk" [START_REF] Tsoulouhas | Regulating broiler contracts: tournaments versus fixed performance standards[END_REF] may lead to inefficiency since growers will provide less effort and or take more risks. [START_REF] Bull | Tournaments and Piece Rates: An experimental Study[END_REF] found that there is a large variance in tournament settings in the effort levels, and despite introducing more information such as the opponent's effort levels, there is still much variance.

Starting from this early experimental tournament paper, several lab experimental studies examine the relationship between effort provision and heterogeneity. For example, Tsoulouhas et al.

(2007), [START_REF] Gurtler | Feedback in Tournaments under Commitment Problems: Expermimental Evidence[END_REF] and [START_REF] Vandegrift | An experimental Test of Sabotage in Tournaments[END_REF] find support for the prediction that equilibrium effort is lower in asymmetric tournaments because reduced effort does not change player's relative position. However, [START_REF] Eriksson | Self-Selection and the Efficiency of Tournaments[END_REF] show that previous experimental evidence regarding the variability of effort in tournaments is misleading because the experiments have not accounted for sorting. That is, agents typically choose to participate in a tournament. So, they used a similar setup to that of [START_REF] Bull | Tournaments and Piece Rates: An experimental Study[END_REF], except that the participants had a choice when they participate: they can choose between piece rates and relative pay. They find that those who choose the tournament provide, on average, higher effort. After running the experiments, they also did a questionnaire with several lottery decisions to elicit the risk aversion of each participant. They found that risk adverse agents tend to choose the piece rate scheme. This sorting leads to two homogeneous groups, which reduces the between subject variance dramatically in the tournaments.

Another solution to sort between heterogeneous agents is to offer a menu of contracts.

Following [START_REF] Bhattacharya | Heterogeneity, Tournaments, and Hierarchies[END_REF], [START_REF] Riis | Efficient Contests[END_REF] shows that when agents are heterogeneous ex ante and the optimal discriminatory prize premium is non-monotonic in ability, efficiency can be restored if agents choose from a menu. [START_REF] Wang | Pooling, separating, and cream-skimming in relativeperformance contracts[END_REF] show that a menu of two contracts may also simultaneously shift surplus from low to high ability growers.

Further, a "cream-skimming" contract that pools only growers above a certain ability level may, under certain circumstances, increase the expected utility of participating growers and reduce the expected profit of the Principal (processor). In contrast, [START_REF] Tsoulouhas | Do tournaments solve the adverse selection problem ?[END_REF] shows that no menu of contract is needed ex ante since the ex post tournament mechanism can sort between growers if they are known to be not very heterogeneous.

In our case, the wine making cooperative tries to screen the growers by their ability and organize contest in subgroups where growers can be the less heterogeneous possible. This is done in two steps. First, ex ante growers are screened and reveal their type by choosing the contract that maximizes their expected utility in the menu of contracts offered by the cooperative. Second, before harvest and contest, the cooperative may downgrade growers and their land blocks that are unable to achieve a minimum quality inside their group. This help to reduce the variance of the outcome inside group once the harvest is done. Once this problem of heterogeneity is solved, the tournament mechanism is probably the best alternative when common shock is sufficiently large.

Indeed, it eliminates the variations of revenues caused by factors common to all growers, either variations of measurement or variations related to the environment. This is particularly true in the case of cooperatives, which are delimited to a geographical area making it more likely for growers to be affected by climatic hazards. Tournaments should also reduce the cost related to measuring performance and maintain incentives for maximum effort, while removing common shocks to all participants5 .

Data and methods: the case of the Saint Mont vineyard

The Saint Mont vineyard 6 , as well as the studied cooperative7 , has experienced a transformation process similar to that of other cooperatives in the French "South West," going from a mass wine production to a more quality-focused production. This shift has translated into a payment system that guides producers towards medium and long-term planning and strongly encourages them to make effort in quality of grapes [START_REF] Chiffoleau | Networks, innovation and performance: evidence from a cluster of wine co-operatives[END_REF]. In this section, we present the different steps of the contractual process from the moment a grower chooses a contract to the arrival of grapes to the cooperative after harvest. This information is registered in the cooperative's traceability database, which allows for a better management, and monitoring, of the grape production. We test in this database (i) the efficiency of the cooperative's tournament compensation system, i.e. if a promotion have a positive effect on effort and thus on final qualitative output; (ii) the effect of the monitoring mechanism and menu of contracts on the efficient contest organization. .

The timing of contracts

The contractual process begins in April of each year (see figure 1), when growers commit one or more land blocks to a quality contract until September, when the grape harvest takes place.8

In step 1, the cooperative offers a menu of contracts <A,B,C>. The quality requirements and the cost of each contract is such that the grower's profit represented by . These contracts, to which the grower has committed one or more land blocks, have certain requirements that must be followed. At this step, the cooperative takes some preventive measures to screen among heterogeneous growers and land blocks. For example, to commit a land plot to contract A, the land blocks should belong to a property9 or they must have been committed to an A contract for the previous three years.

Figure 1: Steps of the wine-grape production contract.

Steps 2 and 3 consist of visits from technicians to evaluate, validate and guide the work of the grower. These visits are part of the "monitoring" process, which aims to avoid moral hazards, or hidden actions such as non-compliance with the contract. 10 In doing so, the cooperative can screen again between growers. Indeed, by monitoring the cooperative aims to ensure homogenous groups before harvest and contest.

If everything occurs according to the plan, the grower that made all of the necessary efforts and complied with the contract should produce a better quality grape than the one that did not.

However, land plot characteristics (e.g., location, pedoclimatic conditions) may not be aligned with the desired quality. Consequently, if a plot committed to certain contract did not correspond to its potential -in our example, land that is not suitable for an A contract -all efforts made by the grower would end up being pointless because he could be penalized after the qualitative analyses. On the contrary, if the land has a greater potential, with only a little effort from the grower the analysis results could show a high-quality wine.11

Nonetheless, the risk, especially regarding land potential, would raise one problem regarding tournaments. If agents know -or believe they know -of the high potential of their land, they could make a little effort and with high-quality production, finish at the top of their tournaments.

On the contrary, those who consider that they own "low-potential land" will make little effort to remedy their situation because they will conclude that their land is going to be downgraded anyway.

In step 4, a committee composed of growers and technicians proceeds to classify -and eventually downgrade -the various land blocks (see figure 2). This classification helps the cooperative to determine the quality of grape that will arrive to their facilities after harvest and foresee the type of remuneration that the grower will receive. For example, a land block engaged in an A contract (at this step) is downgraded to B or C because the requirements of the contract were not met. 12 This constitutes a crucial moment because the fulfillment of the contract is verified. For instance, if the grower engages a plot of land to an A contract, he/she expects to be paid according to the A price scale (pA1 to pA3, see figure 2) depending on the results of the contribution analysis. However, if they agreed to an A contract, but find themselves with several land block downgraded to C1 or C2, this will heavily penalize their compensation because they will only have the right to opt for prices pC1 to pC3.

There is an additional feature in the payment system (a contractual provision). The compensation to each land block is a function of the price and the yield of all land plots within the 12 The difference between the C1 and C2 classification in figure 2 corresponds to quality C grapes for producing red wines (C1) and rosé (C2).

contract, but there are ceiling levels in terms of yield (as a measure of quality). 13 In the case of a contract A (tournament A), a grower's compensation (prices pA1 to pA3) will only be paid up to a yield of 45 hectoliters/ha. After breaching that ceiling, yield will be paid at a price p c (complement price), which is close to 1/5 of pA1 14 .

The penalty for surpassing the fixed yield ceiling, and incurring in a loss, is another incentive for additional effort. The contract, especially for high-quality contracts (A and B), stipulates a mode of cultivation that needs strong management of the expected yield. For instance, the process of disbudding and pruning the vine is very costly in terms of working hours and differs from one contract to another. 15 This means that a grower engaged in contract A will not only play in a tournament A, but he/she must also be careful of their yield and should provide the maximum effort to manage the yield within the respective ceilings. In any case, growers can appeal the step 4 decision (step 5).

In step 6, samples are taken, and three ripeness tests are carried, in order for the cooperative's technicians to allow the harvest of grapes. This evidences the authority mechanism the cooperative applies, which could differ from the grower's interests, who for instance, could prefer to harvest in another moment. In step 7, samples of each contribution are analyzed and a corresponding score is calculated in accordance with its group average quality. In step 8 the remuneration is made according to the final classification (result of the tournament) and to the ceiling criteria in terms of the yield set in the price scale.

The database

The main database, referred to as "Geowine StMont" database, contains two types of information from different sources. The first type comes from the wine cooperative's traceability database. 16 It contains information on each grower's individual contribution of grapes since the year 2000. It provides detailed information on each grape contribution (e.g., yield, grape variety), characteristics of each land block, the type of contract engaged, the land block's classification (at 13 In viticulture lower yields are related to higher quality. 14 Up to 66 hectoliters/ha, which is the maximum yield allowed by the AOP's regulation. After this ceiling it is all losses. 15 The cooperative estimates that there are approximately 1600 euros/ha in between contracts A, B and C. 16 Traceability systems make information available on products' attributes and transformations that can be used to improve safety and quality [START_REF] Galliano | The determinants of electronic traceability adoption: a firmlevel analysis of French agribusiness[END_REF]. Beyond the record-keeping information to respond to a public authority inquiry, the cooperative uses this information to improve their productive and management systems.

step 4) and the final compensation category. These data are further complemented by information provided by the cooperative, such as the price paid for each compensation category and individual information about growers, such as age, gender and total arable land surface. The second source comes from the work of researchers at the École d'Ingénieurs de Purpan [START_REF] Gay | Geowine WP 1 -Organisation de la base de données géographiques[END_REF]. These are geographic variables such as soil, altitude, slope and orientation exposition.17

The test is carried on a sample of 1219 land blocks belonging to 120 growers. Summary statistics and definition of variables are presented in table 1.

Variables

The analysis was performed using data from the 2008 harvest. The main reason for this choice is that, after 2007, the different contracts became more differentiated in terms of quality requirements, but in 2007, many vines were damaged by environmental factors (hail storms). In addition, we only take into account the grape production for red wines because they have three contract types (instead of two for whites) and they represent almost 80% of all grape production in the Saint Mont AOP.

Our dependent variable, REMTOT, is the payment for each land plot provision of grape (in thousands of Euros for each hectoliter/hectare). This payment does not include the costs subtracted by the cooperative for the actual wine production but is an indication of the quality of grapes because the price paid to each land block depends upon the quality category it was assigned to after the downgrading process (step 4) and upon the price category after analysis (step 7). The type of contract initially chosen by the grower can be A (Contract A), B (Contract B) or C (Contract C). The requirements in quality are higher in contract A than contract B and higher than C. These dichotomous variables will be used for the selection equation.

The first group of independent variables concerns the prediction of the tournament model and the contractual provisions. The possibility of a promotion to a higher quality category should have a positive effect on the provision of quality effort. The probability of promotion increases with the number of promotions offered and decreases with the number of contestants [START_REF] Heutel | Testing implications of a tournament model of school district salary schedules[END_REF]. We consider the dummy variable PROMO that equals one if the land block has been promoted from the previous year (t-1 to t). It could indicate that the grower wants to prove that he/she deserved the promotion. Inversely, we consider a dummy variable DEMO that tests if the land plot has been demoted from category from the previous year.

Furthermore, we consider a variable to capture the monitoring activity of the cooperative.

Tournament theory indicates that the higher the monitoring efficiency of the principal, the higher the effort from the agent should be [START_REF] Prendergast | The provision of incentives in firms[END_REF]. The variable DOWN indicates the land block has been downgraded at step 4 (figure 1) during the season (in year t). As previously mentioned, at this stage, a committee of growers and technicians (from the cooperative) evaluate the grower's work and determine if the contract has been followed. If this is the case, the plot of land remains in the same quality category; if not, the land block is downgraded to a lower quality category. In addition, this variable only takes into account the downgrading of a land block where the grower's effort did not meet the contract specifications (moral hazard). It does not take into consideration land blocks downgraded due to a climatic event or a disease to the vine. 18 The variable EFFCD indicates whether a land block suffered from a climatic or a disease event.

The variables YIELD and YIELD2 consider the average yield of each individual land block.

The yield is measured in hectoliters/hectare and is relevant because, in viticulture, higher quality is associated with lower yields. The squared of yield, YIELD2 will allow us to observe if, after a certain ceiling, an additional unit of yield would have a negative effect on quality. The control of yields is probably the most important provision in quality contracts in viticulture. Concerning the grower, we take into consideration the grower's age (AGE), gender (GEND) and the number of year of experience in a type A contract (NYA). We also consider the percentage of vines over total arable land (VINEYARD), which signifies the degree of specialization of the grower in viticulture.

Finally, we consider variables related to the fixed characteristics of the land plot. The variable PROPERTY indicates that the land plot belongs to a chateau or a domaine. SURF refers to the land plot's total surface (in hectares). TANNAT indicates whether the variety of grape is Tannat or not. 19 The variable SOIL, which has five classes, that is, four types of soils representing 74.3% of all land blocks and one class, considered "out of the zone", representing the remaining land blocks. The four types of soil are mainly those with high presence of gravel, clay, molasse and iron-rich sand.

[Insert table 1] 4 The empirical model

In this section, we outline the empirical analysis. The two main objectives are, first, to test the efficiency of the cooperative's tournament compensation scheme system, in other words, to test that a promotion has a positive effect on effort (and thus on final qualitative output). Second, to test for the efficiency of the screening/selection mechanism to reduce heterogeneity among growers and blocks.

We estimate that the qualitative performance of land plots, thus grower's effort, is going to be dependent of their initial choice of contract. The choice of a specific contract (step 1 of the processes) by growers depends on the characteristics of the land block, the grower's experience and the performance of previous years. Thus, we test the existence of a selection bias since the effort level of growers is likely to depend on the type of contract there in. The choice made by the grower seems to be sequential, since he/she first chooses a contract to its land block, either A, B or C, and then he/she chooses his level of effort that in a certain extent defines the total compensation associated to the land block.

The first part is a binary outcome equation that models the probability of accepting a contract i, i=A, B, C. The probability of accepting a contract i can be described as follows

S i * = x 1 ' β 1 + u 1 (6)
where

The binary decision S i to choose a contract i is modeled as the outcome of an unobserved latent variable S i * , and we observe that the contract is adopted ( S i = 1) when S i * > 0 . It is assumed that S i * is a linear function of the exogenous covariates x 1 and a random component u 1 .

otherwise S i = 1 if 0 if ! " # $ # S i * > 0
The second part uses linear regression to model the total compensation obtained by the land block, given the decision on contract adoption. This can be expressed as ( 7)

where π is the total compensation for the land block, x 2 is a vector of exogenous explanatory variables and u 2 is a random component. Since the error terms u 1 and u 2 are supposed to be uncorrelated, then the two parts are assumed to be independent and are usually estimated separately. This can be however viewed as a restriction on the model. Indeed, if the land-blocks generating a positive compensation are not randomly selected from the population, after controlling for regressors, then the results of the second-stage regression suffer from selection bias.

In what follows we use the [START_REF] Heckman | Sample Selection Bias as a Specification Error[END_REF] selection model, where the possibility of such selection bias is considered by allowing for possible dependence in the two parts of the model.

That is, let the latent variable π * denote the total compensation obtained by the land block, where the compensation is observed when π * >0. In contrast to the hurdle model, π * is observed only when S i * > 0 . In such model, the errors u 1 and u 2 are possibly correlated and have a bivariate normal distribution with zero means and covariance matrix:

Since the error u 1 in ( 6) is believed to be correlated with the outcome variable, we need to correct for this bias by finding variables that are associated with holding a contract i, but are not associated with the outcomes of contract j.

The two-step method of estimation is based on the conditional expectation

(8) π = x 2 ' β 2 + u 2 σ ρ ρ 1 ! " # # $ % & & E π x, S i * > 0 ( ) = x 2 ' β 2 + E u 2 S i * > 0 ( ) = x 2 ' β 2 + ρλ x 1 ' β 1 ( )
The method is as follows: (i) first estimate the probit equation by maximum likelihood to obtain estimates of . For each observation in the selected sample, compute the inverse of the Mill's ratio or the non-selection hazards λ = φ x 1 ' β1

( ) / Φ x 1 'β 1 ( )

Results and interpretation

Results from the second step of the Heckman model are presented in table 3. In addition, we present marginal effects of probit and OLS regressions for each contract in table 2.

In the probit results we obtain the factors explaining the choice of a contract (4.1). In the second step of the Heckman models, the factors explaining the qualitative performance of land blocks (4.2). The first group of variables in our regressions correspond to tournament mechanisms and contract provisions, then those related to the harvest, growers' characteristics and finally to land block characteristics.

The determinants of contract choice

The results from the probit model (table 2) show the factors associated with the choice of each one of the quality contracts. For contracts "A", model 1, our results show that four variables may explain this choice. First, the fact that the land block has been promoted from year t-2 and the number of years that the grower has been engaged in A contracts (NYA), but also the fact that the land block belongs to a property, and that the grape variety is TANNAT. The variable NYA

β 1 φ β 2 β λ = ρσ λ x 1 ≠ x 2 λ x 1 ' β1 ( ) x 2 ( )
reflects a reputation effect, or experience, but only related to such high quality contracts. Generic experience, usually captured with an age variable is not significant, at least for high quality contracts.

The fact that high quality contracts are associated with a property is not surprising. First, because it is a requirement in order to get into a high quality contract. Second, because it means that grapes from one property will only be mixed together in making the wine and bottled at the property. Finally, the use of TANNAT is also expected because is the main variety of the Saint Mont AOP and is the one preferred for the production for high quality wines.

For contract "B", we found a negative and significant effect of age (between 21 and 35 years of age) and the number of years with an A contract. It seems that in this case young growers are less likely carry type B contracts, instead they will start with less demanding type C contracts. It also seems that more years of experience in A contracts, the more likely the grower will continue to choose A or B contracts. In addition, the wineries to which the growers belong play a significant role in the type of contract they choose. Belonging to "Cave de Saint Mont" winery, determines in part the choice of B contracts, while those belonging to "Aignan" and "Plaissance" winery are more likely to choose C contracts. With regards to the characteristics of land blocks, we found several factors explaining this choice: the size of the land block (SURF) and the grape variety (TANNAT).

[Insert table 2]

We found opposite results for the selection of "C" contracts, a negative effect of promotion, age (young growers), NYA (number of years in A contracts), grape variety (TANNAT) and PROPERTY. It seems that the cooperative takes some measures, defined in the specifications chart, to screen growers in their contract choices.

The efficiency of the wine grape tournament

In this section we discuss the factors explaining the qualitative output of grapes, measured by the dependent variable REMTOT, that is, the compensation paid to a grower for an individual land block. In table 2 we show the results for OLS regressions for all types of contracts. However, we make the assumption that the qualitative performance of land blocks, thus grower's effort, is going to be dependent of their initial choice of contract. Therefore, we will discuss here the results of the second step of the heckman models, in which we account for this selection bias (table 3).

Using STATA's two-step method for Heckman models, we automatically obtain the inverse Mills's ratio. Using the maximum likelihood method, we obtain a test of chi2 that verifies that rho is significantly different from zero Rejecting the null hypothesis means that both equations are not independent from each other. The results of the maximum likelihood, as well as the two-step, Heckman's model show, first of all, that the correlation between the two equations is significant only for the choice of C contracts. It is not the case, however, for contracts A and B.

The compensation system is organize so that a grower's performance could be taken into account by the cooperative in order to "promote" the land block to a higher quality category, or to "demote" it to a lower category. In models 8 and 11, we observe that once a land block has been promoted (PROMO) to this category (from the previous year), it shows a positive and significant effect on its compensation (on its quality result). For quality B contracts, being promoted to this category does not have a significant influence on final output. However, the fact that the land block was demoted (DEMO), meaning that the previous year it was engaged in a higher quality contract, plays a positive and significant effect for C contracts. This could be interpreted as the fact that growers will exercise greater effort in order to be again promoted, or to "return", to the higher quality they once were.

[Insert table 3] The monitoring variable, DOWN, has a negative and significant effect for all three contract.

This means that the more the cooperative was able to identify and downgrade land blocks that are not complying with the contracts' specifications, (step 4, figure 1). Having chosen an A contract, and then being downgraded at this stage will translate in loss of proximally 2 644 euros for the grower. This variable does not include the downgrading of land blocks affected by a climatic or a disease incident; such effects are captured by the variable EFFCD, which has a logical negative effect on the final output. A similar effect is found in models 9-11 and 12-13, that is in the choice of contracts B and C.

As presented in section 3.1, the ceiling, in terms of yield, imposed on the cooperative's specifications (an additional contractual provision) is both an incentive for maximum effort and a penalty. The quality of grapes is related to a controlled (and fixed) ceiling of yield. But, because the price paid being a function of yield, we have a positive and significant effect for the variable YIELD. However, this relationship becomes negative (variable YIELD2) once a certain ceiling is breached.

The results of Models 8 through 13 indicate that the yield rule has the same result, regardless of the type of contract engaged in. We show this relationship between qualitative output and yield in figure 3. We notice a slight difference between high-quality A contracts and the rest. High quality A contracts are associated with low yields and high compensation. However, for quality B and C contracts, the penalties for exceeding the yield ceilings are less dramatic than that of A contracts. The behavior, at least in terms of respecting yield, is similar whether the initial contract is a B or a C. With regards to the growers' characteristics, age seems to have a role in quality output.

Growers with more that 45 years old produce higher qualitative output for contract B that other growers. However, the experience of the grower in high-quality "A" contracts (NYA) plays a positive role on the qualitative output for contracts C (model 13). This result could mean that the more experience a grower has in stricter high-quality contracts, the more likely he is to do better in terms of quality effort. Overall, this result could mean that once a grower is used to the exigencies of high-quality specifications, it is more likely that he/she will apply those "good practices" to all their contracts. It seems that being specialized in viticulture (VINEYARD) has a negative influence the qualitative output of grapes, for those growers having choose B contracts.

There is also, a slight positive effect for growers engaged in A contracts that belong to the "Cave d'Aignan" winery.

As for the characteristics of the land block, the main grape variety (TANNAT) plays positive role in compensation for contracts A through C. In fact, tannat is the main variety of the Saint Mont AOP and is the one preferred for the production of high quality wines. Quality is thus highly associated with grape variety.

Finally, with regards to the land block's pedoclimatic environment, we tested the influence of type of soil in which the land block is located, on final qualitative output. We found that highquality contracts (Model 11) carried on Molasse soils are likely to increase by 390 euros the compensation of such contract, all things being equal. Without any expertise in agronomy or viticulture, we are not able to explain the relationship of this type of soil and the final qualitative output of grapes. However, if we infer that a positive relationship exists between this type of soil and the qualitative output of A contracts, it would have some management implications for the cooperative. First, it would mean that some types of soils are better fitted for carrying certain modes of cultivation (quality contracts) than others. This can be used by the cooperative to replant their vines or to reallocate the contracts proposed to growers to improve the overall quality of grapes. Second, it could also raise doubts about their incentive tournament system. In fact, growers owning land blocks within "rich" soils could have an advantage, regardless of their effort, compare to their peers and thus provide limited effort.

Conclusion

In this paper, we have focused on the relationship between a wine cooperative and its membergrowers and the incentives mechanisms implemented to produce quality grapes. The cooperative's traceability database provides information to decision makers to better manage the production of quality grapes, which we used to test our hypotheses on the data from the 2008 harvest. More precisely, we show how a wine cooperative in the south west of France uses a differentiated payment system and contractual provisions, where promotion (or demotion) to (from) higher quality contracts works as an incentive for efforts to improve quality. This incentive system is similar to that of a tournament. In addition, the wine cooperative screens the growers by offering a menu of contracts and by monitoring their activities. The first screening mechanism takes place when the grower chooses the contract. The access to high quality contracts is explained by the cumulated experience on higher quality contracts and previous promotions, but also by the fact that land blocks belongs to a property or the grow of a specific grape variety:

Tannat. Age of growers appears as a detriment to access high quality contracts, as youngster start with lower quality contracts.

Testing the tournament system itself, we found that promotion and demotion from quality engagement in previous years are significantly influences of quality performance. Once someone have been demoted from the previous year, he/she will exercise greater effort in order to be again promoted, or to "return", to the higher quality they once were. Monitoring plays a big role in the tournament system, as the decision whether to downgrade a land block of wine grapes to a lower quality when the minimum quality may not be achieved, can reduce the tournament mechanism efficiency. Finally, yield control act for all three types of contracts as both an incentive for maximum effort and a penalty.

Our results confirm that the tournament mechanism built by the cooperative aims at achieving two objectives: (i) providing incentives in presence of common shock that may affect all the growers; (ii) reducing the heterogeneity among the growers embedded in the same contest in order to increase the incentives provided by the tournament compensation scheme. This paper contributes to the tournament and contract literature in viticulture by showing that relative performance compensation systems, with the possibility of being promoted to higher quality contracts, is an incentive for growers to provide higher effort levels.

Figure 2 :

 2 Figure 2: Classifying and downgrading wine-grape land blocks.

Figure 3 :

 3 Figure 3: Land block's compensation by yield.

  where and Φ are the standard normal

	density and distribution functions respectively; (ii) estimate	and	by least squares
	regression of π on x and . For more robust identification, we also impose exclusion restrictions,
	which requires that the selection equation have at least one exogenous variable excluded from the
	outcome equation. In our estimation, we use the variable PROPERTY since it has some effect on
	the selection and does not directly affect the compensation. With this exclusion restriction, we
	have	which may reduce the collinearity problem between the variable	with other
	regressors	in the compensation equation. But since this problem in the two-step method of
	estimation generates higher standard errors than those of the maximum likelihood estimation
	procedure, we use also use this procedure.

Table 1 :

 1 Summary statistics and description of variables

	Variable

Source: Geowine StMont database

[START_REF] Gay | Geowine WP 1 -Organisation de la base de données géographiques[END_REF]

, 2008 harvest.

Table 2 :

 2 Determinants of contract choice and compensation

	Probit results (M.E.)

* p < 0.05, ** p < 0.01, *** p < 0.001

Table 3 :

 3 Efficiency of compensation system with sample selection p < 0.05, ** p < 0.01, *** p < 0.001

			Heckman results Twostep method			Heckman results ML method
		Dependent variable: REMTOT (land plot compensation)		Dependent variable: REMTOT (land plot compensation)
	1st step contract choice:	Contract A	Contract B	Contract C	Contract A	Contract B	Contract C
		(8)		(9)		(10)		(11)		(12)		(13)
	PROMO	0.457 *	(0.186)	-0.026	(0.202)			0.458 *	(0.189)	-0.025	(0.159)
	DEMO			0.458	(0.662)	0.872 ***	(0.213)			0.457	(0.318)	0.792 ***	(0.191)
	DOWN	-2.645 ***	(0.303)	-1.314 ***	(0.118)	-0.315 ***	(0.080)	-2.644 ***	(0.191)	-1.313 ***	(0.112)	-0.315 ***	(0.069)
	YIELD	0.245 ***	(0.040)	0.131 ***	(0.008)	0.119 ***	(0.007)	0.246 ***	(0.031)	0.131 ***	(0.009)	0.119 ***	(0.008)
	YIELD2	-0.002 ***	(0.000)	-0.001 ***	(0.000)	-0.001 ***	(0.000)	-0.002 ***	(0.000)	-0.001 ***	(0.000)	-0.001 ***	(0.000)
	EFFCD	-6.700 ***	(0.334)	-3.888 ***	(0.175)	-2.499 ***	(0.106)	-6.700 ***	(0.326)	-3.890 ***	(0.174)	-2.480 ***	(0.103)
	AGE_21-35	0.200	(0.200)	-0.143	(0.226)	0.011	(0.078)	0.199		-0.140	(0.247)	0.084	(0.116)
	AGE_36-45	0.041	(0.180)	-0.084	(0.117)	0.008	(0.065)	0.040	(0.163)	-0.087	(0.115)	-0.033	(0.072)
	AGE_>56	0.130	(0.170)	0.248 *	(0.110)	-0.039	(0.063)	0.129	(0.146)	0.248 *	(0.121)	-0.056	(0.072)
	GEND_F	-0.375	(0.250)	-0.177	(0.200)	-0.128	(0.108)	-0.375	(0.207)	-0.175	(0.215)	-0.158	(0.138)
	AGE_>45*F	0.149	(0.300)	-0.072	(0.275)	0.156	(0.138)	0.150	(0.283)	-0.074	(0.266)	0.185	(0.165)
	NYA	0.001	(0.046)	0.013	(0.024)	0.031 **	(0.012)	0.002	(0.052)	0.013	(0.025)	0.010	(0.017)
	VINEYARD	-0.518	(0.368)	-0.784 **	(0.303)	-0.061	(0.150)	-0.518	(0.389)	-0.786 *	(0.321)	-0.129	(0.183)
	SURF	-0.358	(0.238)	0.099	(0.235)	-0.115	(0.135)	-0.358	(0.267)	0.094	(0.241)	-0.221	(0.150)
	WINERY_1	0.095	(0.137)	-0.015	(0.137)	-0.033	(0.069)	0.095	(0.189)	-0.015	(0.147)	0.011	(0.079)
	WINERY_2	0.297 *	(0.141)	0.185	(0.115)	0.031	(0.061)	0.297 *	(0.149)	0.187	(0.124)	0.082	(0.072)
	TANNAT	1.603 ***	(0.360)	0.353 *	(0.140)	0.197 ***	(0.053)	1.604 ***	(0.251)	0.347 *	(0.142)	0.024	(0.095)
	Gravel	0.353	(0.213)	-0.337	(0.202)	-0.017	(0.099)	0.354	(0.234)	-0.339	(0.193)	-0.040	(0.117)
	Clay	0.139	(0.170)	-0.164	(0.158)	0.078	(0.077)	0.140	(0.215)	-0.168	(0.155)	0.040	(0.087)
	Molasse	0.337 *	(0.165)	-0.041	(0.120)	0.081	(0.066)	0.336	(0.176)	-0.043	(0.142)	0.047	(0.075)
	Sand	0.186	(0.175)	-0.118	(0.123)	0.073	(0.072)	0.187	(0.169)	-0.122	(0.139)	0.028	(0.082)
	Constant	-0.711	(1.404)	1.030 *	(0.457)	-0.361	(0.226)	-0.721	(0.997)	1.065 *	(0.537)	-0.332	(0.257)
	rho							-0.244	(0.529)	-0.239	(0.242)	0.319 **	(0.109)
	mills	-0.082	(0.159)	-0.160	(0.182)	0.803 **	(0.252)
	N	1219		1219		1219		1219		1219		1219
	Censored obs	1163		1006		269		1163		1006		269
	Uncensored obs	56		213		950		56		213		950
	Robust standard errors in parentheses

*

In this article we focus on grape quality. Wine quality is going to be determined by the quality of grapes but also the technological choices involved in the wine-production process(Gergaud and Ginsburgh,

2008)

As mentioned above, sanitary and physico-chemical proprieties are not completely objective measurements of quality.

Which could be the probability of a promotion as in[START_REF] Heutel | Testing implications of a tournament model of school district salary schedules[END_REF].

As shown in[START_REF] Prendergast | The provision of incentives in firms[END_REF], effort should also increase in the efficiency of monitoring.

In contrast to what is usually analyzed in the literature, we observe that the cooperative adopts cardinal, two-part piece rate tournaments, rather than on rank order tournaments. The rationale is that tournaments based on rank, with prespecified prizes, are informationally wasteful if performance levels can be measured cardinally rather than ordinally(Holmström, 1982).

The Saint Mont vineyard is located in the far west of the Gers department, in the Midi Pyrénées Region. The Saint Mont designation, which was Appellation d'origine Vins délimitées de qualité supérieur (Designation of Origin Delimited Wine of Superior Quality. AOVDQS, for its acronym in French) and recently upgraded to Appellation d'Origine Protegée (Protected Designation of Origin, PDO. AOP, for its acronym in French), comprises an extension of 1,112 hectares and 194 wine growers[START_REF] Inao | Fiche produit "Saint Mont[END_REF].

The studied cooperative, Plaimont Producteurs, is a group which resulted from the "merge" of Plaisaince, Aignan and Saint-Mont cooperatives in the Gers Department. Plaimont Producteurs is composed of approximately 1,000 producers who work in 5,300 hectares of vineyards. It produces 36 million of bottles, which are sold worldwide every year, and generates annual revenues of 64 million Euros (27 million correspond to exports) and employs 150 people.

After conducting interviews with the cooperative's technicians, site visits and reviewing documents provided by the cooperative, we were able to analytically reconstruct the contractual process.

In French called château or domaineΠ A ≥ Π B ≥ Π C

This, of course, will not rule out opportunistic behavior, such as making a maximum effort to show compliance before visits, but it should provide a good indication of the cooperative's control, monitoring and enforcement of contracts.

The issue with land potential could partially come from adverse selection, but in reality this "potential" is not actually known neither by the cooperative or the grower.

This work was carried out by the researchers from the "École d'Ingénieurs de Purpan", as part of the WP1 of the Geowine project. These data concerned geological characteristics (mainly soil type) comes from the BRGM (Bureau de Recherche Géologique et Minière) of the Midi-Pyrénées region, while those concerning the topography (altitude, slope, and orientation) come from a numeric image of the region's landscape[START_REF] Gay | Geowine WP 1 -Organisation de la base de données géographiques[END_REF].

In such cases, growers are compensated with a low price for their grapes by the cooperative, but they also receive a compensation from their insurance independently from the cooperative (not known in our study).

Tannat is the main variety of the Saint Mont AOP. By regulation it must account at least for 60% of the final wine (INAO,

2010)

Acknowledgments

This research was funded by the French Government Fund for Research (FUI) and the Midi Pyrénées Region in the Geowine project (www.geowine.net). We are grateful to Michel Gay (EI Purpan), Olivier Bourdet-Pees and Laurent Seris (Plaimont Producteurs) for making the data available to us. We also thank Jason Franken and the participants at the sixth Annual Meeting of the American Association of Wine Economists in Princeton for their helpful comments. The analysis and comments made here are however our sole responsibility.