Nadine Hermrd

Yves Ie Roux

INM, Rennes Yves Surry

Decemberl995 -revisedMay 1996 MODELLING TRADE IN PROCESSED FOOD PRODUCTS : A GENERALIZED ARMINGTON APPROACH'

Considered as a convenient tool to explain trade flows, the Armington model has been widely used for agricultural raw commodities with few applications to processed food products. It has also been questionned due to its restrictive assumptions. The purpose of this paper is to present a more general differentiated product model which captures non-homothetic consumer preferences but also allows for testable separability conditions. This model framework which is based on the use of the "Constant Difference of Elasticities" (CDE) function is applied to the French imports and home-produced consumption of nineteen processed food products. Results indicate a frequent rejection of the Armington model and the acceptance of less restrictive preference structures.

RESUME

Le modèle drArmington est un outil commode pour expliquer les échanges commerciaux. Ce modèle qui a été utilisé pour bon nombre de produits agricoles bruts a été, d'un côté, très peu appliqué aux échanges commerciaux de biens alimentaires transformés, mais a aussi été remis en cause en raison de ses hypothèses assez restrictives. Cet article a pour objet de présenter un modèle de diftrentiation des produits plus général, qui peut à la fois prendre en compte des structures non homothétiques des préferences du consommateur, mais aussi permet de tester des conditions de séparabilité. Ce modèle qui repose sur I'utilisation de la fonction "Constant Difference of Elasticities" (CDE) est appliqué aux importations françaises et à la consommation d'origine domestique de dix neuf produits alimentaires transformés. Les résultats montrent un rejet fréquent du modèle d'Armington et I'acceptation de structures des préferences du consommateur moins restrictives.

1-Introduction

There has been a long tradition among agricultural economists to explain agricultural trade flows in terms of geographical sources of origin. This type of product differentiation has been mainly applied and/or tested for raw agricultural imports using the Armington modelt. This model assumes that the utility is homogeneously weakly separable so that the consumers' decision process may be viewed as occurring in two stages. The total quantity imported of a given product is first determined, and then allocated among competing suppliers. This two-stage model framework is implemented by assuming that imports of different origins for a given product are imperfect substitutes to each other and are determined by CES demand functions. The assumption of an homogenous weakly separable utility function also means a unitary elasticity of each import source with respect to total quantities (expenses) of imports.

Despite the abundance of empirical studies, the application of the Armingon model to agricultural trade flows have also raised a certain number of concerns (Alston et al., . Helpful contribution from Matthieu Fayolle is gratefully acknowledged.

1990), dealing mainly with the fact that one or all of the underlying assumptions have not been satisfied in numerous cases. Thus, it has been often found that imports by geographical sources were sensitive to the size of the market, thus violating a unitary elasticity of each import source with respect to total imports. In some instances, the condition of constant elasticity of substitution among pairs of import sources was not supported by the data. Another issue which has been overlooked in applying the Armington model to agricultural commodities was the inability to treat the question of separability between home production and different sources of imports. Finally it has also been found that the econometric performance of the basic Armington model was so poor in some cases that additional variables such as a time trend or lagged dependent variables were introduced to capture non price effects and dynamic adjustments.

Two streams of empirical works have tried to overcome these weaknesses of the Armington model applied to agricultural trade. The first one consisted of refining the original Armington model specification by relaering the homogeneity condition (see Ito S. et al., 1990). Other studies suggested to use more general functional forms and models which accounted for both non-homogeneity and the existence of variable elasticities of substitution among import sources2.

The majority of the studies applyrng the Armington model to agricultural trade deals mainly with bulk commodities with almost little attention being paid to the trade flows in pràcessed food products3. This situation is somewhat surprising in light of the differentiated nature of such products, but also due to the growing importance of these categories of products in world trade and the existence of significant intra-trade in food processed products worldwide (Mc Corriston and Sheldoq l99l). The purpose of the paper is to fill this gap concerning the lack of in-depth empirical applications to explain imports in processed food products.

More specifically we first develop a differentiated product model framework that enables us to remedy the weaknesses of the Armington model. The proposed procedure is based on the use of an indirect implicitly additive consumer preference to explain imports and home production of commodities and its implementation through the "Constant Difference of Elasticities" (CDE) functional form developed by Hanoch Qg7r4. Such a framework is attractive for three reasons. First, it allows to capture more general consumers' preference structures without imposing conditions of homogeneity and constant elasticity of substitution. These latter conditions are nested within the CDE functional form and thus can be easily tested. The second advantage of the CDE framework is that it offers the possibility to simply check the separability condition between imported sources and home production. Finally, depending upon certain conditions, the CDE could be globally valid over its regularity domain and is more parsimonious in parameters than the more general flexible functional forms such as AIDS, translog, normalized quadratic. The second objective of this study is to apply this proposed differentiated product model framework to French data on the consumption and imports of processed food products, and then test the Armington model, and homogenous and separable structures.

-Model framework

The proposed differentiated product model framework is similar in spirit to Armington model but more general in the sense that it takes into consideration the non- homothetic structure of consumers' preferences and allows for imperfect substitution between various import and domestic sources of a given commodity. As in Armington's, J we distinguish commodities that are differentiated by kind as "goods" and "goods" that are differentiated by origin as "products" but also make the following additional assumptions: (i) direct weak separability (non-homotheticity) of the utility funûion; (ii) varying elasticities of substitution between any two products of a good in a given market;

(iii) distinct elasticities of substitution between any two any pairs of products in a given market; and (iu) imports are viewed as final good supplies entering the decision process of the consumers Therç it is possible to define a direct weakly separable consumer preference structure where each good qlfor i = 1,2,...n can be supplied by a set a m geographically differentiated products {* for s:1,2,...m. The products qri, can be ordered into a set of n separable and mutually-exclusive groups. The utility function corresponding to this separable structure is also direct weakly separable and is defined as follows:

Utql : U [vr(Q,,,Q,r,...9m), vz(gzt,gzz,...Qr),..., v,(gnr,gnz,...q)J Il ] where viO are viewed as sub-utility functions which depend upon a set of geographically differentiated products ex. It is assumed that U[.J and vi(.) satisff the usual regularity conditions of monotonicity, quasi-concavity and differentiabiltty. A utility function such as the one described bV [1.] implies subgroup conditional demands of the form, for all s belonging to group l: U.:g.[p*,RJ s=1,...m and i=\,...n 12) m where 4 =Zp* g* is total expenditure of purchasing supplies of goods i. The optimizationprocedure behind the utility function [1.] can be viewed as a two- stage decision process whereby consumers allocate first the various supplies of good i to generate sub-group indirect utility functions u1= vi(p1,R) and then mae<imize a macro utility function U[.J : U[ur,ur,...,ui,...,u,J subject to the budget constraint B =) 4[r,,p, J . However due to the non-homothetic structure of the utility functioq j=l it is not possible to replace this maximization problem by one which involves a single price and quantity indices for each good i. As a result, we cannot proceed in developing exact product aggregates among the subgroup supplies. This may constitute a major drawback in applied analysis like ours. As suggested by [START_REF] Winters | Separability and the specifications of foreign ftade functions[END_REF], it is possible to overcome this problem by adopting approximate aggregation procedures such as Theil's differential systems (Rotterdam model, for instance) or a decomposition of each group cost function into a component measuring costs at constant prices (a quantity or utility indicator) and a cost of living index @eaton and [START_REF] Deaton | kornmics and Conswner Behavior[END_REF]. This aggregation issue does not arise in the Armington model because it assumes an homogenous separable utility function which allows for the derivation of aggregate quantity and price indices for the total supplies of each good. At this stage and since the purpose of this study is to focus mainly on the lower stage of the utility function U[.J,we are leaving aside this concern of product aggregation over competing supplies for further research.

To capture and measure the various interrelations among subgroup competing supplies, we represent each subgroup utility function yi by an indirect implicitly additive CDE function: fu,u"o ,"u" = | t3 ] s=l where ," = (&J is the product price norm alized by the total cost of purchasing products. The subscript i is now omitted for reason of convenience.

In [3.], B" and e, are called distribution and expansion parameters, respectively. à" or d,: | -b, arethe parameters associated with the normalized price variables 2,. d, is also called the substitution parameter. Note that for every CDE function there are 3m parameters. It is required that B,)0, ê,)0, b,<1, and either ô"<0 for all s or 0 < â" < 1 for all s (Hano ch, 1975, p 4ll)5. Apply.g Roy's identity to [3.] and making use of the logarithmic transformation enables us to derive linearized CDE demand functions which are expressed in a log-ratio of shares form (Surry,1993):

t"-(*) --A"t g,tos(v)+b",o*(9 -r,r"seÀ) s =1,2 .-.m-1 t4 l where: n,=^t<#*), g"=ê"b"-e.b^, S,=#-, and the last supply rn is considered to lr,a, be the numeraire.

Allen partial elasticities of substitution can be computed using the following expressions (Ilanoch, 197 5, p. 412):

os1: Q,,* O'-iso ak -6"9 k=l ,S
where ô", is the Kroenecker sign equal to 1 for s : I and 0 elsewhere.

Notethatfors*l*k,6,1-0*=d"-dk:constant'Aninspectionof expression [5.] indicates that a high value associated with a' means that supply source s is à net substitute with other competing supplies. On the other hand, any pairs of supplies s and I can be complements under global validity (all the d's are positive) if m (a,*d,)<ZorSo.

&=I

The CDE function is general enough that it can also take into consideration inferior supplies sources. In fact, income elasticities may be negative, depending upon the values taken by the parameters of the CDE (a", e,) andby the shares,S". The last two properties attributêd to the CDE show that it can accommodate specific consumer preferences and thus be more general than an Armington model.

To further show the attractiveness of the CDE, it is necessary to explain how to derive various restrictive structures such as homogeneity, separability and explicit additivity. a) homogenous CDE: ês : e for all,s = 1, . ..m . The income elasticities are equal to one and the associated sub-utility functions are homogenous. The interesting point to make is the incidence on the CDE function [3.] when the parameter e is equal to unity. In this case, the CDE functional form is linearly homogenous, allowing us to define aggregate price and quantity indices for the good I so that & = p,q,. Expression [3.] can t5l be simplified and defined as an implicit CDE price function with arguments being the aggregate price of good I (P) and the price of each supply sourcepir Éa(ra)'=t 16l r=I Applying Roy's identity to expression [6.] leads to a "generalized" Arminglon model with varying pair-wise elasticities of substitution. The associated linearized CDE demand function can be written as follows:

.ç t"r(f) = A,+b,t"t(+)-htoe(br) s =t,2 ...m-r 17l

Theq the basic Armington model with constant elasticity of substitution o can be imposed on expression [7.] by setting all the ô" equal to a constant ô (and then the a" equal to a constant a). b) explicit versions of the CDE function. We include herein the non-homothetic Armington model and the explicit indirect CDE. In the former case, all the d, (respectively the b") are equal to a constant a (respectively b) and the CDE function can be expressed as a selÊdual and non-homothetic cost function. An explicit indirect CDE is obtained if all the terms ep" are all equal to a constant term g. It results in an explicit reciprocal indirect utility function (HanoctL 7975,p. 415). This case is also worth mentioning because it generates income elasticities which only depend upon the substitution coefficients a, and consumer expenditure shares d (" = l, ...m): fr 4": d,+l -laosr k=1 c) separable CDE structures. To tackle the issue of weak separability between domestic and import sources of supplies for goods i, it is necessary to develop appropriate separable forms within the CDE model framework. For this pu{posg let us assume that a given set s of supplies of goods i are partitioned in two mutually-exclusive subsets, one for imported sources denoted IS:{1, ...m-l } and one for the domestic source DS={z}. Imported supplies {q,.,,...gi,^-t} are weakly separable from the home-produced sourc e at a point if o hn = o n for k and/ e IS at that point @erndt and Cluistensen,lgT3). Using expression [5.], we see that ohn=o,. implies d,o=a, for k and / e IS. This also means that we can aggregate all import supplies in a CES framework with a common elasticity of substitution equal to: dk=dt=d, (Conlon, lee3).

The It is also worth closing this section by discussing the properties and derivation of Morishima elasticities of substitution implied by the CDE function. This measure which can be viewed as a measure of curvature of the indifference curves is given by: ) dl MES* = âlog(pr)

The Morishima elasticities of substitution associated with the CDE function are positive, thus implying that competing supplies are substitutes in the Morishima sense. They are bound by the two parameters a" and ar, and are asymmetric. There is another interesting property of the Morishima elasticities worth noting: that is, the raw totals of the MES matrix are constrained to be equal to the same value, due to the zero degree homogeneity of the compensated demand functions with respect to prices Slertel, 1991):

VMES, = SMES =itns,o= -É Soo* k=t k=t tg ]

=-i"u=irr-sr)ou v s=r,...m k=l k=t where e*is the own-price elasticity.

From [8.], it can be seen that in the CDE function, the term SMES is equal to the weighted sum of the substitution parameters dr. Although it can give a global and indirect measure on the curvature of the indifference curves, SMES will also be used to test the hypothesis of linear homogeneity within a homogenous CDE structure.

-Empirical model and statistical test procedures

The proposed differentiated product model is applied to imports and home- produced supplies of processed food products in France. Over the last twenty years, Èrench imports of food products have steadily increased to reach 150 billion French Francs (FF), among which 100 billion FF concern processed food products. Such pattern is associated with a gradual integration of the European Union (EU) agri-food sectors, and the development of intra-trade in this kind of products (Chevassus-Lozza and Gallezot, 1993). French imports of processed food products originating from the Rest of the EU are now representing 760Â of the total while the rest of the World share is only 24Yo. Girven this situation, it is interesting to know how the various competing supplies of a given processed food product intersect each other. In addition, do French consumers discriminate between imports and home-production? Or do they favor instead a European preference ("preference commwurutaire") at the expense of imports from the Rest of the World EO!V)?

The CDE differentiated product model developed in the previous section is ideally suited to answer these questions and applied to processed food products consumed in France. For each of the goods considered, we distinguish three sources of competing supplies, namely imports from the Rest of the EU (s=1) and from the Rest of the World (s=2) and consumption of home-produced products (=3). A time trend is also incorporated in the CDE function to capture non-price effects. The empirical CDE demand specification that will be estimated with the French data has the following form:

t*("rJ = A,* s,tos(v).r"t"r(#) +4rog(9 + f, rIME + ( s=1,2 [e] =âlog(x": {t) = srd,+(r-,so)a o for s+ k ôlos(p*)

where A"=bgfu), R= F_ro*r, g"=ep"-erb3, .f"=d"-d, (dris the time trend coefficient relative to the demand from source k:1,2,3) and f is a random term error.

The implementation of [9.] raises several estimation problems. First, the distribution, expansion and time trend parameters cannot be estimated since only m-l equations are estimated. Second, the presence of the total cost variable among the right hand side (RIIS) where sr=!= u-:2:-t!:

, Hr= Ar-er4, and f =.fr-st.fz. gz e2D2 -e3D3 pis a normally distributed random term error with an expected value equal to zero and a constant variance d. Note that in the case of three sources, only one equation has to be estimated.

Expression [0.] which includes now two RHS endogenous variables (R and SrlSr) will be estimated using a nonlinear two stage least squares (NL2SLS) estimation procedure. The resulting estimated parameters are asymptotically normally distributed [START_REF] Amemiya | Advanced Econometrics[END_REF]. The identification problem noted earlier worsens in the sense that we need now one more restriction for each set of distributioq expansion and time trend parameters. Despite this, the price parameters (ô) are still identifiable and the various homogeneity, separability and explicit additivity conditions can be tested or implemented with expression [0.].

o Homogeneity and linear homogeneity An homogeneous structure (e, = ", = % = e) is imposed if the parameter er=(&lgz) is set to be equal to (4 -br)l@r-br).It can be seen that the expansion parameter e vanishes from equation [0.]. Consequently, it is not possible to discriminate between the various degrees of homogeneity of the CDE and more especially between the case where e: I (linear homogeneity) against e*l (non linear homogeneity) with equation [0.]. This can be overcome by using an indirect testing procedure which consists of computing the indicator SMES under the linear and non linear homogeneous conditions and then statistically test whether they differ from each other. As the computed SMES is a weighted combination of normally distributed random variables (assuming that a1 are normally distributed)6 for given shares ,S,, it is a normally distributed variable with an expected value E(SMES) equal ,o f tf -S,)â, and a I=l variance v(sMES) equal to ift-s)2r(At)*zj j1r-s,Xl-s)cov(àr,à,7. The I=l ,=l &=l test of linear homogeneity is then implemented by companng SAIES under the null hypothesis Ho: D = SEluIS6r, -SEIIIS6T) = 0, against the alternative hypothesis Hr'. D= SfuISq"=t,-SEIuISç*ry É 0. The null hypothesis will be accepted if Z=E(D)f JV(D is smaller than 1.96 for a significance level of 5%. Note that this suggested test on linear homogeneity of the CDE is an approximate one because it is tested at a point (i.e. for given shares ^S, ).

o Explicit additivity An indirect explicitly additive structure is imposed on the underlying CDE by imposing a value of zero to e, in [0.] (IlanoctL 1975). Such a condition corresponds to a situation where the various ep, are all equal to a constant g. . SeparabiliA

The implementation of the separability conditions using expression [10.] can be easily done. The condition that imports are weakly separable from home production is performed by letting br=b"*br. Another worth considering separable structure is to impose b, = b, + à, . This implies that French consumers, for a given good, distinguish European products (imported from the Rest of the EU and home-produced) from these originating from the Rest of the World (that would indicate that French consumers are influenced by the "preference commutututaire').In these two cases, the CDE function can be viewed as an aggregation of two CES functions. Finally, the condition that the elasticities of substitution are constant as in the Armington model is imposed by incorporating the restriction that b,b, = bt = b .

To test the various hypotheses andlor alternative model specifications, v/e adopt a three-stage procedure. First we estimate the full model [0.] and then check the statistical significance of the time trend variable using a "t"-test. Then, homogenous, explicitly additive and separable structures are tested individually and independently from each other. We use the Quasi Likelihood Ratio (QLR) test for homogeneity and separability hypotheses. In the context ofNL2SLS estimation procedure, the QLR test is defined as follows:

QLR= T(Qo -Q) I t'
where po is the value of the minimum distance criterion for the null hypothesis, Q is the minimum distance criterion under the unrestricted estimator, ,s'is a consistent estimate of the variance of the disturbances under the maintained hypothesis, and 7 is the number of observations. The statistic QLRis asymptotically distributed as a 7' t,nthr degrees of freedom, where r is the number of restrictions imposed on the parameters (Jorgenson and Gallant,1979). When homogeneity has not been rejected, we further test for linear homogeneity using the previously defined "2"-statistic calculated at the sample mean point.

Concerning the hypothesis of explicit additivity, a QLR test can also be used. However, since this hypothesis only involves testing one simple restriction (i.e. e, = 0), we opt for a statistical procedure based on the "t"-test.

The last stage of the testing procedure consists of analyzing feasible combinations of different structures such as homogeneity and separability. A first case occurs with homogenei$ (er=€2=ez=e) and br=bz*b, ("preference communautaire"): in this case, tr = 0. On the other hand, an homogenous structure where home production is separable from imports is accepted when b, = b" * ôr, which involves tr = L These two sets of restrictions can be imposed and tested with expression [10.] using a QLR test.

However, there remains a situation where separability and homogeneity cannot directly be tested with equation [0.]. This has to do with the case of constant elasticity of substitution (b, = b, = b) where we impose homogeneity. In this case, the parameter e, is indeterminate, and there is no way that such a condition can be tested with equation [10.]. This inconsistency can be overcome using the two previous tests which are conducted independently. In fact, it can be seen that an acceptance of both tests on separability and homogeneity leads to the non-rejection of the homogenous model with constant elasticity of substitution.

-Econometric results and interpretations

Data used to estimate the CDE demand specification [0.] stem from two reference sources. Import data by origin were obtained from the French Customs trade data base while the prices and quantity consumed of home-produced goods are aggregates from the French National accounts developed by INSEE. Before we proceeded with the econometric estimatioq both data sources had to be harmonized to generate comparable prices and quantity aggregates on the various competing supplies of the processed food products. Such a task is very difficult, if not impossible, to perform at an aggregate level (3 SITC digit levels for instance). On the other hand, it is possible to obtain satisfactory and comparable data if we develop all these quantity and price aggregates at a more detailed and disaggregated level. For this pu{pose, we used the NAP 600level of the French National Accounts nomenclature (about 700 products) and matched it with the corresponding nomenclature of the French Customs data base. There are about 50 processed food products at the NAP 600 level but we only retain the ones for which each of the three import and home produced supplies represent at least lYo of the total consumption. This selection led to the a set of 19 products, the consumption of which represents about 300 billion FF in 1994.

Data for all the dependent and explanatory variables were available on an annual basis over the period 1977-1994. The set of instrumental variables used in the NL2SLS estimation includes a constant, price indices of each import source and home-produced products, the time trend variable and general economic variables such as real GNP and its corresponding price deflator. These last two variables are supposed to capture some overall factors influencing the total demand for each processed food good.

Gven the purpose of this paper which is to test a new differentiated product model framework, we only give an account of the regularity conditions associated with each estimated CDE function and present the statistical test results reported in Table l. A ut"- test applied to the estimated parameterf in equation [10.] led us to conclude that the trend variable is not statistically significantly different in all cases but three (fresh meat, canned fruit and janq and seasonings and salad dressings). An analysis of the regularity conditions gives a varied picture (see column 1 of Table l). Test results for explicit additivity, homogeneity, and separability Note:The null hypothesis for homogeneity and for the two first separable structures is not rejected if the QLR statistic is smaller th:rrl: I1./"(1) = 3.8+; the null hypothesis for the last separable structure is not rejected if the QLR statstc is smaller than : f!"r"(2) = S.gg .

  sl

  above restrictive structures are intermediate.cases between the general CDE function and the basic Armington model charactenzed by linear homogeneity and constant elasticities of substitution. In fact it has been shown that the only functional forms which satisfy simultaneously homogeneity and explicit additivity belong to the family of Bergsonian functions, that is Cobb-Douglas or CES (see Berndt andChristensen, 1973). Consequently we can conclude that any combination among homogenous, explicitly additive and separable structures leads to a single or multi-stage CES preference structure.

  variables requires the use of a simultaneous equation estimation procedure in order to overcome any simultaneity bias. FinallS the output variable y is an unmeasurable utility index. As a result, rrye must eliminate this latter explanatory variable from equation[9.].This problem can be overcome by adopting a modified procedure developed byHanoch (1975, p. al2). It consisted of generating a new specification made up of the difference tog(S, /Sr) -e, tog(^tr/^tr), *d then rearranging the various terms leads (after some manipulation) to the derivation ofthe following estimable specification:

	'"r[*) \J3,/ :H,*",t*[9 +4 ros(&o) -b,,,bs(H \; -\ /t /	t10 l
	-b,(r-e,)t"r[*) + f uIME + p '\R/ J

Table 1

 1

Six estimated CDE functions are globally valid with estimated à coefficients falling within the acceptable range of possible values. We have then eight processed food products for which the local validity conditions are satisfied. Finally, five estimated CDE functions (fresh meat, canned vegetables, prepared feeds and miscellaneous food products) do have estimated ô coefficients, the values of which are not acceptable and outside the permissible range. Given this, it would make sense to discard these five processed food products and proceed with the fourteen remaining ones. At this stagg we did not follow this strategy and present statistical test results for the full set of processed food products considered.

Turning now to each kind of restrictive structures, we find that explicit additivity will be accepted for the following goods at a significance level of 50Â: game and poultry meat; cookies and bakery products; coffeq tea and other herbs; seasonings and salad dressings; and soup mixes. In these cases, it means that the underlying consumer supplies preferences for each good are represented by a subgroup utility function of the form ( m \l/g (yr)=[I A"@"lD') Homogeneity conditions were tested (conditionally to the non-constance of elasticities of substitution) by imposing two nonlinear restrictions on the parameters tr and 0.. An inspection of the calculated QLR statistic reported in the second column of Table 1 indicates that we do not accept homogeneity in only five cases out of nineteen. The category "baby and dietetic foods" deserves a special comment. In fact, various attempts to estimate expression [10.] under the condition of homogeneity led to a non convergent solution and degenerate econometric estimates for some of the parameters. This situation is not surprising due to the high nonlinear nature of the restrictions imposed on the b parameters. In all other cases, convergence was easily attained.

When homogeneity has not been rejected, the next step was to check about linear homogeneity (e=l or et 1) through the "Z"-test performed on the SMES indicator.

Results of this test presented in the third column of Table I show that linear homogeneity is rejected for only prepared feeds, and for the category "seasonings and salad dressings".

In all other cases, we can accept the idea that supplies ofeach processed food product could be specified by a linearly homogenous CDE function given by expression [7.].

Statistical test results on non-homogenous separable structures are reported in the last three columns of Table l. Their interpretation is more difficult because it involves several outcomes. To facilitate the interpretatioq let us begin with the case where all the à coefficients are all equal to a constant (last column of Table l). This situation corresponds to the non-homogenous Armington model and is only accepted for seven goods including fresh meat, cheese, milk industry by-products, the category "coffee tea and other herbs", miscellaneous food products, brandies, and the category "fruit and vegetable juices". Note also within this set of goods, we rejected the condition of explicit additivity for the category "coffee tea and other herbs" while accepting homogeneity for the other categories ofgoods.

In all other cases where a non homogenous Armington model has been rejected

(this concerns twelve goods), three possible alternatives could occur. First, no separable structures would seem acceptable and all of them would be rejected by the QLR tests. This case arises for four categories of goods (canned fruit and jam, prepared feeds, baby and dietetic foods and brandies). The two other alternatives which are mutually exclusive t2 will apply to the eight remaining goods. Both of them are charactenzed by nested CES structures within the consumers' supplies preferences. The first of this nested structure which refers to the case where home-produced and imported products are separable (br=br*br) is not rejected for game and poultry meat, canned vegetables, starch products and the category "chocolate and confectionery products".

Finally, the separable structure associated with "preference communautaire" is accepted for canned fistr, cookies and bakery products, soup mixes, and the category "seasonings and salad dressings".

The last aspect of the econometric results we must discuss concerns the possible existence of both homogenous and separable structures among the supplies of processed food products. As it has already been pointed out, two possible cases can be imposed in the CDE model framework and tested independently from each other. The first one which consists of imposing homogeneity (er=€2=es=e) and separability betrveen imports and home production (br=br+br) is rejected for all the processed food products analyzed except for fresh meat, and baby and dietetic foods at a 5Yo level of significance (denoted a), and canned fruit and juices, and the category "fruit and vegetable juices" if we assume cr equal to l%o7. The second testable structure is to impose homogeneity and separability between ROW imports and the European and French supplies (br=br*br). These conditions are not rejected for only one product (milk industry by-products) if v/e assume a 5% significance level and two other ones (frestr meat and-cànned fruit juices) at a level of 1To8. Finally, if both separable and homogenous structures are not rejected, then we can infer that an homogenous Armington model is acceptable. This last case will only occur for two categories of products (fresh meat, and canned fruit and jam) at a Io level of significance.

-Summary and conclusions

This paper presents a "generalized Armington" model framework capable of explaining trade flows on the basis of geographical sources of differentiation. It also allows for non-homogenous preference structures among competing supplies of a given product but could be used to test separable structures such as differences between home- produced products and imports. This model framework is applied and tested in the neglected area of trade in processed food products. Our empirical application has to do with the various supplies of nineteen processed food products consumed in France.

Preliminary results clearly show that the homogenous Armington model is often rejected while more complex separable and non separable structures provide better specifications for the data analyzed. Another important finding of this study is that there is a possibility that French consumers do distinguish not only between home produced and imported food products but also between imports from the Rest of the World and supplies originating from the European Union.

Despite the fact that the results are quite encouraging, there is a need to refine the proposed differentiated product model from an empirical and methodological standpoints. On the empirical side, more applications of this model should be conducted at a more disaggregated level by considering a larger number of supplies sources. In addition, there is a need to integrate this differentiated product model framework with the upper stage ofthe consumers'preferences and hence be able to derive total responses of each supply sources to changes in prices. Since non-homogenous structures are I I l3 prevalent, ways to estimate the CDE demand specification with the unmeasured utility index must be found in order to identift expansion parameters and to measure income elasticities. In this respect, the approach developed by [START_REF] Rimmer | An implicitly directly additive demand system: estimatesfrom Australia[END_REF] for an implicitly additive CRESH functions is promising and worth considering in a CDE context.

FinallS we should not lose sight that this research only considers one form of product differentiation based on geographical sources of origin. In fact, this model can be enriched by incorporating other forms of product differentiation such as product variety.

Footnotes

t Whithout being exhaustive, a review of the main agricultural economics journals spanning the period 1980-1995 showed that the Armington model has also been applied to the following agricultural commodities: corq cottorç fruits and vegetables, poultry products, red meat, soybeans, wheat.

2 In this vein, we should mention the work of Henning and Martin for wheat (1988) who used an AIDS model.

3 To our knowledge, there have not been any single studies focussing mainly on the application of Armington-like models to processed food products. The only existing applications have been conducted at a very agregate level (usually 3-digit level of the Standard International Trade Classification) and were part of a more general empirical work covering a wide range of manufacturing sectors. For examples of such studies dealing with Europe, let us mention the work ofBrenton (1989). o K. H.lort (1988) applied the CDE function to estimate elasticities of substitution among class and source of imported wheat on a world wide basis.

5 Weaker (local) conditions on the existence of the CDE function can be obtained if (l one b,> | or (ii) some.B" and ô" are of different sign.

6 To generate the a1's under the null hypothesis (e:l), we would have to use the system of equations given by expression [7.] and estimate it by iterative three stage least squares. The resulting estimated a, artê asymptotically normally distributed.

7 Infact,the null hypothesis of homogeneity and separability between imports and home produced consumption is accepted if the calculated QLR statistic is smaller than a y2 with 3 degrees of freedom (X'Q):7.81 for cr:0.05 and ll.3 for a = 0.01). The calculated QLR statistics associated with fresh meat, canned fruit and jam, baby and dietetic foods, and fruit and vegetable juices are respectively 2.00, 8.70, 1.10 and 5.49.

t The calculated QLR statistic for fresh meat, milk industry by-products, and canned fruit and jam were 8.55, 0.7 and 10.6.


Overcapitalisation and public interventions

. The combination of these properties naturally leads to a phenomenon of overcapitalisation. This combination supplies some negative externalities between fishermen who exploit a same fish stock.

Consequently, every fisherman is vulnerable to the actions of the others. These peculiarities of fish resource leads to a situation of overcapacity which is the natural consequence of the exploitation even if the natural exploitation is not efficient.

Overcapitalisation, which inevitably induces smaller stocks, leads to endanger the very existence of fishermen. This is the reason why the European Commission tries to obtain a better balance between vessels and fish resource availability. Overfishing due to overcapitalisation is a real threat for fish and fishermen. This justifies the necessity of public interventions to decrease fishing capacity.

The European structural policy of the Common fisheries policy introduced in 1983 the first Multi-Annual Guidance Program (MAGP) with for main goal the limitation of excess in fishing capacity. Even if overfishing and fish stock decline was obvious, this first program had a very low impact on the European fleet structure. Nobody was really concerned by fishing resource protection.

However, at the beginning of the nineties the actors of the fishing industry and the state members become aware of the fact that there are too many vessels in the European Union for the fish availability. This new awareness of the overcapitalisation really appears when the European Commission threatens state-members to suppress their subsidies for new vessels' construction if they do not decrease the fishing effort of their fleet. It was up to each member state to decide how to reach the restricting targets agreed in the MAGP.

In March I99I, the French government chooses to introduce a policy of public financial incentives to boat decommissioning to meet the European requirements of the 2"d MAGP concerning fleet capacity reductions for the period I98l-199I. The launch of the first decommissioning scheme -known as "the Mellick Plan"-intended to reduce the power capacity of the French fleet by 10%. The aim was to withdraw as quickly as possible more than 100.000 kW.

The idea was to scrap vessels, to use them in other sectors, or to transfer vessels outside Community waters.

Since 1993, several other plans were adopted, aiming like the first one at fulfilling European fleet capacity reduction targets, but the first scheme stays the plan where the highest amounts of grants were allocated. Indeed, financial support to decommissioning, which had fallen in relative and absolute terms after the achievement of the "Mellick Plan" at the beginning of the decade, increased again with the new schemes which were launched from 1993, without however reaching the level of 1991 (see table 1).

The two following tables depict the place taken by decommissioning schemes (in bold characters) within the general frame of EU and Government assistance to the French fishing industry and aquaculture over the period 199I-1996 (MAP, 1997) (INSEE 1997ll for the price index)

Table2. EU and French government expenditures in aid to the French fishing industry and aquaculture.

Yearly average 199l-1996 (constant French Francs) * millions of constant 1996 French Francs. Calculated from MAP 1997 (INSEE 1997ll for the price index)

With an avetage of 56 million French Francs per year (see table 2), amounts allocated by the EU and the French Government to decommissioning schemes represent only slightly more than lYo of the total expenditures of these authorities in aid to the sector over the period I99I-96.

The financing of decommissioning schemes represents about 13% of the total EU and government expenditures for the "exploitation of natural resources" area (without including aquaculture), far behind subsidies to investment (representing 50o of the whole compensation of reduced interest rates of loans to fishing firms), and support to landing prices (24% of the whole set) (Giguelay,1999).

During the period under survey, it appears that EU and government subsidies, aiming at reducing the pressure on fish stocks, were outnumbered by subsidies liable to have the opposite effect (Giguelay, 1999). The priority of most policies remains targeted out the investment and the competitiveness of the fleet. This phenomenon is taken into account when we interpret the results of DEA models.

1.3 Characteristics of the decommissioning schemes.

The evaluation of a public action is not always simple since various parameters and constraints have to be taken into consideration. In the case of financial incentives policy launched by the French government to withdraw vessels from French fleet, the direct effects of the scheme are obvious enough to bring to the fore. Indeed the withdrawal of a vessel is the direct consequence of a grand aid allocation. Thus, it is possible to quantify the direct effects of this financial support. In the evaluation of a public action this is not always the case. As regards French decommissioning schemes the judicious moment for a policy evaluation is when every vessels are withdrawn consequently to the allocation of the grand aid.

Thus it allows us to provide a"real" evaluation of French decommissioning schemes.

French public decommissioning schemes can be appraised according to two points of view.

The instigator of public measures appraised the effects of the action however fishermen who benefit of this program have an opinion and their own appraisal of the public action .

In this paper we assess the consequences of the launch of decommissioning schemes according to the sole view of the public actors financing these programs. From a public point of view, this study provides an evaluation of the performance of subsidies, involved in the decommissioning scheme policy, in reducing fishing capacity.

This approach rests on an ex-post evaluation of the launch of a decommissioning scheme. The analysis is based on the use of different input-oriented DEA models [START_REF] Charnes | Measuring the efficiency of decision making units[END_REF]), (Banker et al. 1984).

This paper provides an original use of DEA models. Most of the time, they are used in a production context. How produce better? How produce cheaper?

However, in this study, the objective is the suppression of a capacity of production. This kind of policy remains relatively rare. 2Data and models

Objectives of the paper

The aim of this study is to assess the performance of public subsidies according to the view of public authorities. The interest of the society (public actors and taxpayers) is that public authorities launch the least expensive policies as possible.

Thus we consider the funds allocated and their consequences in term of excess capacity eliminated.

Indeed, the official aim of the schemes is not the withdrawal of vessels but the destruction of the excess of fishing capacity.It is more worth withdrawing a very powerful vessel than two little small fishing boats if the state really wants to get the requirements of the European Commission. We can underline that the elimination of excess capacity is an intermediary goal. The official aim of this policy is the preservation of fish resource to insure the durability of the activity of fishermen. Some contractions seem to exist between the tables adopted by the European Commission and the announced targets. The tables are based on the tonnage of the vessels while the objectives are expressed in terms of kWs. Consequently, the fishing capacity is reduced, in the models of this paper, to one technical attribute (the engine-power or the tonnage of vessels) to represent the reality of the objectives.

From a political point of view, the question which guides our interpretation of the results is : could a similar fishing capacity reduction (engine-power or tonnage of vessels) have been obtained from a lower amount of public financing?

The aim of this study is not to discuss the requirements of the UE but to analyse the performance of public subsidies allocated in function of the official targets announced. That is the reason why two DEA models are computed. In the first one the fishing capacity is represented by the engine-power of the vessel and by the tonnage of the fishing boat in the second one.

Then, DEA results allow us to underline the windfall effects which are always present in most incentive policies.

2.2Data

The first decommissioning scheme, launched in France in 199I, is the subject of this study for two reasons. It inaugurated the beginning of the use of a new tool and it was the most important scheme launched in terms of funds allocated.

It was necessary to collect data by getting in touch with each region and department, a task which up to now has been undertaken only for the region of Brittany and the department of Morbihanl.Three kinds of subsidies are allocated because the first decommissioning scheme was co-financed by French govemment and local communities (region and department) Brittany was chosen for its prominent position in the French fishing industry.

This study only considers the department of Morbihan for which a complete set of data concerning public subsidies at the national, regional and department levels has been collected. The DEA approach was used to assess the performance of public subsidies.

The Decision Making Units (DMU) are the vessels of Morbihan withdrawn in the scope of the first decommissioning scheme. Each vessel corresponds to a fisherman who was ready to end his fishing activity.

The inputs are the three grand aids allocated by the French State, the region of Brittany and the department of Morbihan to each fisherman who wanted to withdraw his vessel from the French fleet. These subsidies take into account not only the cost of the vessel but also the psychological cost of the end of fisherman's activity.

These subsidies are supposed to have been just incentive enough to incite fishermen to withdraw their vessels from the fleet.

Moreover, even if all these subsidies are expressed in French Francs, we don't aggregate these allocations because the sources of these firnds come from different administrative levels. A French Franc allocated by the region or the department is not similar to a French Franc allocated by the French government.

A recent report of the European Commission highlights the fact that the decrease of the fishing capacity can represent a good indicator of the reduction in fishing effort even if fishing effort is defined as capacity multiplied by activity expressed in days spent at sea. For each vessel scrapped, all its technical attributes have been collected to assess a certain decrease in fishing efforl. However for the different reasons explained above the evaluation of excess capacity is represented by the engine-power or the tonnage of the vessel.3

3 In further research all technical attributes ofthe vessel will be taken into account to evaluate its fishing capacity.lndeed, this type of modelling model seems more realistic as regards the ofhcial targets announced. The table below sums up the inputs and outputs used in our different models Let's note x oi 2 0 the amount of subsidies p allocated to the owner of the vessel j to withdraw it from the fleet and yçi> 0 the fishing capacity c eliminated by the fisherman j in the scope of the decommissioning scheme.

In this modelling a withdrawal is deemed inefficient when a lower level of subsidies could have led to a higher or an equal fishing capacity reduction.

Model I.

When the fishing capacity eliminated is measured by vessels engine-power

The first model is an input-oriented model with 3 inputs (the grand aid allocated by the French State, the region of Brittany and the department of Morbihan). To meet the first requirements of the European Community, which goal is to reduce the fishing engine-power capacity of the European fleet, we just consider one output: the engine-power of the vessel expressed in kW.

Reducing fishing capacity to the power of the vessel is not very rigorous. A vessel can be fewer powerful and can bring a high pressure on the fish resource if its tonnage is important, Even ifthe fishing capacity is not the fishing effort, the capacity ofa vessel, represented by all technical attributes ofthe boat, can be considered as a good indicator ofthe pressure on the fish stocks ofa vessel. it depends on the kind of fishing activity practised. As the same, the age of the vessel is an indirect indicator of the fishing effort. Indeed, new vessels have greater fishing power than old ones thanks to advances in technology. The impact of technological progress on the fishing capacity of the fleet is real.

Let us consider a vessel t (f = L...J).

In this DEA analysis, the mathematical program consists in J optimisations (one for each vessel withdrawn in the scope of the scheme.)

For each vessel withdrawn, the model searches if it is possible to eliminate the same fishing capacity with an equiproportional reduction in all subsidies. If this reduction is not possible, the withdrawal is deemed efficient. The observed vessel was scrapped with the lower amount of the three grants as possible. If this reduction is possible, withdrawal is deemed inefficient.

The same engine-power capacity or tonnage could have been eliminated with a lower amount of public financing.

The DEA model used is defined as follows:

Min ho s/t ZL.,E, 2Eo -ZLoix ri + hox no z 0 p = 1,...,P (v ro) (p) 21,, = I 1r,'-o j ho free 1,..., J A variable returns to scale assumption is made since we cannot assume the existence of a proportionality between the allocated grants and the eliminated fishing capacity.

The constraint | 1,,, :1 represents the assumption of variable returns to scale. l0 l,,i : the intensity variable of the vessel fr associated with the withdrawn vessel 7 , hk : efficiency score.

A vessel AE is efficient if every variable is equal to 0 except )"oo and if hoequals 1 while a vessel fr is inefficient if fto is less than unity.

As regards the inefficient vessels,the )"0, are equal to 0 excepted when the vessel 7 is used to construct a "virtual vessel" with which the vessel k can be compared. We try to minimise the subsidies allocated to this "virtual vessel" which is a linear combination of the real efficient vessels.

In order to obtain an efficient allocation, the non-efficient vessel should have had all attributes of the "virtual vessel".

Model II:

When the fishing capacity eliminated is measured by vessels tonnage. This programs can be solved by using the tonnage as the only one representation of the fishing capacity of the vessel. Indeed the French schemes allocate subsidies in function of the tonnage of the vessel even if they want to reduce the power of the fleeta.

Then, it will be useful to compare the results provided by of model I and II.

Each withdrawn vessel deemed efficient is used to build up a frontier of optimal subsidy allocation. All vessels deemed inefficient are projected on this frontier to evaluate how far they are from their optimal grants. However, this projection onto the frontier is not always pareto-optimal [START_REF] Koopmans | An analysis of production as an efficient combination of activities[END_REF]. This is the case when the efficiency measurement is derived from a point which is on a section of the piecewise linear frontier which runs parallel to the axes as shown in figure 1.

a The possible correlation between the engine-power and the tonnage, as it can be seen in the next section, does not influence DEA results. In figure 1, X1 and X2 represents two subsidies allocated to reduce the fishing capacity of the fleet and yy' is the frontier of lower subsidy allocation as regards a same fishing capacity eliminated. The vessel A' is technically efficient and pareto-optimal since it is not possible to obtain a better subsidy allocation. The vessel B' is efficient based on Farrell's definition (1957) (equiproportional reduction of each grant allocated). However, it is still possible to reduce the amount of subsidy X2 since vessel C contributes to the same fishing capacity elimination as B'with the same amount of subsidy Xl but with a lower amount of subsidy X2.

Thus, B' is not pareto-optimal as defined by [START_REF] Koopmans | An analysis of production as an efficient combination of activities[END_REF].

The introduction of slacks variables allows us to capture this difference between the two definition presented aboves. These variables are introduced in DEA models to change each constraint of (2) in equalities. Now, a withdrawn vessel is deemed efficient if and only if ho =I and simultaneously all slack variables are equal to zero.

t Other methods, like the non-radial measurement, for example, allow to find a pareto-optimal efficient projected point according to Koopmans (Koopmans, Based on these first results, it seems that the use of tonnage as a representation of the fishing capacity of the French fleet is not in contradiction with the objective of reducing vessel power capacity. We can even notice that the funds allocated to the tonnage of the vessels are more efficient when we consider that they have contributed to the elimination of kW.(the efficiency score of model I is higher than the one of model II)

3.2 The issue of correlation between the tonnage and the engine of the vessels

The correlation between the tonnage and the engine-power of a vessel seems to be obvious.

However this correlation exists only for the biggest units when we considered the smallest boats of our population it appears that this correlation is not so evident. In fact the link between the tonnage and the engine-power of a vessel depends on the fishing activity practised. Thus it seems to be interesting to compare results obtained by the computing of model I and model II on two different populations.

The first population is the whole sample which presents a correlation between the tonnage and the power-engine. (Results have been presented above).

l3

The second population is a sub-sample of the whole sample characterised by the smallest vessels (56 vessels of less than 9m) for which no significant correlation exists.

In the two cases, results are going in the same way: whatever the model used, each population presents similar performances.

Thus financing the withdrawal of GRT is not in contradiction with the main goal which is to suppress kW from the fleet whatever the vessels considered.

Thus the logic of the policy is not challenged by the adoption of tables based on the tonnage as regards the empirical results obtained. Tables 7 and8 present the distribution of estimated efficiency scores in model I and IL More than half of the vessels withdrawn in the scope of the first reduction program in the department of Morbihan present an efficiency score equal to 1. (this result is almost the same for the two models computed.)

The 35 vessels identified as efficient in model I (score:l) are efficient in model II. The gap between old and recent vessels concerning the savings of subsidies allocated is stronger in model I especially as regards funds allocated by the French government. Indeed, the French State would have save almost 30% of the subsidies allocated to old vessels and only almost 19% of those allocated to recent vessels.

The gap between the potential savings in model II is smaller; except for the allocation of Brittany.

Conclusion

Since the launch of the first decommissioning scheme, in France in I99I, no estimation of funds involved in these programs was done.

The use of DEA methodology is perfectly reliable for evaluating the co-ordinated performance of the subsidies allocated by the three sources (the French State, the region of Brittany and the department of Morbihan).

This paper allow us to come back on the validity of the tables used to evaluate the funds allocated in function of the tonnage of the vessel scrapped.

According to this first study, these tables would be quite efficient and more particularly as regards the kW withdrawn. A comparison made between the EU objective in terms of enginepower reduction and the French implementation in terms of tonnage points out that there is no contradiction between the financing of tonnage withdrawal to obtain a engine-power withdrawal.

Moreover DEA results bring to the fore a windfall effect, effect which is difficult to underscore even if it can seem obvious. Indeed, the owners of old vessels seem to have benefited of larger amounts of subsidies than necessary to leave the French fleet.

However, even if the results underline the fact that the withdrawal of old vessels was over- subsidised, this study highlight that this obvious political ineffrciency can be the consequence of an other political line of the French fishing policy since ensuring the competitiveness of the French fleet remains the priority of the French government.

  ) and compares it with the technical attributes of vessels withdrawn in the scope of the first decommissioning program in all Brittany region. We can underline the absence of statistical ' Brittany is shared in four depaftments : Côtes d'armor, Finistère, Ille-et-Vilaine and Morbihan 2 One vessel has been suppressed from the original sample because it presented extremal values in the amount of subsidies. These values can biase DEA results. 1 differences between the means of the whole population of Brittany and the means of the Morbihan sub-sample (except for the age of the vessel).

  scheme : rnean of the technical affributes

Figure

  Figure 1. Measurement of efficiency according Koopmans X2

Table 1 .

 1 Evolutior-r of EU and French government expenditures in aid to the French fishing industry

	:
	-t

and aquaculture, 1991-1996 (millions of constant i996 FF) Calculated from

MAP 1997

Table 3 .

 3 Summary of Data for efficiency analysis (69 vessels of Morbihan2)

		Construction year length (m) tonnage (GRT) horse-power (kW)
	Mean	69,65	10,26	29,30	114,65
	Standard deviation	5,31	8,81	92,86	228,07
	Min	57,00	4,00	0,75	3,00
	Max	81,00	54,25	58,64	1472,00
		Subsidies from	Subsidies from	Subsidies from the
		Brittanv*	Morbihan*		French state*
	Mean	45263	22585		1 55304
	Standard deviation	39021	30036		295687
	Min	25000	3560		1 7800
	Max	215250	1 75580		1 755800
	(*subsidies expressed in French francs)

Table 4

 4 presents the technical characteristics of the sample (department ofMorbihan

Table 5 .

 5 Variables description 2.3 Models Consider there are N vessels scrapped in the scope of the first decommissioning scheme in the department of Morbihan and P subsidies allocated by the French public institutions (the French state, the region of Brittany, the department of Morbihan) to withdraw C fishing aapacity from the fleet.

Table 6

 6 presents the population mean and standard deviation of estimated technical efficiency scores for model I(engine-power) and II(tonnage). On average, the estimated technical efficiency score of model I is 0.86 with a standard deviation of 0.182. It indicates that, on average, a l4%o reduction in grant allocations could have been realised to withdraw the same fishing power capacity.In model II, the potential reduction is of 15.3% since the estimated efficiency score is 0.847 with a standard deviation of 0.224.

Table 6 .

 6 Radial technical efficiency estimates of model I and model II model l* modelll** I: the only one output is the engine-power **model II: the only one output is the tonnage.

	Mean	0,860	0,847
	Standard deviation	0,182	0,224
	Min	0,242	0,242
	Max	1,000	1,000

xmodel

Table 7 .

 7 Distribution of estimated technical efficiency scores in model I These vessels are efficient according to Farrell that is to say that all these productive units are not pareto-

	KW VRS	vessels	ot TO
	of '1"	35	50.72
	SCORE between 0.95 and 1	2	2.90
	SCORE between 0.85 and 0.95	b	8.70
	SCORE : below 0.85	26	37.68
	Total	69	100.00

* efficient.

Table 8 .

 8 Distribution of estimated technical efficiency scores in model II

	GRT VRS	vessels	ùt to
	of 1*	36	52.17
	SCORE between 0.95 and '1	4	5.80
	SCORE between 0.85 and 0.95	6	8.70
	SCORE below 0.85	23	33.33
	Total	69	100.00

* same remark as above.

Table 12 .

 12 Efficiency gain in%o efficiency gain in % Saving for Brittany Saving for Morbihan Saving for the French state 20 years old and more

	Model I	34,72	38,66	30,1 6
	Model ll	30,46	33,22	22,51
	Iess than 20 years old
	Model I	24	,30	28,20	18,96
	Model ll	23	,59	30,1 6	20,01

3.3 Underscoring the windfall effect of decommissioning schemes by DEA.

The underscoring of the windfall effect needs to introduce slacks variables presented in Figure 1. Indeed, these slack variables lead to evaluate the optimal performance of the different suppliers.

The different estimations below take into account these slacks variables. In table 9, recent and old vessels are small vessels (on average less than 12 m). Recent vessels have on average a higher tonnage and engine-power than the older. All the more a new kW is always more powerful than an old one. This shows thata vessel, with the importance of the technical progress, always becomes more destructive for fish resource. Consequently, to a real protection of fish resource, it is worth withdrawing a recent vessel than an old one which would present the same technical attributes.

On average, subsidies allocated to recent vessels are higher than funds allocated to old vessels however it seems to be justify by the technical attributes of recent vessels.

Almost 600Â of the vessels withdrawn from the fleet are 20 years old and more. Both old and recent vessels appear to be over-subsidised in the two models. Old units seem to have obtained even more allocations than recent vessels as regards the power fishing capacity withdrawn. Indeed efficiency scores for old vessels are lower than for recent ones. (0.840 and 0.888 respectively for model I ; 0.862 and 0.838 for model II).

According to empirical results obtained, in model I and in model II, public authorities have encouraged the withdrawal of the oldest vessels. Consequently the owners of these old vessels have benefited of a windfall effect when the first decommissioning scheme was launched in the Morbihan.

Moreover, subsidies allocated to the decommissioning scheme are deemed less effrcient in model ll than in model I .

In this way, this public action appears to be inefficient as for the losses observed in the withdrawal of old vessels. However an other explanation may be put forward. It is highly likely that the hidden target of public authorities had been the elimination of "the old scraps" from the French fleet. Indeed, this would allow to maintain the fleet competitiveness while meeting the requirement of the European Commission. Consequently, results have to be interpreted with cautious. Figures do not always reflect the announced target but they allow to lift the veil from other goals less respectable as regards the protection offish resource!

Sources of inefficiency

The tables below enable us to identify the main sources of inefficiency among the different grant suppliers.

To obtain the optimal level of subsidies which would have been allocated to the vessels, we still need to take into account slack variables. They allow us to calculate the minimal fund necessary to withdraw a vessel from the fleet. Technical efficiency score is not enough. Indeed a vessel can present an efficiency score of 1 but, in function of its position on the efficient frontier (see Figure 1), it is sometimes possible to reduce more of the subsidies allocated to it.

Thus the allocations presented in table 10 are pareto-optimal allocations. l6 However the results are going in the same way as for the fact that the old vessels have been much more over-subsidised than the recent ones. (table 12)