J I Jin 1~~~-Àl L~nolvhë

1 ln all developped countries there is a growing concern about the level of nitrates in drinking water. ln the European Community the per liter Maximum Admissible Concentration (50 mg of N03) is reached in many areas, with peaks over 100 mg in some places. lt is significant that the more accute problems occur in ragions characterized by intensive farming and thus agriculture liability is clear.

The main sources of nitrate contamination of drinking water are -nitrogen fertilizers used to increase crop yields -animal manure resulting from intensive animal husbandry particularly -mineralization of nitrogen from the N-pool where agricultural practices play a role -other sources, including natural sources ln countries where nitrogen fertilizers are heavily used figures show a stagnation since 1980 (W. Germany) or since 1985 (Belgium). ln the Netherlands, the country with by far the highest rate of nitrate input per square kilometer, there is even a substantial decrease since 1980 from 56.2 tonnes/km 2 to 46.7 tonnes in 1988 (OECD, 1991 p. 35). Such a decrease occured when the Dutch agriculture -environment debate became a central issue. But generally the change of farmers'behaviour needs support from appropriate regulatory measures to provide adequate incentive at the farm level.

Although the fertilizer N use remains worrying this question have received growing recognition and some results are obtained or may be expected. Animal manure is a more accute problem for reasons presented in point l where the implementation of the idea of nitrogen excess is also detailed.

Among the economic incentives relevant to improve the situation the analysis emphasizes nitrogen taxation, the most feasible means. lt would increase the opportunity cost of organic nitrogen and would encourage a better utilization of manure.

To deal with the potential impacts of a tax put on fertilizers we consider nitrogen demand, first using the cost function approach which is a conventional one to derive input demand. Af+er that, a more adapted methodology based on a Tobit specification is discussed. This paper is restricted to the intensive livestock industry. However for arable farming in France it has been shown [START_REF] Vermersch | L'allocation du travail dans les exploitations céréalières : une modélisation Tobit d'une demande de facteur semi-fixe[END_REF]) that taxation would be consistent with a process of extensification.

. Focus ON MANURE

Manure is an important concern because -The N production level per ha in animal manure is generally as the same order as in chemical fertilizers in almost European countries.

-There is a higher long term trend for an increase of quantities of manure applied to agricultural land, than for fertilizers. As a consequence the proportion of N manure in total nitrogen increases (TEAGASC, 1989 p. 24) -ln animal manure production there is a shift from cattle to intensive husbandry (pig and poultry). The liquid manure coming from intensive rearing, especially pigs is less efficient, and a part, in the form of ammonium, can readily volatilize giving acid rains.

-There is a regional concentration of intensive livestock farming which leads to the emergence of so called manure surplus areas.

These factors are leading intensive livestock rearing regions to face difficulties regarding the environment, particularly in the Netherlands. Although the general French situation is pretty good, there are areas experiencing nitrate pollution problems because there is an excessive livestock intensification. Thus, Brittany with less than 5 per cent of the French Utilised Agricultural Area represents about 40 per cent of total intensive rearing output by value. Over fifty per cent, 53 % exactly, of national pig farming in concentrated in this region.

There is a local nitrate problem whenever the nitrogen applied, of one kind or another, is not ta ken up by plants and reaches ground water aquifers, or is lost in surface run-off. N uptake depends on yield response by the plant, and soil type. The excess is defined in relation with agronomie threshold determined by the self-cleansing capability of the soil (for more details see appendix) ln fact, the affects of nitrogen surplus are more intricate because ground water

r. •-~ c•; 1, .~ •
•;•'pollution de pends on the nitrogen cycle in the soils. Furthermore the affects of on-site c:: • ni~iiJ}k spreadinq are related to the nature and the state of the soi 1. According to the s:, We~th~~ • cciriditions soils can • be classified in three kinds : th ose on which slurry , .. ii~~i~àcèlinr'il 1 urisuitable at any time of year, those on which slurry can be spread at any time of year, and those on which it is unsuitable only winter. So the relationship between a certain amount of fertilizers and the consequent damage is nota simple one.

Using the French Farm Accountancy Data Network we have estimated the / nitrogen excess at the farm level for intensive livestock rearing farms (over than 1.5 animal units per ha). A panel with 100 holdings has been selected from 1982 to 1986. This panel excludes farms with less than 5 ha.

As indicated in table 1 about 80 % of all farms have an excess of nitrogen. This excess, expressed in kg of N per ha of Utilisated Agricultural Area (UAA), varies according to the type of farming. Logically the average surplus is greater for pig and poultry farming than for cattle an dairy holdings : the ratio is from 10 to 1 . If minerai nitrogen bought by farmers is not taken into account to estimate the N excess, it appears that only 15 per cent of all farms have surpluses. This proportion is lower for cattle and dairy farming (9 %) but reaches 24 per cent for mixed farming and 59 per cent for pig and poultry farming. This difference between the proportions of holdings with a N surplus means that a large part of the units do not need minerai fertilizers since organic nitrogen can be substituted for bought fertilizers.

Despite huge surplus of animal wastes, an important utilization of artificial fertilizers is made. This behaviour reveals technical and allocative inefficiencies because a cost minimizer would have bought a smaller amount of minerai fertilizer.

Let define for each farm a threshold (nitrogen units which can be spread per hectare without damage) above which there is an excess of nitrogen. Thus it is a, farm

~::-r ••) •:
specific threshold which can be interpreted as an upper bound and therefo, ~t :fa[TT]~~~Tare classified into two categories according to whether they respect it or, -~-~-f: T, l], i_ ~---~U11ple

' j : •~' • ._ .. ,. l -~ • .J '•• • I' •
typology is instrumental as we will see because response to nitrogen price variations .:r'...;'7' :'J.' ~ q( !• "": •iii:: ;1:p.:

slqnificanttv differs according to categories.

ESTIMATING NITROGEN DEMAND: A COST FUNCTION APPROACH

Our starting point is a specification of the technical possibilities that intensive livestock farms face. These are summarized by the production possibilities set Y that gives all feasible input and output combinations. Therefore let y denote an r -dimensional vector of non-negative outputs and (x, z) denote an (m + n)-dimensional vector of nonnegative inputs. Thus the input vector is derived into two sub-vectors x for variable inputs and z for fixed inputs. Define the variable input requirement set :

X(y, Z) = {X ; (x, y, z) € Y}
which represents the set of all variable -input combinations capable of producing output bindle y using fixed inputs z.

lt is well known that if X(y, z) satisfies general properties (see fo example

X
where Px is a vector of variable input prices. As every cost function CR is non decreasing concave, continuous and linearly homogeneous in factor prices. Furthermore it is positive and non decreasing in outputs and equals zero when y = 0m. Finally it can be shown that CR is non-increasing in fixed inputs.

Also notice that if X(y ,z) is a strictly convex set then CR (px, y, z) is differentiable in Px and Shepard's lemma applies. Moreover if it is twice -continuously differentiable, demand elasticites can be derived.

For econometric estimation, we have two outputs : y 1 is pig output whereas y 2 is other animal and crop output, both are measured in monetary terms. Notice that crops only represent a minor share of total production, so the second category Y2 essentially includes livestock and milk output. Four variable inputs are included : fuel and oil, fertilizer, farm capital consisting of buildings and machinery and purchased feed. ln the dual approach their prices are used rather than physical quantities or monetary evaluation. We suppose a perfect substitutability between minerai and organic nitrogen so the price of the former equals the opportunity cost of the latter. Finally four fixed inputs are taken into account : family labour in standard labour units, miscellaneous inputs (pesticides, electricity, maintenance) in monetary terms, livestock in animal units and agricultural land in hectares.

The restricted cost function specified in this paper is a quadratic with an annual index of time. Derived input demand equations are linear in all their arguments, but only nitrogen demand will be reviewed in this paper. Nitrogen demand equals :

(1) N = ao +~ai Pi+~ bJ-yJ• +~Ch Zh + u, i j h

where i,h = 1, ... ,4 ; j = 1,2 and u is the error term.

The sample is split down into two sub-samples according to whether the upper bound for nitrogen is respected or not. The former refers to an "efficient" behaviour whereas the latter involves inefficencies. Moreover in order to deal with farm dimension, an error component model is specified. So the error term is divided into two random components :

Ujt = 8j + eit ; i = 1, ... N, t = 1, ... T
ai is the farm component, and eit a white noise.

Table 2 shows the estimated coefficients of the nitrogen demand equation for both sub-samples. They are obtained by the quasi -generalized -least -square method which is based on a two stage process. lt gives consistent estimators which are asymptotically equivalent with generalized least squares estimators. They are more efficient than "within" estimators for finite values of T with N tending to infinity providing there is no correlation between the explanatory variables and the error term.

,. ln both estimated equations, the coefficient of minerai fertilizer price is significantly different from zero with the right positive sign. Furthermore family labour, total livestock and available land positively affect demand. So there is some consistency between the two equations but there are also differences. Only in the "inefficient" subsample there is a significant impact of the price of fuel and oil, and animal feed on ~ ;, nitrogen demand. The equality between regression coefficients is rejected since the .:, rcomputed F -value (with 13 and 500 degrees of freedom) is 19.56. Thus we can --u,Gohclût1e• • that the two categories of farmers are heterogeneous regarding minerai ~,;dfêrtili, zer:dem• and. Scale affects are captured through fixed inputs, specially livestock and ::crànd:J,Slô~tl1è i'iifluence of outputs is not significant. lnstead of regression coefficients let consider own-price elasticity of minerai . , iirnitrogéfi ~êrnâfleJl wfiicHl :j' s•• the interesting parameter for economic pur poses. lt is smaller ;:. f, o~&êff-1e;i• ét'lt'rf.atmi:fthàf:l for "inefficient" farms : -0.36 and -0.68 respectively. These values can be compared with estimates obtained from French aggregate time series : -0.33 for short run elasticity and -1.10 for long run elasticity [START_REF] Bonnieux | Agricultural policy and environment in developed countries[END_REF]. Various authors (see [START_REF] Hanley | The economic of nitrate pollution[END_REF]) report figures from -1.20 up to -0.08 for Europeans countries (UK, lreland, FRG and Denmark) on the basis of different methods , (econometric and linear programming). But the important point is concerned with the difference in magnitude between the two categories of farms. A similar conclusion has been obtained befére in a slightly different context [START_REF] Vermersch | L'allocation du travail dans les exploitations céréalières : une modélisation Tobit d'une demande de facteur semi-fixe[END_REF]) since elasticities result from a system of factor share equations derived from a restricied translog cost function and estimated on a cross-section. Therefore farmers'response to a uniform tax put on nitrogen would largely vary according to the technical and allocative inefficiencies.

ESTIMATING NITROGEN DEMAND : A TOBIT MODEL

The preceeding derivation relies on the minimization of a restricted cost function therefore elasticities have to be understood as short-run Hicksian elasticities depending on the level of fixed inputs. Furthermore fixed factors are not required to be at a long-run optimum level and there is some evidence of a disequilibrium for land and family labour.

A discussion of this point is helpful to get a better insight of nitrogen issues because they can be considered in terms of a similar disequilibrium.

For each farm, there is a constraint on land availability. If it is binding long-run equilibrium level can be derived [START_REF] Brown R | Estimating elasticities of substitution in a model of partial static equilibrium : an application to U.S. agriculture[END_REF]. For instance for arable farming in France, land is a rationing factor, so in the long-run there is a pressure towards an increasing acreage of holdings. So land is a quasi-fixed factor since if the constraint was relaxed farmers would adapt acreage in order to reach the long-run optimal size originating a process which would result into more land under cultivation.

On the labour side, the level of available family labour gives a lower bound-tor the total amount of labour input. This constraint is not necessarily binding because-some farm operators have to hire wage earners because there is no enough }amfl.Y::: ,,lç:1Qour available on the farm. If labour is demanded in amount smaller or eqw-al..__to:, 9 ;Vailable family labour then the constraint is binding. The latter case is. ,qfteij p;m_s1;ry~i:ç:1nd involves a low mobility of agricultural labour due to poor job opportunities.

Farms can be classified into two categories accorg_iijg>;;tiq./ \!'!lf!ê~J:f : 1:Q~r{çimily labour constraint is binding or not. For the second category f P,~rWh~~-lil 1 r=th1;1;ii;Q!î!Str• aiRl .t is not effective there is some hired labour on the farm. Therefore given a cost-minimizing behaviour, the optimal level of labour input equals family labour plus hired labour. The basic idea is to use this information to derive the optimal level of input for the first category of farms for which the constraint is binding. A Tobit modal can be specified in order ta include bath categories [START_REF] Vermersch | L'allocation du travail dans les exploitations céréalières : une modélisation Tobit d'une demande de facteur semi-fixe[END_REF].

Regarding manure utilization farm operators face a similar constraint. Let N 0 the provision of nitrogen through liquid manure then, if there is no opportunity ta sell it, the farmer has to spread this minimum quantity. The amount of nitrogen effectively spread is:

it includes N O plus nitrogen Ne provided by chemical fertilizers.

For a g1ven crop mix there is a threshold above which pollution occurs, sa two cases have to be considered :

where Nm equals total nitrogen requirements. For the first case total nitrogen spread respect the threshold and a cost-minimizing behaviour is assumed. So observed amount of nitrogen spread is optimal.

The second case involves nitrogen excess corresponding with technical and allocative inefficiencies since a cost minimizer would have bouqht a smaller amount that Ne of minerai fertilizers. Both cases can be covered by : Chi-square in parentheses. It is used to test the significance of regression coeffi~fents 1 (asymptotic likelihood ratio test). The observed value has to be compared with a critical vslueC1fo~ a•'chlf;,squàre distribution with one degree of freedom: for example 6.31 for a 0.90 Level of confidence. The price of nitrogen, the level and livestock and land available affect significantly nitrogen demand whose own-price elasticity equals -0.31. This value is close to the value obtained from the efficient sub-sample. This is consistent given the rationale of the Tobit approach.

FINDINGS AND CONCLUSION

The response to a nitrogen taxation would vary according to farm operators' efficiency. ln a first stage a greater decrease in nitrogen demand by the least efficient farmers than by the most efficient ones can be expected. This point can be illustrated on the basis of own-price elasticities obtained for each farm category. A 10 % tax would induce a 3.6 % reduction in the use of nitrogen by farmers who respect nitrogen requirements and do note create environmental damage. But the decrease would be greater and reach 6.8 % in the second category characterized by an excess in nitrogen spread. So if we assume that the sample of farms is representative, a 4.6 % reduction could be expected for the whole population of intensive livestock farms.

The tax on minerai fertilizer would increase the opportunity cost of organic tertilizer and would push farmers towards more efficient practices at the micro level.

These practices would involve a smaller amount of nitrogen spread and would be more friendly for the environment. Therefore a tax could help to improve the efficiency of the livestock industry and would be consistent with a policy based on education and extension services. But in a second stage after the elimination of these inefficiencies the response to a 10 % tax would diminish and would be roughly equaled to a 3.1 % decrease.

Efficiency has been defined by using a ad-hoc procedure based on exogeneous information. Specific farm thresholds equal nitrogen requirements and are derived from agronomical standards which take into account the assimilative capacity of the environment. Obviously other thresholds could be imagined, consistent with very drastic constraints imposed on the farm sector. An ecological approach expressing environmentalist preferences could be considered. lt could for example result in a threshold tailored by location.

Above results are derived under family labour and land fixity. As many people put forward the argument it is true that in the short run the impact of a tax on nitrogen would be moderate. But now if input fixity is relaxed a new equilibrium involving the .. utilization of less labour and more land would emerge. Long run own-price elasticity of nitrogen demand would be greater than short run elasticity implying a stronger response to a tax.

  [START_REF] Chambers R | Applied production analysis -a dual approach[END_REF] p. 261-281, Guyomard and Vermersch 1989[START_REF] Vermersch | L'allocation du travail dans les exploitations céréalières : une modélisation Tobit d'une demande de facteur semi-fixe[END_REF]) there exists a multioutput restricted cost function : CR (Px, y, z) = min [Px•X; X€ X(y, z)]

  equals the optimum for N c. Following Shephard's lemma, derived factor demand is easily obtained. Then J f). IL •~:•◄•:-:i;, -~ ê; ; .. ~5 ' ~;: é eAuation; ( 1) . . baccmes : (2) N*=N*c + No = ao + !: ai Pi + !: b• Yj + !: ch Zh + dT + u J )a:°fL r:. :-:.; •.. ! : f;•.:r: t1n;~: ,•.; i j h * But now the dependent variable N is not observed for the whole sample but only for farms below the threshold. A Tobit model can be used to estimate equation (1 ).The basic idea is to use the "efficient" sub-sample for which observed demand N equals * N to derive what would be the demand of the other farms if they where efficient. Thus using an exogeneous information, i.e. nitrogen requirements, it is possible to include bath categories of behaviours in a single model. The Tobit specification relaxes the costminimizing hypotheses for farmers above threshold. lt is maintained for the rest of the sample. Table3shows the estimated equation for nitrogen demand. The same panel of 100 farms observed during 5 years has been used and an error component structure for the error term has been considered.

  ' "' ~ •... =:, *-~ . . . ~.:.-• ••• ' " : v.• 1_ ~:

Table 1 .

 1 Distribution of holdings by type of farming according to the importance of N excess (in percent), and Level of N excess (kg per ha of UAA).

		Holding distribution	Level of N excess
					(kg per ha of UAA)
		Deficit	Balanced	Excess	Deficit	Balanced	Excess
		Units	Units	Units
	Cattle and dairy	13.9	7.9	78.2	• 37	16	145
	Mixed farming	8.8	9.9	81.3	• 30	15	262
	Pig and poultry	7.7	7.7	84.6	• 27	14	1457
	Al l farms	12.2	8.5	79.3	• 30	16	226

Table 2 .

 2 Estimated equations of nitrogen demand: 11 efficicient 11 vs 11 inefficient 11 farmers.

	Parameters	11 Efficient"	"Inefficient"
	Intercept	• 4 277.39	-10 923
		(2.27)	C 1.89)
	Variable ineuts erices
	fuel and oil	1.33	82.85
		(0.12)	(1. 70)
	nitrogen	-216.95	-719.65
		(6.10)	(3. 73)
	farm capital	-1 073.37	3 039.69
		(0.59)	(0.35)
	animal feed	-10.53	172.44
		(0.92)	(1. 70)
	Outl)UtS
	pig	-0.002	0.001
		C 1.46)	(0.62)
	other animal and crops	-0.001	-0.001
		(0.43)	(0. 17)
	Fixed ineuts
	fami ly labour	0.35	-4.45
		(1.11)	(2.69)
	other materials	0.02	-0.22
		(O. 77)	C 1. 85)
	l ivestock	9.87	6.71
		(10.69)	(4.79)
	land	1. 11	3.27
		(6.37)	(3.20)
	Time trend	139.69	636.84
		(2.18)	(2.43)
	nb of farms	70	30
	nb of years	5	5
	R. square	0.56	0.34

Asymptotic t -ratio in parentheses.

Table 3 .

 3 Estimate equation of nitrogen demand: tobit specification

	Parameters
	Intercept	-5 060.12
		(12.37)
	Variable Înf2!:!t erices
	fuel and oil	15.10
		(1.54)
	nitrogen	-220.99
		(30.51)
	farm capital	-1 750. 71
		(0.73)
	animal feed	-9.05
		(0.46)
	0Utf2!:!tS
	pig	€
	other animal and crops	€
	Fixed inJ2!!tS
	family labour	€
	other materials	• 0.007
		(0.07)
	l ivestock	3.97
		(47.21)
	land	2.01
		(104.61)
	Time trend	225 .18
		(10.46)
	Nb of farms	100
	Nb of years	5
		. . -:;

APPENDIX : The estimation of N excess

Sorne holdings do not produce crops and they have only animais. Their acreage is very small, so animal manure is not spread on the spot but transported to other farms.

But export flows of manure are unknown. To avoid bias farms with less than five hectares of Utilised Agricultural Area are excluded.

For each farm nitrogen inputs are estimated -Concerning animal manures, the Farm Accountancy Data Network is used to have the livestock according to 22 categories. For each one a technical coefficient permits to estimate the N production. ln fact it is the nitrogen available on the spot which is estimated since volatilisation of ammonia following surface spreading is deducted.

-Concerning artificial fertilizers, N bought by farmers is given directly by the Farm Accountancy Network.

The nitrogen uptaken by plants is a function of the type of soil, the type of plant and the yield. lt also depends on temperature, radiation and water supply. The nitrogen export is determined for the 1 9 types of cultivation as given by the Farm Accountancy Network. For each type of plant, according to the average yield, the nitrogen uptaken is estimated.

If the application rate of total nitrogen from animal or minerai origin is greater than the plant export there is an excess. lt is assumed that 30 kg of nitrogen per ha of Utilised Agricultural Area is an agronomie threshold below which there is no utilisation by the crops. There is excess when the surplus of nitrogen is over this threshold.


THRESHOLD PRICE, EXPORT, SPLL-OVER EFFECT, Disequilibrium

MODELLING OF AGRICULTURAL MARKETS AND ECONOMETRICS OF DISEQUILIBRIUM

Keywords: IE AGRICOLE, ECONOMETRIE, DESEQUILIBRE, PRIX- PLANCT{ER, EXPORTATION, REVIEW, AGRICULTURAL MARKET, ECONOMETRICS

A Revia,v of Some Applications tu Markas with Minimum Prices and to Export Models RESUME Ce papier présente quelques applications de l'économétrie du déséquilibre à la modélisation des marchés agricoles. Certaines spécifications issues de l'économétrie du déséquilibre sernblent particulièrement adaptées pour prendre en compte les caractéristiques spécifiques des marchés agricoles. C'est particulièrement le cas des modéles de marchés soumis à un prix minimum, en vue de représenter le système européen d'intervention, pratiqué pour la plupart des produits agricoles.

Mais les résultats d'estirnation permettent de montrer qu'une telle spécification n'est pas nécessairement la plus appropriée. Elle conduit à des résultats peu satisfaisants lorsqu'elle est utilisée pour modéliser des marchés qui sont presque toujours dans le même régime de déséquilibre. Cette situation structurelle peut être observée lorsque les données utilisées ne sont disponibles qu'avec une périodicité annuelle. De plus, cette spécification n'est pas appropriée lorsqu'il est nécessaire d'utiliser une hypothèse de non-observabilité du prix minimum. En effet, dans ce cas, la séparation de l'échantillon est inconnue. En revanche, l'économétrie du déséquilibre, sous sa forme "originale" et éventuellement avec quelques adaptations visant à prendre en compte I'hétérogénéité, peut être utile lorque le but est d'identifier et de mesurer les effets de la demande et de I'offre sur un marché, et de déterminerex-postles occurences et les causes des changements de régime, L'estimation de modèles d'exportation de produits agricoles en fournit une application satisfaisante.

A Review of Some Applications to Markets with Minimum Prices and to Export Models 0. lntroduction Public regulation of agricultural markets involves unique features which are to be taken into account in the process of modelling. On the one hand, these specific features act upon the market functioning itself. Then, it is not possible to specify models as if markets are cleared in a competitive way. The existence of a minimum price at the producer level involves non-equilibrium situations on the domestic market, when the market clearing price is below this minimum price.

Then, classical equilibrium models are not necessarily appropriate. Furthermore, the EC trade regulation with third countries (through export refunds and import levies) involves specific export and import models. For an EC member state, there are two distinct markets to face. So there are two different export or import demands which turn toward this country. Then, in a disequilibrium frameworkr it is necessary to take into account the possibility of spill-over effects between these two markets.

On the other hand, these specific features can influence the agents' behavior. For example, producer price expectations are settled by the existence of price regulation policy, rather than by past information. ln this case, the accuracy of adaptative or rational expectations is not ensured, or it is necessary to adapt them to this specific context (cf. Le Roux, 1991-a).

This paper deals with only the first point. That is to take into account structural features of agricultural markets when modelling them. Thus, we will see how econometrics of disequilibrium can be used to model some characteristics of agricultural markets, and we will present some illustrations of this methodology.

Section 1 provides a brief outlook over econometrics of disequilibrium when applied to the market of one good. lmplications on estimation procedures are mentioned.

One particular case of markets in disequilibrium is the case of markets characterized by threshold -or minimumprice regulation. For such markets, disequilibrium does not necessarily occur at each period: it is only the case when the clearing price is lower than the minimum price. Section 2 presents econometric models of markets with a minimum price, and an application to the French cereal market.

1 That is disequitibrium between export (or import) suppty and demand i Another field of application for econometrics of disequilibrium is trade modelling. This field of application is not reduced to agricultural commodities, and in fact most applications have been made for industrial sector (e.9. Artus, 1987). Section 3 is about the econometrics of disequilibrium applied to export models2. ln this case, the transacted quantity results of the confrontation -and is the minimumbetween a domestic supply for exports and a foreign demand.

When applied to European agricultural commodities, it is required to specify a disequilibrium model on two markets. Within the Common Agricultural Policy (CAP), trade regulation with third countries induces two kinds of demands which turn toward two kinds of supplies. The specification of a multi-market disequilibrium model allows the existence of spill-over effects among these markets. These effects are transfers of constraints (on supply or on demand) from one market onto another one. One application concerns French wheat exports to third countries. Another one is about a European model of intra and extra-EC exports of cereals.

1. Econometrics of Disequilibrium : principles and canonical models Econometrics of disequilibrium has been developped following the post- keynesian advances involving the theory ol macroeconomic disequilibrium. But basic models of disequilibrium only deal with markets of one good, not the whole economy.

The canonical model

The canonical model of disequilibrium assumes that the transacted quantity on a market is, at each period, the minimum between a demand function and a supply function. An observed quantity belongs either to the demand curve, either to the supply one, but never to both. lt can be explained, for example, by the rigidity of the price, which cannot instantaneously clear the market. So either the demand or the supply is constrained. Such a model of market is also called a quantity rationing model.

The model of disequilibrium was first specified in the seminal work of Fair and Jaffee (1972)3. This canonical model usually consists of the following functions:

Dt= xttbr+uu St = xztb, +u", Q, = Min (4 , S,) t = 1,... T
where Q is the demand function, ,S, is the supply function, Q is the transacted quantity, x,, and x2t ate sets of explanatory variables, ur, and u2t are vectors of random errors with standard errors o, and o, A price adjustment could be added to this model. Then the regim could be determined by the direction of price movement. Without loss of generality, such an assumption is not required. lf demand and supply are unknown (that is, sample separation between excess supply and excess demand is unknown), only data on transacted quantity and explanatory variables are given. ln this case (assume that error terms are normally distributed and not contemporaneously correlated), the density of Q is: Parameter estimates can be given by maximizing the likelihood function:

L = fIlt I,(q,) Then, for each period I , it is possible to get an estimation of the probability that the observation belongs to the demand function (or, consequently, to the supply function).

Two major criticisms can be made about the specification of the previous disequilibrium model. First it is not realistic to assume that such a structural model is valid at the aggregate level. Secondly this model assumes that disequilibrium, when occurs, exists at each period: equilibrium periods cannot be observed. Some modifications or extensions of the canonical model can solve these problems.

Some adaptations of the canonical model

The first problem is about the validity of the 'Min' condition at the aggregate level. That is, it is not realistic to assume that the whole economy, or a sector of it, switches, from one period to the following one, from one regim to the other. ln fact, allthe agents are not in the same disequilibrium regim at the same time, and only a part of the set of agents switches from one regim to the other. Then, if the market is a set of different micro-markets, the transacted quantity at the aggregate level is the sum of supplies on markets in excess-demand plus demands on markets in excess-supply. This quantity is necessarily less than the minimum between the aggregate demand and the aggregate supply.

Once more in economic analysis, it is the problem of heterogeneity which has to be taken into account when modelling economic behaviors or activities. lt is also the classical problem of switching from the micro-level to the macro-level, that is the problem of aggregation.

A solution here is to consider that the aggregate market is set up by ir/micro- markets. For each of them the canonical model of disequilibrium applies: Dl = xr,br+ Eir, Sl = *r,br+ elr, Ql = Min (Di , Sl) i -1,... N t -1,... T

x,, à, and xr, b, are deterministic parts of demands and supplies, which are common to all micro-markets.

When only aggregate data are available, it is possible to estimate such a model of aggregation over micro-disequilibria by several methods. lt is possible to write a pseudo-likelihood of the model and to maximize it (Pseudo-Maximum of Likelihood method, see Le Roux (1991-a)). Under several assumptions, it is also possible to get an expression for the expectation of the transacted quantity at the aggregate level:

lf Dr and ,Sr are the deterministic parts of demand and supply at the aggregate level, then:

Ee, =s, o(f 1 +D4, -.(D'; 3'

)r -o,ltSl

where o=var(er,-er,).

Then it is possible to get estimates of demand and supply parameters (and to characterize the distribution of micro-markets) by using a Non Linear Least Squares estimator. For applications of these two methods, see later and Le Roux (1991-a, 1991-b).

The second problem is about the assumption that the market is always in a disequilibrium regim. That is, with the canonical model, the probability of disequilibrium is either one, either zerc. A class of disequilibrium models avoids this problem:these models are relative to markets with a minimum price.

lf the market clearing price is greater than the minimum price, supply equals demand and the effective price is the market price: the market is in an equilibrium state. lf the market price is less than the minimum price, the effective price equals this limit:the market is in excess-supply.

Specification and estimation of such a model of market depends on whether the minimum price is endogenous or exogenous, and moreover whether it is observable or not. The following section presents some of these situations and an application.

2. Models of Markets with a Minimum Price Markets which are regulated by a minimum pricea are characterized by two possible regims: equilibrium and excess-supply (or demand regim). The latter occurs when the minimum price is effective. Within such a market the demand is never constrained: allthe observations belong to the demand curve.

Models of markets with a minimum price seem to be particularly relevant to represent European agricultural markets, where market prices are guaranteed through intervention system (and through intervention prices which arc minimum prices). However regulation of these markets is a little more complicated than a simple market with a minimum price, due to specific modes of enforcement (e.9. periods of intervention, limitation of quantities which are bought by the European Community, through tenders for meat purchases, for example, ...). First, we present the canonical model of market with a minimum price. Then we will see which improvements can be made to take into account these specific features, with an application to the French soft wheat market.

The canonical model

Within the canonical model, both the effective price and the minimum price are observable. Moreover the minimum price is assumed to be exogenous. This model is written as following:

D, = at pt * xttb, + ur, S, = az p,*xz,b, +u", pi tf pT < pi Qhen Q, = D, < S,) pi rf pi > pi QhenQ, = D, = S,) t = 1,... T where p, is the effective price, pf is the minimum price, pi is the market clearing price, other variables have the same definitions as previously a Similar models can be buitt for markets with a maximum price, or with both a minimum price and a maximum price (see Maddala, 1983).

Pt

Within this specification, sample separation is perfectly known. So it is possible to write the density of the model according to the prevailing regim. For equilibrium observations, the endogenous variables are the effective price and the transacted quantity, whereas for excess-supply observations the endogenous variables are the transacted quantity (which equals the demand) and the supply. Given a probability density function for the error terms, joint density is given for each observation. Then Maximum of Likelihood estimator can easily be applied. The likelihood of the model is: ' ='ll' \'(q" P')''\"1''(8" t') where 0, is the set of equilibrium observations, 0, is the set of excess-supply observations, lr,(q,,p,)=(az-a) "f (A,-ar pt -xr,bt,gt -oz p, -xz,bz) Iz,(Q,,s,) = f (Q, -at pixr, br,st -e2 pi -xz, bz) where f (. , .) is the joint density function ol (ur, ,uz,).

An estimation of this model has been made by Vigier (1987), in the case of the French bovine meat market. He used monthly data from 1977 until 1986. At the monthly level, it is possible to observe both equilibrium and excess-supply data, while at the annual level the market is always in a disequilibrium state.

Using specification tests, Vigier concluded that it is better to specify and estimate a model of market with a minimum price rather than independent estimations of supply and demand.

Because monthly data are available for this market, on which both demand and supply are observable, the canonical model can be used without particular trouble. As shown in the following paragraph, it is not always the case.

The case of an unobseruable price limit

Through the case of the French soft wheat market, here we deal with a market where the effective price is always higher than the 'administrative' minimum price, but on this market excess-supply quantities are bought by public authorities.

This case can be met when the effective price is only observed at the aggregate level and on an annual average. This situation can also be explained, for the French soft wheat market, by the fact that the minimum price is not effective all along the marketing year, and this 'posted' minimum price can be altered according to cereal quality.

The solution of an estimation with monthly data is not possible here, because we are interested in an annual crop production.

Another solution is to consider that the national market is an aggregation of micro-markets which can be in different regims at the same period.

As previously seen (paragraph 1.2.), this methodology can be used even if data are only available at the aggregate level. But in the model of aggregation over micro-disequilibria, it is not possible to explicitly deal with the minimum price situation. The previous model (1.2.) assumes that disequilibrium on a micro- market only occurs according to the values of error terms (because deterministic demands and supplies are common to all micro-markets). And only distribution assumptions are made on these error terms.

However, estimations of models of markets with aggregation over micro- disequilibria have been made for the French soft wheat market (Le Roux, 1991- a). Different specifications for the supply function (with different formulations for price expectations and supply adjustment) have been introduced. ln all cases, estimation has shown that demand is always observed: even if the minimum price regulation is not explicitly introduced in these models, it is the proof this regulation is correctly taken into account in such a model of aggregation. See Le Roux (1991-a) for details on different specifications and results of estimation using Pseudo-Maximum of Likelihood and Non Linear Least Squares estimators.

Finally, with the original specification of a model of market with a minimum price, the last solution is to add an assumption about the observability of the price limit.

We assume there exists a virtual price limit which is not observable, and consequently which does not equal the posted price limit (intervention price). This assumption allows to specify the model at the aggregate level. lt involves to build a supplementary endogenous variable. This new endogenous variable is the virtual minimum price which actually determines switching between equilibrium and excess-supply regims.

The model has to be re-written as following: Dt = ot pt * xttb, + ur, S, = oz pt * xztb, +ur,

o. =[oi ,f pi < pi Qhen Q, = D, < s,) L' lpf ,f pf >pi QhenQ,=4=S,) PT =xs, br+ur, t = 1,... T
where xr, is a set of exogenous variables which explain the minimum price By the same way as previously, it is possible to determine the density of the model. An additional difficulty is that the sample separation is unknown. So it is necessary to integrate over the unobservable variable (pi) lo get the density.

Then an estimation can be obtained by the Maximum of Likelihood method.

Finally, an estimation of the regim probability for each period can be derived.

Even with simplifying assumptions (on the independence among the error terms, for example), the expression of the likelihood function has a complex form. lt forces to retain simple specifications for demand and supply functions. lf the advantage of such a model is to perfectly take into account the non- competitive functioning of the market (through the minimum price regulation), it does not allow functional forms which could closely represent the actual complexity of supply and demand. When applied to the national wheat market, total demand has to simultaneously catch domestic and foreign demand. Domestic demand would have to be divided into feed, food, and non food demands. The supply function would have to take into account price expectation formulation, and not only the existence of a minimum price. ln spite of the necessity for such simplifying assumptions, the model with an unobservable minimum price has been estimated on annual data for the French soft wheat market. Demand is a function of the observed price and of terms representative of the export variations. Supply is a function of the per-hectare product (that is, the producer price multiplied by the yield), and of the relative price of soft wheat to corn.

Due to the model specification, estimations for parameters of demand are the same with an independent estimation by ordinary least squares, or under the assumption of the minimum price regulation. On the other hand, estimates for supply parameters are widely altered with the minimum price regulation specification. Particularly, supply elasticity to producer price is greatly higher within the disequilibrium framework. lt induces a fitted series for supply which is always higher than the transacted quantity.

The estimation of this model gives fitted values for the unobservable minimum price, which almost everywhere equals the effective price (see graphic). lf such a specification gives a close representation of the actual market, estimation results are not satisfying (in terms of explanation power) because of the structural excess-supply. Estimation can just confirm this result and can

give an idea about the magnitude of the disequilibriums.

Price expectations

Another specific feature has to be considered when modelling most agricultural markets. Because there is not simultaneity between decision production and the time supply faces demand on the market, producers have to form expectations about these prices.

Formulations of adaptative or rational expectations can be introduced into the supply function. Within the model of market with a minimum price, it is possible to substitute the effective price by an expected price in the supply function, then to add a relation to determine this price expectation. Chanda and Maddala (1984), and Shonkwiler and [START_REF] Shonkwiler | Modeling Expectations of Bounded Prices: An Application to the Market for Corn[END_REF], have developed a full specification with rational expectations, and suggested relevant methods of estimation. An application was completed for the US market for corn. But their method only applies for an (observable) exogenous price limit.

We specified supply models with a kind of adaptative expectations (following Nerlovian works) but with an additional source of expectation due to the posted minimum price. When writing such a model in a reduced form, it is possible to get a model of market with price expectations. This model has been estimated by the method of aggregation over micro-disequilibria (Le Roux, 1991-a). But, as we previously said, the minimum price regulation cannot be explicitly taken into account in this case.

Due to structural features about the market under study, and to the data availability, model of markets with a minimum price are not perfectly suitable when structural disequilibrium occurs. They are appropriate when sample separation is perfectly known and when infra-annual data are available, in order to better catch regim switching.

Original econometrics of disequilibrium is more suitable when the aim is to correctly identify supply and demand effects on actual transactions, as seen in the following section.

s Full results about this estimation can be found in Le Roux (1991-a). o

Export Models with Spill-over Effects

Traditional modelling of trade is based on the assumption that the trade level is constrained by the demand. This assumption involves that the import demand (from the domestic economy to foreign producers) and the export demand (from foreign economies to national producers) are not bounded by supply effects.

For several fields this assumption is strong enough: production capacity can often constrain the demand, for example.

So modelling of trade has progressively taken into account this feature: export (or import) relations have to be specified with both demand and supply effects.

Moreover, econometrics of disequilibrium may be helpful to specify such models in a structural manner. lt is possible to determine a relation for export demand and another one for export supply (the same for import). Then the traded quantity is the minimum between demand and supply. Estimation provides information on the regim which prevails at each period (is the demand bounded by the supply constraint ?), and on relative weights of demand and supply effects.

ln the case of export modelling, and at an overall level, supply effects are essentially the stock of capital, the production cost relative to the producer price, the profitability of export relative to the domestic market, the rate of utilization of production capacities, and so on ... On the other hand, demand effects are the price competitiveness (in fact the world price relative to the export price) and the actual revenue of foreign consumers.

We present here applications to cereal exports. ln this case, supply effects may be represented by the level of production (or the yield) and by the level of domestic stocks. Demand effects are mainly the EC export price relative to a representative world price, and the total world demand for cereals, which can be a proxy of the actual revenue of foreign consumers.

First a generalization of the disequilibrium model is presented in the two- markets case, with an application to French soft wheat exports. Then, we end with another application -only inspired by econometrics of disequilibriumand relative to European models of intra and extra-EC exports of cereals.

Multi-Market Disequilibrium Models with Spill-over Effects

Multi-market disequilibrium models have to take into account the fact that the demand (or the supply) on one market may be altered by constraints stemming from another market.

One particular case can be found for European exports of cereals (or for exports of most agricultural commodities). For one EC member state, say

France, it is necessary to distinguish two markets. The first one is the European market, which is not actually a domestic market. There are differences between supply and demand on the national market and supplies and demands of the other EC countries (differences of specialization, production costs, types of farming).

Overall is the monetary problem. European Monetary System and Monetary

Compensatory Amounts have to correct -in theorydifferences between exchange rates. Assuming they do, it is only true for intra-EC trade6. But monetary differences stay at the internal level, so they have different effects on national supplies and demands.

The second market to face is of course the world market. lt is actually a different market because of the European trade regulation with third countries through export refunds and import levies.

Then a possible linkage may exist between these two markets: the level of trade on one of them can act upon -or can be influenced by -the level of trade on the other one. lf on one market the demand (or the supply) is constrained, a spill-over effect on the other market can appear. Such a multi-market situation with spill-over effects can be written as following:

DY = xtt at + T, Qf" +u, Sy -z,br+vrQfc +v, Df' =xzt oz+yrQ! +ur, sf' = zr, b, + v, Q! +vr, QY = Min(D! ,sY)

8": =uinlnfc,s!c) For example, vrQf is the spill-over effect on the French supply to third countries (Sy ), due to constraints on the EC market.

This general specification leads to the formulation of the likelihood function, under assumptions on error terms. This likelihood function has a rather complex form. Simplifying assumptions on the separation between endogenous and exogenous variables allow more tractable computation (but a direct estimation of the previous model is made in [START_REF] Sylvain | Modélisations économétriques des échanges intra et extracommunautaires de viande bovine: déséquilibre multi-marchés[END_REF], with an application to bovine meat trade).

Applications

A model of French soft wheat exports ln the case of the French soft wheat exports, we assume that French exports to EC are exogenous: only spill-over effects of these quantities (on exports to third countries) are taken into accountz.

The disequilibrium model has been estimated for French exports to third countries, with the method of aggregation over micro-disequilibria and with the Non Linear Least Squares estimator. Estimation results are presented in the following table (monthly Except the trend, all variables are in logarithmic form. 7 We assume that French suppty to the EC and demand to the EC can act upon supply to the world market and demand from the world market, but not the opposite. lt does not seem to be a strong assumption, at least for demands.

Among others, one result to be pointed out is the high level of the pricecompetitiveness effect on export demand (the elasticity of demand to the world price relative to the EC export price equals 2.6). The significance of this parameter emphasizes the actual importance of this price-competitiveness on exports, but it proves too that the 'law of the one price' does not apply for cereal trade. At last, the significance of the spill-over effect is particularly strengthened by these estimation results.

This estimation has been made on monthly data, in order to better catch supply and demand effectss. lndeed, estimation results lead to the computation of the estimated proportion of micro-markets in each regim, for each monthly period.

We present in the following graphic an average annual proportion of micromarkets in excess-demand. Unlike results on annual data, this proportion is not unimportant. That means supply may be sometimes constrained by demand.

Annual 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 From 1970 to 1976 there are more micro-markets in excess-demand than in excess-supply (on an average), except July and August because of the harvest effect. Then, in 1977 and 1978, micro-markets are equally shared in both regims. From 1979 to 1985 the proportion of micro-markets in excess-supply is more important. But finally the end of the period shows more excess-demand micro-markets (at the monthly level).

The interest of such models is to get export forecasts under price and production scenarii. Then, these models may be appropriate to measure effects of the Common Agricultural Policy reform on intra and extra-EC exports of cereals.

The period of simulation is 1992-1997. lntra-EC prices are assumed to follow the same variation as intervention prices (in real Ecu) until 1995. Relative prices (in US dollars) on the world market are assumed to be constant all over the period of simulation.

Existing supply models measure effects of price variations (and other CAP instruments) on production levels. lt is the case of the French model AROPAJ, for example (an extension of it is made for United-Kingdom and ltaly: see Jayet communication, this workshop). we used another supply model, due to its specialization in crop production and to its existence for the major EC producers and exporters of cereals (France, United-Kingdom, and Germany). This model is the MONlCll model. Scenarii are built under all these previous assumptions. They lead to following results for soft wheat tradel2 (see graphics).

lntra-E0 trade of soft wheat would increase (about 3 million tons), due to price- effects stronger than production-effects: the demand-side seems to prevail over the supply-side. This evolution is not in favour of the United-Kingdom, because of an assumption of a very large production decrease. At the extra-EO level, European exports of soft wheat would not be greatly altered: they stay at about 12 million tons. Only France would increase its exports on the world market, to the detriment of Germany and the United- Kingdom. Finally, effects of the CAP reform would only be significant on barley exports, and globally European cereal exports on the world market would decrease of about 20%.

Extra-EC Exports of soft wheat (cumulated quantities) This paper has attempted to cope with some applications of econometrics of disequilibrium to modelling of agricultural markets. Some specifications derived from econometrics of disequilibrium seem to be quite relevant in order to take into account specific features of agricultural markets. That is particularly the case for models of markets with a minimum price, in order to represent the European intervention system on most agricultural markets.

But according to estimation results, such a specification is not necessarily the best one. lt leads to poor results when applied to a market which is always in the same disequilibrium regim. This structural situation may occur when data are only available at the annual level. Moreover, this specification is not appropriate when it is necessary to add an assumption on the unobservability of the price limit. ln this case, sample separation is unknown.

Conversely, econometrics of disequilibrium -in its original specification and eventually with adaptations to take into account heterogeneityis appropriate when the aim is to identify and to measure supply and demand effects on a market, and to determine -ex-postswitching between excess-supply and excess-demand. Estimation of export models have given a satisfying application of it.

Fronce

  Proportion of Micro-Markets in Excess-

  Moreover, estimations of the equilibrium probability give very small values (about .4 at the beginning of the estimation period, but less than .05 after). That means that aggregate data on transacted quantities never belong to the aggregate supply function. lt involves very large standard errors for parameter estimations of supply.

		Unobservable Minimum Price: The French Soft Wheat
		Market
	2400,00		Effective Price
	2200,o0 5 zooo.oo o\ $ raoo,oo	\, \,	lntervention Price '' Minimum Price
	F 1600,00
	r400,00
	r200.00
	19é6 1968 1970 1972 1974 1976 1978 1980 1982 1984 t9B6
		I

Imports can be modetled by the same way.

SeeLe Roux (1991-a) for a list of references.

Single currency should exist at the frontiers

Estimation on annual data has shown a proportion of micro-markets in excess-suppty targer than the proportion of micro-markets in excess-demand, almost all along the estimation period (seeLe Roux, 1991-b).

Modète d'Offre Nationale et Internationate de Céréates, ON\C, Bureau de ta Stratégie, Paris.

Other results can be found in LeRoux (1992)

I ,)

European models of intra and extra-EC exports of cereals An extension of the previous model has been made to all the major exporters of cereals. lntra-EC imports have been added in order to balance intra-EC trade for each cereal. Due to the linkage between all these models, it was not possible to preserve the pure disequilibrium specification which would have lead to untractable computational difficulties.

But for each country and for each cereale a simultaneous model is written, with one relation for intra-EC exports and another for extra-EO exports. ln each of these relations, supply and demand effects are introduced. For one country; and one cereal j the model is: AECu = f ( XIV., (ECPij)i =r,... N, PRODï ) XWi = g ( AECii,(Wi / EXECPIj),=r,... N, PRODij ) where AEC,, = lntra-EC exports of country I in cereal 7 Xlryij = Extra-EC exports of country i in cereal j ECP. = lntra-EC export price of country i in cereal j EXECPT= Extra-EC export price of country i in cereal i WPj = World Price of cereal j PRODij= Production of cereal j in country i .

These models have been estimated on annual data (1977)(1978)(1979)(1980)(1981)(1982)(1983)(1984)(1985)(1986)(1987)(1988)(1989)(1990) by full- information maximum of likelihood estimatorlo.

At the intra-EO level, we get negative own-price effect, positive cross price effect (intra-EO price competitiveness), and positive effect -when occursfor production.

At the extra-EC level, the ratio of the world price to the exporter (i ) price has a positive effect: when the world price is higher than the fob-EC export price, exports are facilitated. But the ratio of the world price to the EO-competitor (i'*i) price is positive or negative: that means the competitor may have a 'following' behavior relatively to the concerned exporter.

At last, the production effect on extra-EO exports is positive, when occurs.

e ln fact: soft wheat and barley. Only France has a significant level of trade for corn.

1o Fuil results can be found in Jayet and Le Roux (1992).