Final report - uni-bonn.de · Based on experiences from an earlier project phase (BRITZ & HECKELEI 1998) and some further tests it was decided to abolish the model specification based

Associates: G. Barbero, Roma G J. M. Boussard, Paris G M. Cuddy, Galway G J. M. Garcia, Valencia GW. Henrichsmeyer, Bonn G J. Marsh, Reading G L. C. Zachariasse, Den Haag

Reference: Contract n° SOEC 782200002, dated 31.12.1997,Prolongation letter dated 02. April 1998

Statistical Services:

Estimation of gross-margins elasticities for the SPEL/EU-MFSS model

Thomas Heckelei, Ph.D. and Dr. Wolfgang Britz

Content1 SUMMARY ............................................................................................................................................................. 3

2 OBJECTIVES ......................................................................................................................................................... 6

2.1 OBJECTIVES OF THE OVERALL PROJECT ................................................................................................................ 62.2 OBJECTIVES OF THE EXPLORATIVE ESTIMATION PHASE ........................................................................................ 7

3 THEORETICAL MODEL (REVIEW) ................................................................................................................. 9

3.1 GROSS MARGIN ELASTICITIES IN SPEL/EU-MFSS ............................................................................................... 93.2 AN EXPLICIT TWO STEP OPTIMISATION APPROACH............................................................................................... 93.3 LIMITATIONS OF ESTIMATIONS BASED ON THE TWO-STEP APPROACH................................................................ 113.4 GENERAL THEORETICAL RESTRICTIONS OF THE APPROACH.................................................................................. 12

4 MODEL SPECIFICATION AND ESTIMATION APPROACH ..................................................................... 13

4.1 SEPARABILITY STRUCTURE ................................................................................................................................. 134.2 EXCLUSION FROM AND AGGREGATION OF SPEL-ACTIVITIES BEFORE THE ESTIMATION...................................... 134.3 TOP LEVEL SYSTEM ............................................................................................................................................ 154.4 CASH CROP SYSTEM ........................................................................................................................................... 164.5 FUNCTIONAL FORM ............................................................................................................................................. 16

4.5.1 Experiences from the First Project Phase: Translog Revenue Function.................................................. 164.5.2 Flexible Functional Forms ....................................................................................................................... 174.5.3 Functional Form Employed ...................................................................................................................... 19

4.6 MODEL SPECIFICATION: EXPECTATION MODEL................................................................................................... 234.6.1 Experiences from the First Project Phase ................................................................................................ 234.6.2 Endogenous Estimation of Gross Margin Expectations ........................................................................... 26

4.7 ESTIMATION APPROACH ...................................................................................................................................... 274.7.1 SUR and 3-SLS as Estimators................................................................................................................... 274.7.2 Recovering Missing Parameters ............................................................................................................... 274.7.3 Imposing Curvature Restrictions: Bayesian Approach............................................................................. 284.7.4 Interpretation of the Results...................................................................................................................... 304.7.5 Multicollinearity in the Independent Variables ? ..................................................................................... 314.7.6 R2 as the Measurement of Fit ?................................................................................................................. 32

5 TECHNICAL SOLUTION................................................................................................................................... 34

5.1 DATA AGGREGATION AND IMPORT INTO EVIEWS................................................................................................ 34

EuroCARE EUROPEAN CENTRE FOR AGRICULTURAL, REGIONAL

AND ENVIRONMENTAL POLICY RESEARCH LUXEMBOURG F BONN

Final report

Date : 30.10.1998



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5.2 AGGREGATION OVER ACTIVITIES AND PRODUCTS AS A MORE GENERAL TASK................................................... 345.3 DEFINITION OF THE SYSTEM TO ESTIMATE .......................................................................................................... 365.4 TECHNICAL INTEGRATION IN SPEL/EU-MFSS ................................................................................................... 365.5 CONCLUSIONS FOR THE APPLICATION TO OTHER MEMBER STATES .................................................................... 37

6 RESULTS............................................................................................................................................................... 38

6.1 RESULTS FOR CASH CROP SYSTEMS.................................................................................................................... 386.1.1 France....................................................................................................................................................... 386.1.2 Italy........................................................................................................................................................... 446.1.3 Spain ......................................................................................................................................................... 456.1.4 Germany ................................................................................................................................................... 47

6.2 RESULTS FOR TOP LEVEL SYSTEMS..................................................................................................................... 496.2.1 France....................................................................................................................................................... 496.2.2 Italy........................................................................................................................................................... 526.2.3 Spain ......................................................................................................................................................... 55

7 FINAL EVALUATION OF THE PROJECT ..................................................................................................... 60

7.1 DATA BASE ......................................................................................................................................................... 607.2 THEORETICAL MODEL......................................................................................................................................... 627.3 PARAMETER ESTIMATES ..................................................................................................................................... 637.4 APPLICATION TO OTHER MEMBER STATES: ......................................................................................................... 647.5 POSSIBLE CONSEQUENCES FOR THE SPEL/EU- MFSS........................................................................................ 64

8 REFERENCES...................................................................................................................................................... 66



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1 Summary

Objectives

The overall project aimed at developing and evaluating a methodological and technical approach which potentially allows to regularly update the set of gross margin elasticities in the SPEL/EU-MFSS by econometric estimations based on the SPEL/EU-Data for all EU Member States. The project is considered a test on the feasibility of such an econometric approach and the evaluation of the results will be used for further decisions on activities in this respect.

The assessment of the theoretical background of gross margin elasticities revealed that the underlying assumption concerning technology and behaviour are quite restrictive (HECKELEI 1997). Nevertheless, both in order to test the currently applied methodology in the SPEL/EU-MFSS and to ease the integration of possible results into the system, it was decided to literally estimate "gross margin elasticities" of activity level response using pre-determined gross margins provided by the SPEL/EU-BS.

For the explorative estimation phase of the current project phase it was envisaged to test several alternative estimation approaches for at least two Member States to potentially identify a more or less standardised operational approach which could be later extended to all Member States. The ultimate decision on the consequences of the explorative estimation phase have to be based on the plausibility of estimation results, statistical properties of the estimated parameters and the work load connected with the application of the approach to all Member States and the integration of the results into the SPEL/EU-MFSS.

Empirical Approach

For the empirical specification of the model a two level optimisation process is assumed: At the top level, farmers decide upon the land allocated to cash crops (and implicitly upon fodder production on arable land) and the level of animal production activities. The level of permanent crops, vegetables and industrial crops (apart from oilseeds) is exogenous to the model. The remaining arable land, grassland, milk and sugarbeet production are also pre-determined but enter the model specification. At the second level land is allocated to dissagregated crop production activities, generally to wheat, barley, maize, other cereals, pulses and potatoes.

Based on experiences from an earlier project phase (BRITZ & HECKELEI 1998) and some further tests it was decided to abolish the model specification based on the Translog functional form. Instead the more flexible “Symmetric Generalised Mc Fadden” functional form was chosen for the final phase for the project.

Various estimation methodologies were employed to appropriately account for microeconomic restrictions and other specification issues: the Seemingly Unrelated Regression technique was used for the cash crop system. Three Stage Least Squares was employed for the top level system to account for simultaneous equation bias due to the milk quota specification. In order to test and impose curvature restrictions, a Bayesian approach was applied. Serial autocorrelation of the residuals made the use of an appropriate correction technique necessary.

Technical solution

Access to the SPEL/EU-Data base was partially managed by existing software (DAOUT). However, to allow flexible aggregation of activities, a FORTRAN based program was developed which can be used for other purposes as well. Further data calculations and estimations were done with EViews



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3.1. All programs are - as far as possible - designed to be flexible with regard to different expectation models, separability structures, Member States, and updating from the SPEL/EU-Data base.

Results

Generally, the results do not look very promising. Parameter estimates related to gross margin expectations show high standard errors and are consequently sensitive to minor changes in model specifications and sample period. Extensive experiments with different expectation models did not result in a satisfactory stabilisation of the estimates.

Own gross margin elasticities - especially in the case of the top level system - often show negative signs. Cross gross margin elasticities partially have doubtful magnitudes. None of the estimated systems "voluntarily" satisfied all restrictions derived from the underlying theory. The curvature restriction was strongly rejected by most of the estimated models.

Generally, the described shortcomings of the results were not as severe for cash crop systems (especially for France and Germany) as in the case of the top level systems. The use of intervention prices for the formulations of gross margin expectations in case of Germany clearly improved the results for this Member State.

Final evaluation

(1) Data base: When evaluating the results of the projects, the nature of the data used for estimation should be kept in mind. The content of the SPEL/EU-Data base differs from many other agricultural data sources as it combines data from the Economic Accounts for Agriculture with basic physical statistics (e.g. farm and market balances, herd inventories) in a consistent framework. The current study covering several Member States, many production activities and relative long time series was only possible due to the availability of the comprehensive and consistent layout of this data base.

However, with respect to the compatibility of the employed data base with the estimation of behavioural response to changes in economic incentives several problematic issues possibly leading to less than satisfactory estimation results can be summarised as follows:

• Unit value prices may not appropriately reflect the economic incentives for agricultural producers.

• The SPEL/EU-BS consistency algorithms have some influence on the variance of dependent and independent variables and the effects on estimation results are difficult to evaluate.

• We have considerable doubts that a set of synthetic gross margins from a sectoral data base such as the SPEL/EU-Data base can be successfully used for estimation purposes. They are a perfectly suitable and useful tool for an ex-post description of the agricultural sectors of the Member States, but might create considerable problems for the estimation of product differentiated, sectoral supply response to changes in economic incentives

• For projects such as this one it would be useful to have a data base with time series on relevant political variables (administered prices, quotas, premiums, etc.) matching the definitions of the SPEL/EU-Data base.

Another data problem, independent from the data source, is the policy intervention affecting main agricultural markets during the observation period. They tend to considerably reduce price variation



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and consequently render the statistical detection of behavioural reactions difficult. Also, changes in the policy regime (for example with the CAP-reform in 1992) can cause structural breaks in behavioural reactions of producers which can only be partially reflected in the empirical model.

(2) Theoretical model: Generally, the underlying micro-economic model - as most empirical applications of short term, duality based approaches at the sectoral level - does not explicitlyaccount for certain aspects, for example risk behaviour and the existence of transaction-, adjustment- and information costs with potentially negative effects on the quality and interpretability of the estimation results.

Although the theoretical model generally allows for the effect of the primary factors labour and capital on the production decisions, for lack of data they have not been explicitly introduced in the estimation but were instead subsumed under the trend variable which may cause additional problems.

For crop production, the assumption of non-jointness in variable inputs and the independence of production intensity from the level of the production activities are considered important limitations and might be partially responsible for the estimation problems.

The static nature of the employed theoretical model might be especially restrictive for modelling animal supply response. The estimation results for the level determination of animal production activities might indicate this problem. Another related problem is that the production cycles - and with it the relevant expectation formulation - for most of the animal production activities does not coincide with the yearly observations used for estimation purposes.

(3) Application to other Member States: Although the programs, work files etc. used in this project phase were set-up to allow a technically easy application of the approach to other Member States, the time demanding part of such an application is connected to empirical questions in the light of estimation results achieved: choosing an appropriate separability structure, evaluating a suitable expectation model, deciding upon the introduction of correction measurements for serial auto-correlation, deleting insignificant parameters from equations etc.. Here, mechanical solutions are impossible. Knowledge and experience in the fields of duality theory, econometrics and the content and set-up of the SPEL/EU-Data base are necessary to obtain appropriate model specifications within the frame of the general model layout.

(4) Possible consequences for SPEL/EU-MFSS: The estimation results must be seen in light of the various theoretical and empirical shortcomings of the employed approach. Due to the extensive experiments conducted in this project we have considerable doubts that an econometric estimation of gross margin elasticities using the SPEL/EU-Date base can provide an empirical validation and updating approach of the supply response specification in the SPEL/EU-MFSS model, at least for activities other than crop production activities.

Given the outcome of the estimations and the prevailing need for some empirical validation and update of behavioural parameters, we propose for further developments of the SPEL/EU-MFSS to consider an alternative specification of the behavioural supply model based on price elasticities. This switch would make it much easier to compare the parameter set employed in the SPEL/EU-MFSS with other modelling system and to feed the model with synthetic elasticities. Furthermore, there is some hope - at least for the crop sector - that an econometric estimation of price elasticities might yield more stable and plausible results than the current project.



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2 Objectives

2.1 Objectives of the Overall Project

The current supply component of the SPEL/EU-MFSS employs gross margin elasticities to steer the production activity level determination in simulation runs. These elasticities are partially derived from estimated supply elasticities with respect to own and cross prices in the literature, and partially based on estimated gross-margin elasticities stemming from WOLFGARTEN (1991). They are calibrated to comply with microeconomic restrictions implied by the assumed optimisation approach (WEBER 1993, pp.50-57). Subsequently, they are used to formulate linear behavioural equations within an NLP framework of the overall model containing technical and accounting equations in addition (WEBER 1995, p. 27).

In the initialisation phase of the overall project the usefulness of an updated and consolidated set of behavioural parameters for the SPEL/EU-MFSS has been agreed upon. Despite some general scepticism about the possibility to estimate behavioural parameters using a sectoral data base such as the SPEL/EU-data base and an ex-post time period with strong policy interventions on agricultural markets, this project nevertheless intends to perform and evaluate the explorative estimation of supply response parameters in order to base decisions of further activities in this regard on the outcome of this test.

After the exploration of several alternatives regarding the theoretical and methodological background of estimating sectoral supply response (HECKELEI 1997) it has been decided to choose an approach that stays as close as possible to the current structure of the SPEL/EU-MFSS. This implied to literally estimate "gross margin elasticities" of activity level response using pre-determined gross margins provided by the SPEL/EU-BS. The resulting response parameters, based on theoretically consistent estimation procedures and comparable model and data specifications between Member States, have a considerable potential to improve simulation and forecasting performance of the overall model:

• Supply response behaviour of the agricultural sector would be based upon data from the SPEL/EU-BS. Regular updates of estimations can be done contingent upon new data provided by the system and the methodological as well technical results of the study.

• Gross margin elasticities (effects) consistently estimated with respect to the underlying theoretical model could substitute the gross margin elasticities from the literature, whose underlying data definitions, theoretical assumptions and time horizons are most likely not consistent with each other and the SPEL/EU-MFSS model. A calibration procedure to impose theoretical restrictions would be unnecessary.

• Regressing activity levels simultaneously on gross margins and a trend function would allow to isolate gross margin own and cross effects from changes in fixed factors and technology and could potentially improve the representation of these effects in the overall model. Currently, trend estimations (representing changes in fixed factor quantities and technology) subsume gross margin-effects which could involve unnecessary information loss by not separating these effects.

• The estimated equations could be directly used in model simulations without the side step of a linearised elasticity representation.



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2.2 Objectives of the Explorative Estimation Phase

For the explorative estimation phase of the project it was envisaged to identify a more or less standardised operational approach for the estimation of gross margin elasticities that could be later extended to all Member States and be the basis for a regular update of behavioural parameters contingent upon new data in the system. However, the ultimate decision on the consequences of the explorative estimation phase have to be based on the plausibility of estimation results, statistical properties of the estimated parameters and the work load connected with the application of the approach to all Member States and the integration of its results in the SPEL/EU-MFSS.

In detail the agreed upon objectives and work contents for the current explorative estimation phase are mainly determined by the results of the preceding project which were described in the final report for contract 781400001 of 14.03.1997, part III “Estimation of Elasticities for SPEL/EU-MFSS: explorative realisation of estimation” (BRITZ & HECKELEI 1998). They are summarised by the following points:

• The main objective of the first explorative estimation phase was to test the feasibility of estimating level elasticities with respect to changes in expected gross margins of agricultural production activities based on SPEL/EU-Data.

• The resulting estimation results based on a hierarchical-Translog-revenue-function system for Germany were ambivalent and did not allow a final evaluation of the employed theoretical model in general or of the Translog functional form specifically. In particular, the estimation results show signs of serially correlated errors, which can be the results from different factors: erroneous expectation models, non-suitable functional form, dynamics in the underlying decision process not accounted for in the static model specification.

• Promising, however, was the fact that most of the estimated own gross margin elasticities had the expected positive sign and that the equation fit measured by R2 was high.

The discussion of these results with Mr. G. Weber from Eurostat on June, 24th,1998 lead to a more specific definition of the tasks involved in the current project. The work progress was structured according to this agreed upon outline and encompassed the following steps:

• According to the agreement on the hierarchical structure of the supply system an aggregation routine for the production activities has been written. The use of the software package GAMS is now being avoided in order to limit the cost of new software packages at a later stage when the possible extension of the estimation to other Member States is done in direct co-operation with Eurostat. Consequently, some of the preliminary calculation routines (aggregation, expectation models, data adjustment to better represent product specific incentives) had to be rewritten in EViews or FORTRAN.

• Due to differing data problems and particularities of the Member State’s agricultural sectors different aggregations are necessary for the estimation of the different Member States, i.e. in the current project at least for one Mediterranean Member State and for one of the „big“ northern Member States (D, F or UK). Consequently, the routines for preliminary data calculations are written in the most flexible way.

• Alternative functional forms for the revenue function had been tested with the hope to avoid some of the serial correlation problems observed for the Translog specification. The “symmetric generalised McFadden” (or “symmetric normalised quadratic”) has been chosen for this purpose. Contrary to the Translog function, this form allows to explicitly introduce a land



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constraint into the system.

• A problem of all tested functional forms is the fact that convexity of the revenue function can be incorporated by inequality constraints only which lead to a rather complex estimation approach not applied in here. This means that negative own-GVA-elasticities or curvature violations cannot be avoided a-priori and that these important properties of supply behaviour can only be tested after the estimation. A possible remedy for this is the application of a Bayesian estimation approach. An EViews program has been written that allows to test and impose curvature restrictions on the specification of the system. Preliminary tests based on the Translog form with smaller arable crop groups showed that curvature is strongly rejected by the model and the imposition is neither defendable nor even feasible. However, the approach was applied to the larger - at first sight more promising - specifications of the arable crop system and to the alternative functional form.

• In the light of the results achieved so far it has become clear that the livestock part of the system is more difficult to estimate than the crop part. One of the reasons is that the activity specific gross value added in the database for livestock is often negative. Some of the problems have already been avoided by using appropriate expectations instead of realised gross margins and by an adequate aggregation of activities. The translog specification of the revenue function cannot even work with negative gross margins (negative logs are mathematically not defined). Additional approaches shall be investigated to attack this problem: One is to adjust the gross margins for the included fixed cost items (e.g. repairs and maintenance) by excluding an estimated share of fixed costs in total costs from the profit indicator used for the estimation of the revenue function. Also, it seems that the employed price series for feed inputs in the animal activities might be partially responsible for the often observed low gross margins. Possible adjustments are currently discussed.

• A particular problem for the estimation of a supply system poses the existence of the production quotas for milk and sugar. Quotas were introduced as fixed quantities in the formulation of behavioural equations. With this approach, gross margin elasticities for the quota products cannot be derived. Consequently it is not possible to obtain parameters that allow to simulate the impact of an abolition of a quota system. Alternatively, one could employ an approach which generates shadow prices for quotas allowing to derive behavioural parameters for these production activities.

In the process of addressing these objectives for the current project phase, new information made it necessary to adjust the weights and time allocated to the different issues. For example, we concentrated our efforts on the more flexible functional form and abolished the Translog specification after analysing results for cash crop production. Also, after preliminary investigation of the shadow price formulation for quotas this approach has not been further pursued, since it requires a non-linear estimation procedures involving a whole new layer of technical problems that are considered prohibitive within the scope of the project. The validity of the potentially derived behavioural parameters is anyway restricted to simulations around the observed quantities and are consequently of limited use in liberalisation scenarios. On the other hand, the regional scope of the estimations has been extended to more than two Member States in order to test whether general characteristics of the estimation results differ between different data sets. Furthermore, a considerable amount of time was again invested into various expectation models. For further discussion on the decisions taken during the research process we refer to the subsequent sections of this report.



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3 Theoretical Model (Review)

In this section, the theoretical model underlying the estimation of gross margin elasticities in this study is reviewed. It is mainly a short summary of the relevant parts in HECKELEI (1997), with some minor notational changes and extensions reflecting additional insights gained during the process of empirical implementation.

3.1 Gross Margin Elasticities in SPEL/EU-MFSS

The current supply component in SPEL/EU-MFSS describes the medium term horizon response of producers to changing price expectations in a recursive-dynamic framework as a two stage decision process (WEBER 1995, p. 16):

1. In the first stage, farmers decide upon the quantities for the variable inputs per unit of production activities and determine the (expected) yields. Resulting output and input coefficients determine (expected) gross margins per activity unit.

2. In the second stage, farmers decide upon the levels of the production activities based on the expected gross margins per activity unit.

Gross margin elasticities come into play in this second step: They are, correctly speaking, "level elasticities with respect to expected gross margins per activity unit". They are partially derived from estimated supply elasticities with respect to own and cross prices in the literature, and partially based on estimated gross-margin elasticities stemming from WOLFGARTEN (1991). Subsequently,the elasticities are calibrated to comply with microeconomic restrictions implied by the assumed optimisation approach (WEBER 1993, pp.50-57). For model simulation purposes, they are linearised based on calculated changes in gross margins and trend driven activity levels and incorporated into an NLP framework which is used as a solver for the overall model including those behavioural equations as well as technical and accounting equations (WEBER 1995, p. 27).

We now turn to an explicit representation of the two step optimisation underlying the SPEL/EU-MFSS in order to derive the theoretical properties of gross margin elasticities - or more generally of gross margin effects in activity level determination - and to lay out potentially restrictive assumptions within this structure.

3.2 An Explicit Two Step Optimisation Approach

In the first step producers maximise gross margins per production activity unit by adjusting output and variable input coefficients given the respective prices and technology, latter depending on the quantity of fixed factors. The optimal gross margins have to be independent of the level of the production activity in order to ensure a recursive structure of the two steps.

More formally, the indirect objective function of this first step optimisation for production activity i is defined as

(1) { }[ ]iiiii

uvi Tzuvuwvpzwpgm

ikl

i∈−= ,,:''max),,(

,

that is defined by adjusting the vector of output coefficients vi (Ox1) and the vector of input coefficients ui (K×1) to achieve the maximum gross margin per unit of activity i, gmi(p,w,z), for given vectors of output prices pi (Ox1) and input prices wi (K×1), and quantities of fixed factors z



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(M×1), under the restriction of the technological possibility set Ti.

This indirect objective function is in fact a restricted profit function exhibiting certain regularity conditions: it is positive, monotonically increasing in pi and z, monotonically decreasing in w, linear homogeneous, convex and continuous in prices, and concave and continuos in z. Consequently, optimal output and input coefficients can be derived by applying Hotelling's lemma as

(2) Olp

zwpgmzwpv

i

iil ,...,1

),,(),,( =∀=

∂∂

(3) Kkw

zwpgmzwpu

k

iik ,...,1

),,(),,( =∀−=

∂∂

In the second step producers determine the level of the production activities in order to maximise overall gross margin (GM) subject to a "level technology". In the case of crop production activities we can explicitly incorporate the land constraint to obtain

(4) { }

=∈= ∑

=

Ll;Tz,l:l'gmmax)L,z,gm(GMN

1ii

l

l

defined by adjusting the vector of production activity levels l (N×1) to achieve the maximum gross margin for a given vector of crop specific gross margins gm (N×1), a vector of quantities of fixed factors z (M×1), under the restriction of the technological possibility set Tl and total Land availability L. Equation (4) is the definition of a "revenue function" (see CHAMBERS 1988, p. 262ff.), which exhibits regularity conditions analogous to those of a profit function: It is positive, monotonically increasing in gm and z, linear homogeneous, convex and continuous in gm, and concave and continuos in z.

A special case of the optimisation problem underlying (4) is a linear program, that maximises the gm'l subject to linear inequality constraints ensuring that requirements do not exceed availability of fixed factors and total land. The revenue function (4) is more general, however, in the sense that fixed factors need not be allocable to the activities and that the relationship between activity levels and fixed factors can be non-linear. In any case, the optimal levels of the production activities are assumed to leave the technology underlying the first step optimisation (determination of gmi's) unchanged, i.e. the "level-technology" Tl is in this sense independent from the activity specific technologies Ti. One should note that this is a rather severe restriction on the sectoral technology in agriculture which is probably hard to justify. We will later pick up that argument again if we discuss the outcome of the estimation.

If a unique revenue maximising vector of activity levels l(gm,z,L) always exist (which is not the case for the LP technology), the GM(gm,z,L) is differentiable in gm (Samuelson-McFadden lemma, CHAMBERS 1988, p. 264) and the elements of l(gm,z,L) can be obtained by

(5) Nigm

LzgmGMLzgml

ii ,...,1

),,(),,( =∀=

∂∂

.

The system of equation (5) determine the optimal (area) levels of the different production activities. Each specific equation is homogenous of degree 0 in gross margins and the matrix of marginal gross margin effects of the system is symmetric. Formally, those properties can be expressed as



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(6)

Njigm

Lzgml

gm

Lzgml

andNigm

Lzgml

i

j

j

i

M

j j

i

,...,1,),,(),,(

,...,10),,(

1

=∀=

=∀=∑=

∂∂

∂∂

∂∂

.

Differentiation of the total land constraint further implies additivity constraints on (5) of the form

(7)

.1),,(

,,...,10),,(

,,...,10),,(

1

1

1

=

=∀=

=∀=

∑

∑

∑

=

=

=

M

i

i

M

i k

i

M

i j

i

L

Lzgml

andMkz

Lzgml

Njgm

Lzgml

∂∂

∂∂

∂∂

One could easily express the restrictions (6) and (7) in terms of elasticities and mirror the conditions in WEBER (1993, p. 54) for symmetry and homogeneity restrictions. It should be noted at this point that for the empirical specification of the models, the total land variable, L, was not included in the revenue function describing cash crop production, because the separability structure requires that the gross margin per activity unit of the cash crop aggregate is independent of the land allocated to this group. The required linear homogeneity of cash crop revenue in L was imposed by expressing the revenue function (4) as revenue per unit of land allocated to the cash crop aggregate. The land constraint (and consequently the resulting additivity constraints (7)) is certainly irrelevant for revenue functions involving animal production activities (the "aggregate level" in our estimation approach, see below).

3.3 Limitations of Estimations Based on The Two-Step Approach

From the pragmatic point of view concerning the integration of the results, estimation of gross margin effects on activity levels based on the Two-Step Approach described above is advantageous simply by staying close to the current modelling structure of the SPEL/EU-MFSS because the requirements to adjust the simulation methodology of the model are minor. Compared to the current status the potential improvements provided by the estimations are manifold and have been describedin the objective section above.

One limitation of the two-step approach lies in its restrictive technological assumption. All published econometric models of multi-output multi-input supply response systems that actually distinguish between level and intensity of production activities and are known to the authors, do not impose the fundamental restriction that intensity is independent of the level of the production activity - for good reasons. In fact, it is quite likely that the dependency between the gross margin per activity unit and the activity levels is of a simultaneous nature. Imposing exogeneity of gross margins per activity unit when estimating "activity level functions" is consistent with the structure of the SPEL/EU-MFSS but will most likely violate the true data generating process. One can still view this approach as a pragmatic way to update the gross margin-elasticities hoping that the identified statistical relationships are stable and represent the behavioural response of the agricultural sector in a sufficient way.

Naturally, by choosing an approach which differs from publications available, more time must be invested to derive estimation equations and results achieved cannot be easily compared to existing



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studies.

Another problem with the two-step approach is related to the data requirements. In order to estimate gross margin effects on the activity levels, variable inputs need to be allocated to the different production activities to obtain an ex-post series of gross margins. The SPEL/EU-BS performs this task using technological information and consistency checks with sectoral accounting data. The input allocation, however, is characterised by a significant amount of uncertainty and potential errors in representing changes of relative competitiveness between production activities over time expressed by the relative changes in gross margins. We will discuss that point in more detail in the final evaluation.

3.4 General theoretical restrictions of the approach

Some further more general limitations of the theoretical approach should be mentioned. The underlying micro-economic model is a great simplification in the sense that it does not explicitly account for certain aspects potentially relevant for adjustments in activity levels, for example risk behaviour and the existence of transaction-, adjustment- and information costs. In these respects our approach is not different from most empirical applications of short term, duality based approaches at the sectoral level, but nevertheless these shortcomings with potentially negative effects on the quality and interpretability of the estimation results exist.

By assuming risk neutral decision takers, neither variances of yields, input coefficients nor price but only their expected mean outcome play a rule in the model. For example, it is irrelevant if the expected mean of prices in cereal markets are based on stabilising market interventions or more uncertain market outcomes. Consequently, the effect of changes in income risk in grandes culture before and after the '92 CAP reform is not captured.

The existence of adjustment costs and irreversibilities may be an argument to use dynamic model specifications and to introduce lagged endogenous variables in the model, and, if neglected, may lead to residual autocorrelation problems which we observed in all estimations (see below).

Although the theoretical model generally allows for the effect of the primary factors labour and capital on the production decisions, they have not been explicitly introduced in the estimation but were instead subsumed under the trend variable for lack of appropriate data for the Member States. This may cause additional problems, although other studies show that the introduction of aggregate capital stocks and labour not necessarily have a relevant effect on other estimated parameters (see GYOMARD, BAUDRY, CARPENTIER 1996).

Generally, without testing appropriate more complex models, the effect of the simplifications on the current estimations is hard to evaluate. One should keep in mind, however, that introducing additional explanatory variables in the estimation models would lead to a much more complex simulation model later on, if the results would be incorporated in a system as SPEL/EU-MFSS. The mentioned simplifications are rather typical for the application of duality approaches at the aggregate level.

Last but not least the aggregation problem of applying micro-economic models at the level of aggregated producer response might potentially bias the empirical results due to the additional implied restrictions on the characteristics of the technology.



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4 Model Specification and Estimation Approach

4.1 Separability Structure

In order to keep a sufficient degree of product differentiation and still render the estimation feasible, a subdivision of the underlying optimisation problem into two levels is necessary. At level 1, farmers decide upon the levels of aggregates of production activities maximising a revenue function based on gross margins and levels of aggregated production activities, for example on the level of the activity "cash crops".

At level 2, farmers determine the level of disaggregated production activities based on a revenue function per unit level of the aggregate. This two-level-approach assumes that the level allocation within each aggregate is independent of the level of the aggregate. It is implied that gross margins of activities outside of an aggregate are relevant only for the level of the aggregate but leave the substitution within the aggregate unchanged.

Note that the gross margin of an aggregate used in level 1 represents an index of the disaggregated production activities at level 2. The appropriate index is determined by the optimisation process in level 2 and must be independent of the level of the aggregate. For the case of the aggregate "cash crops", for example, the index weights are the optimal land shares given a vector of gross margins for the production activities of the cash crop group. Hence, shares of disaggregated crop production activities of land allocated to the group are already determined when determining aggregate activity levels.

In terms of the estimation sequence this results in a two step procedure where one first estimates the level equations of the activities within each subgroup depending on all the activity gross margins in the subgroup and fixed factors (if applicable). In the second step, a system of level equations for the aggregates is estimated depending on subgroup gross margin indices (calculated on the basis of first step estimation results) and fixed factors.

It should be noted that the validity of the separability structure is an empirical question and the specification can be subjected to statistical tests. However, for practical purposes one needs to at least restrict those tests to a limited set of alternatives which have been identified on plausibility grounds. After the first project phase, we decided (in agreement with G. Weber) to set the separability structure a-priori as has been done in most related applications in the literature (see for example JENSEN (1996); GYOMARD, BAUDRY & CARPENTIER (1996); LANSINK & PEERLINGS 1996).

4.2 Exclusion from and Aggregation of SPEL-Activities before the Estimation

Permanent crops as well as vegetables and industrial crops apart from oilseeds were excluded from the analysis for the following reasons:

• Permanent crop levels are mainly determined by investment decisions in the past so that short term substitution with annual crops as a reaction to gross margin changes is largely irrelevant.

• Vegetables and industrial crops differ substantially in labour and machinery need and the marketing process from other cash crops.

• For a similar reason, the SPEL/EU-MFSS model is not designed as an instrument to make simulations for permanent crops.



- 14 -

Intermediate crop production on grassland - SPEL activity GRAS - and arable land – SPEL activities SILA, OROO - cannot be considered explicitly in the model set-up due to the data generation process in the SPEL/EU-BS. Prices for these intermediate outputs are set as to cover the production costs. Consequently, the gross margin as a level weighted average from GRAS, SILA and OROO is always zero. Differences in the gross margins of the three activities generated by the algorithm are according to W. Wolf of a stochastic nature. Due to the fact that physical and valued flows inside of the agricultural sector are always consolidated, the pricing mechanism completely maps the costs from intermediate crop production to the animal activities. Insofar, with fixed factor arable land and pre-determined levels of permanent crops, vegetables and industrial crops apart from oilseeds, the activity level of cash crops - determined in the aggregate (level 1) system below -implicitly determines the level of fodder production on arable land. The level of the grassland activity (GRAS) is treated as a fixed quantity.

Alternatively, one could define level 1 as a profit function which also determines variable input quantities including the intermediate production and subsequently determine feed production levels with a cost function approach (see for example HUFF & MOREDDU 1990). However, due to the lack of meaningful gross margins for intermediate fodder production in the SPEL/EU Data base, this type of approach would require substantial additional data work which is not within the scope of the project.

The chosen approach is also more in line with the structure of the current SPEL/EU-MFSS. WEBER

1995 (p.33ff.) determines the level of intermediate crop production not based on behavioural parameters directly, but depending on the level of animal activities, the feed module and trend values for the level of intermediate crop production activities.

Another question concerns activities with small levels in crop production. Although one of the big advantages of the SPEL/EU-Data base is its deep product differentiation, a higher aggregation level is more suitable for certain purposes, for example the estimation at hand. Based on the production structure of the individual Member States, certain activities may just be slightly above the minimum area requirement to be included in the SPEL/EU-BS.

Crop activities whose level drop below 250 ha are discarded in the SPEL/EU-BS and added to a residual category as, for example, "other cereals" (OCER). The same happens if the output generation of a production activity is zero. In both cases, the level of the respective activity and the output generation of the residual activities such as OCER are affected. The afflicted observations can create problems during estimation due to the (data related) zero level for one the activities and the implicit re-definition of the residual activity. (WOLF 1995, p. 112).

Therefore, such activities which show small levels in some years and zero in others are added to the connected residual category. Generally, the residual categories are error-prone for other statistical problems, too. Therefore, W. Wolf suggested to aggregate these residuals (OCER, OOIL, OIND, OFRU, OVEG) to less important elements of the same group.

Both levels and income indicators for the overall residual category “Other crops” (OCRO) cannot be interpreted easily and are therefore excluded from the analysis, the same holds for “Other animals”. In most countries (with the exception of Spain and Sweden) the level of other crops is only a very small percentage of the total area. For practical purposes, it should be either kept constant or trend-shifted in simulation runs of the SPEL/EU-MFSS.

In the animal sector, another reason for aggregating activities is based on the valuation problem of intra-sectoral flows of young animals. Take pig meat and piglet production. Depending on the value attributed to a piglet, the income indicators for e.g. pig fattening (PORK) and sows (PIGL) can be



- 15 -

shifted against each other without affecting the consistency of the total framework. Although the SPEL/EU-BS is naturally trying to find the most appropriate sources in price statistics to value young animals, errors cannot be excluded but naturally influence the relative competitiveness between the animal activities. Due to the fact that the activities can be thought as strongly coupled to each other, the estimation can be improved by adequate aggregations. The same is actually done in the SPEL/EU-MFSS.

Another problems refers to the fact that the definition of some animal production activities – cows, raising calves, heifers for breeding, sows, laying and sheep and goat for milk production - is based on herd size statistics rather then on flow data based on slaughtered heads. These herd size statistics represent inventories at a specific day of the year. As long as the development of the herds over time is stable and fluctuations low, problems for the current estimation are few. However, we observed especially for laying hens some curious fluctuations in the activity levels which corresponded to changes of the yield coefficient in the opposite direction. Here, we related the gross margin not to the activity level but to eggs produced and estimated the production quantity instead. It should be noted that this does not change the two-stage decision model.

4.3 Top Level System

At level 1 of the decision process farmers are assumed to determine the level of the following aggregate production activities in order to maximise revenue subject to fixed production quotas of milk and sugar, arable land, grassland, and an underlying "level” technology, where the fixed factors capital and labour are subsumed under a time variable:

1. Cash crops

2. Other cows

3. Beef

4. Pork

5. Poultry

6. Eggs

7. Sheep and Goats

The milking cow herd is determined by the milk quota for given milk yields, the same holds for sugar beet. As explained above, the level of cash crops (cereals, oilseeds, pulses, potatoes) implicitly determines the level of fodder production on arable land.

The category “beef” covers the SPEL activities BEEF (male > 1 year), CALF (calves fattening, < 1 year) and the slaughtered heifers as part of the activity HEIF. In the latter case, heifers used for breeding – according to the output coefficients DCOW and SCOW – were subtracted. The income of the heifers for slaughtering was based on the meat output, costs were distributed to the fattening and breeding part of the herd according to the DCOW and SCOW-positions. Accordingly, the income from raising calves (RCAL) was distributed over milk cows, other cows and the beef activity. In the case of pork production, breeding sows (PIGL) were aggregated with the pork meat activity (PORK). As explained above, eggs production quantity produced was estimated instead of the herd size of laying hens.



- 16 -

4.4 Cash Crop System

At level 2 producers maximise revenue of the sub aggregate “cash crops” which is divided into the following production activities for the results presented for Germany, France and Spain:

1. Wheat (SWHE+DWHE)

2. Barley (BARL)

3. Maize (MAIZ)

4. Rest of Cereals (OATS,RYE,OCER)

5. Oilseeds (RAPE, SUNF, SOYA, OOIL)

6. Pulses (PULS)

7. Potatoes (POTA)

Due to differing data problems and particularities of the Member State’s agricultural sectors different aggregations can be advised for different Member States. In the case of Italy, for example, durum wheat (DWHE) has been treated as a separate activity due to its special importance in this Member State. At the same time, barley (BARL) has been aggregated to the "Rest of cereals" activity so that the number of activities in the group remained the same.

The separability structure described has the following consequences for the estimated gross margin elasticities:

• There will be no elasticities estimated describing the substitution between those SPEL production activities which were aggregated to a new production activity before the estimation. For example, within the "rest of cereals" activity no cross price elasticities are estimated between oats, rye and other cereals.

• Cross gross margin elasticities between a certain production activity in the cash crop group and all activities of level 1 will be the same. For example, the beef activity will have the same cross gross margin elasticity with each activity in the “cash crop” group.

The specification of the separability structure of the model reported here is a product of certain data problems as described above, difficulties in statistically identifying meaningful substitution relationships between activities of large and very small importance, as well as the necessity to limit the number of parameters in each system estimated. Therefore, it might be useful - and easily done with the current programming solution - to adapt the structure of the model to the relative importance of production activities in the different Member States and - possibly - as well as to changes in the functional form.

4.5 Functional Form

4.5.1 Experiences from the First Project Phase: Translog Revenue Function

A Translog revenue function was employed in the first project phase for the estimation of different



- 17 -

crop production systems:

(8)

∑ ∑

∑ ∑∑∑

=

+

+=

=

+

+===

+

+++=

N

i

MN

Nkkiik

N

i

MN

Nkkk

M

jjiij

N

iii

zgm

zgmgmgmgm

1 1

1 112

1

10

lnln

lnlnlnlnln

β

ββββ

with gm = (expected) gross margin per unit of aggregate output, where aggregate output is calculated

as a simple sum of crop production activity levels (=> gm = ∑∑==

N

ii

N

iii llgm

11

with li = land

allocated to product i) gmi = (expected) gross margin per activity unit of product i, i = 1,...,Nzk = "fixed factors", k = N+1,..., N+M, where k = N+1 indicates a time variable subsuming

other fixed factors such as labour and capital and k = N+2,...,N+M are production rights (sugarbeet quota, milk quota) or total land (applicable at the aggregate level).

Contrary to the usual Translog specification of profit functions, no exclusive "fixed factor terms" are included on the right hand side of the equation, since this would imply that fixed factors have an effect on per unit revenue of the aggregate independent of the effect on revenue shares of the individual products which is not possible.

By Hotelling's Lemma, derivatives of (8) with respect to ln gmi result in the following revenue share equations:

(9) Nizgmwgm

lgm

gm

gm MN

Nkkik

N

jjijii

ii

i

,...,1lnlnln

ln

11

=∀++=== ∑∑+

+==

βββ∂∂

where the first equality sign in (2.1) follows from

(10)∂∂

∂∂

ln

ln

gm

gm

gm

gm

gm

gml

gm

gm

gm l

gmi i

ii

i i i= = ⋅ =

For the derivation of parameter restrictions (symmetry, homogeneity and adding-up restriction), see BRITZ & HECKELEI (1998). One specific problem of the Translog formulation is the fact that adding up of land cannot be imposed. Together with the overall not very promising estimation results -especially the prevailing severe problem of serially correlated errors as described in BRITZ &HECKELEI (1998) we decided to concentrate estimation efforts on a more flexible functional form.

4.5.2 Flexible Functional Forms

Since the middle of the 1980ies, most econometric work in supply and demand analysis based on duality theory use so-called flexible functional forms. The term flexibility refers to the fact that these functions allow an approximation of the “true” (but naturally unknown) function up to second order terms at a specific point. Flexibility is bought at the price of a relative high number of parameters to be estimated. Flexibility can be defined in terms of prices, and/or fixed netputs and/or time.



- 18 -

Most of these functional forms are defined such that linear restrictions on the parameters can be derived from micro-economic theory (homogeneity, symmetry, additivity) lowering the degrees of freedom problem. However, the limited number of observations often does not allow to relax all restrictions simultaneously, thereby rendering tests of one type of restriction contingent upon the validity of the maintained types.

Several of the functional forms allow straightforward tests on the curvature of the Hessian, and, if necessary, to impose this property by restricting the parameters. The restrictions involve either the matrix decomposition techniques proposed by LAU (1978) or WILEY et.al. (1973) or the use of Bayesian estimation techniques (HECKELEI et.al. 1997) which was employed in here.

The functions considered here are all of the general linear form (CHAMBERS 1988, p.161):

(11) ∑=

α=k

1iii )(b)(h zz

where bi(z) is a known, twice-continuously differentiable function of z. The function (11) is linear in the parameters αi (which simplifies estimation) but not linear in z. Importantly, as mentioned above, it is flexible in the sense that the function value, the gradient and the Hessian can approximate any arbitrary twice-continuously differentiable function at a specific point z0.

Some of the suggested functional forms are distinguished between an asymmetric and a symmetricform. In order to impose linear homogeneity in prices of the typical indirect objective functions (cost, profit and revenue functions), prices are often normalised. In so-called asymmetric functions, normalisation is done by choosing one of the prices as the numeraire. Estimation results then generally depend on the choice of the numeraire good. A similar problem exist if linear homogeneity in fixed netputs is assumed.

So called “symmetric” flexible functional forms try to circumvent the problem by normalising with a price index instead. There are however two potential drawbacks of the symmetric forms:

1. Typically, the price index must be pre-determined and cannot be estimated simultaneously with the other parameters. Insofar, the arbitrary choice of the numeraire good is replaced by an a-priori decision on the weights employed in the price index. Consequently, results generally depend on the choice of the weights. The asymmetric form is in fact a special case of the symmetric form with the index weight for the numeraire price set to one.

2. Symmetric functions usually lead to more complex terms in the equations to be estimated. However, in asymmetric functions, the equation for the numeraire good is usually equally complex as all equations in case of the symmetric forms.

Two often used flexible functional forms in supply analysis are the following (in profit function notation where p denotes a N×1 vector of variable netput prices, z a M×1 vector of fixed netput quantities factors and t time):

Generalised McFadden (GM)

(12)

( ) ( )

∑ ∑∑ ∑∑∑ ∑

∑∑ ∑+

+= =+= ===

+

+=

==

+

+=

+

+

++

++≡Π

MN

Nkk

N

iiikt

M

Nkk

N

iiik

N

iiit

N

i

MN

Nkkiikt

N

iii

N

i

MN

Nkkiik

tzpczpctpctzpc

pbzpbpgtzp

1

2

11

2

111 1

11 1

,,

γβα



- 19 -

The asymmetric form uses the following function g (good 1 chosen as the numeraire):

(13) ( ) ∑∑= =

−≡N

i

N

ijiij ppbppg

2 2

112

11 where jiij bb = for Nji ≤≤ ,2

whereas the symmetric form defines g as follows:

(14) ( ) ∑∑∑== =

≡N

iii

N

i

N

ijiij pppbpg

12 22

1 θ where jiij bb = and 01

* =∑=

N

jiij pb for p*

Where b, c must be estimated, θγβα ,,, are usually pre-selected if the number of observations is too

low. If degrees of freedom are no problem, the ktkt ddd ,, can be set to unity and γβα ,, . are

estimated. θ are the weights of the pre-selected price index.

Normalised Quadratic (NQ)

Asymmetric form with good 1 and fixed factor 1 chosen as numeraires:

(15)

( )

21111

11

11

1 11

1 112

11

1 112

1,,

tczptczptzcptpcz

zpbzzzbppppbztzp

ttt

MN

Nkkk

N

iii

N

i

MN

Nkkiik

MN

Nk

MN

Nlmllm

N

i

N

jjiij

++++

++≡Π

∑∑

∑ ∑∑ ∑∑∑+

+==

=

+

+=

+

+=

+

+== =

Symmetric form (SNQ):

Let ∑=

=N

iiiI pp

1

θ denote a price index for the netputs with pre-selected weights θ and ∑=

=M

kkkI zz

1

ϑ

a quantity for the fixed factors with pre-selected weights ϑ . The SNQ can then be written as:

(16)

( )

22

1

11

1 11 12

1

1 12

1,,

tzpctzpctzcptpcz

zpbzzzbppppbztzp

IIttIIt

MN

NkkkI

N

iiiI

N

i

MN

NkkiikI

MN

Nk

MN

NlmllmII

N

i

N

jjiijI

++++

++≡Π

∑∑

∑ ∑∑ ∑∑∑+

+==

=

+

+=

+

+=

+

+== =

where b, c must be estimated. Normalising for the fixed factors by choosing an index ZI is necessary only if linear homogeneity in fixed factors is assumed. THIJSSEN (1996) e.g. estimated a SNQ without normalising for fixed factors.

Neither one of the NQ and GM functional forms is a generalisation of the other. The NQ treats fixed factors and prices symmetrically and consequently incorporates cross products between fixed factors that do not appear in the GM form. The GM form, on the other hand, is more flexible regarding the time variable as it includes cross products between prices and fixed factors multiplied with t.

4.5.3 Functional Form Employed

In order to avoid the problem of estimation results depending on the chosen numeraire a symmetric functional form was selected. This was judged more important than the higher burden in terms of



- 20 -

functional complexity during estimation. Linear homogeneity in fixed factors was not assumed and hence a normalisation for fixed factors was not necessary.

Originally, we decided to use the Normalised Quadratic functional form, because it treats prices (in our case gross margins) and fixed factors symmetrically. It turned out later, however, that additional necessary zero restrictions on parameters lead to system specifications that can be thought of special cases of both the SGM and the SNQ functional form (see below).

4.5.3.1 Cash crop system

From the description of the separability structure above we know that the gross margin index of an aggregate needs to be independent from the output decision at the aggregate level. For the cash crop system, marginal revenue per ha must be independent of the land allocated to cash crops. Hence, we imposed linear homogeneity in land by defining the revenue function in terms of revenue per ha land allocated to the cash crop group. Level equations in this system consequently determine land shares of the individual production activities.

Let ∑=

=N

iiiI gmgm

1

θ denote a gross margin index with pre-selected weights. The revenue function per

ha is then defined as:

(17) ∑∑∑∑== ==

++++=N

iIttItiitI

N

i

N

jjiij

N

iii tgmctgmctpcgmgmgmbgmbgm

1

22

1

1 12

1

1

with gm = (expected) GVA per unit of aggregate output, where aggregate output is calculated as a

simple sum of crop production activity levels (=> gm = ∑∑==

N

ii

N

iii llgm

11

with li = land

allocated to product i).gmi = (expected) GVA per activity unit of product i, i = 1,...,Nt = a time variable subsuming other fixed factors such as labour and capitalθi = pre-selected weights for the gross margin index ∑

iii gmθ with 1=∑

iiθ

By Hotelling's Lemma, derivatives of (17) with respect to gmi result in the following level share equations:

(18)

22

1

2

1 12

1

1

1

tctctc

gmgmgmbgmgmbbl

l

gm

gm

tththht

I

N

i

N

jjiijhI

N

jjhjhN

ii

h

h

θθ

θ

+++

−+==∂∂ ∑∑∑

∑ = ==

=Nh ,...,1=∀

Equations (18) describe the system if fixed factor effects are removed. In the following, theoretical restrictions reducing the number of parameters are derived which lead to the system being estimated.

Differentiating (18) again with respect to the individual gross margins yields:



- 21 -

(19)

3I

N

1i

N

1jjiijhg

2I

N

1jjgjh2

1

2I

N

1jjhjg2

1IhgN

1iig

h

gh

gmgmgmbgmgmb

gmgmbgmblgm

l

gmgm

gm

∑∑∑

∑∑

= ==

=

=

θθ+θ−

θ−=∂

∂=

∂∂∂

Nhg ,...,1, =∀

Symmetry of the matrix of second partial derivatives requires that

(20) Njibb jiij ,...,1, =∀=

Since level shares for the cash crop system add up to 1, further additivity restrictions can be derived. Let v denote any variable in (18), i.e all of the gm’s and t. Additivity then requires that

011

≡∂∂

∂=

∂∂ ∑∑

==

N

i i

N

i

i

vgm

gm

v

l. Specifically, the following restrictions need to be imposed during

estimation:

(21) NjbN

iij ,...,10

1

=∀=∑=

(22) NjgmbN

ijij ,...,10

1

=∀=∑=

Equation (22) implies that additivity can only be imposed for a specific, pre-determined vector gm*. In our case we have chosen the mean of the gross margins in the sample period as gm*.

In the case of the time variable t, 01

≡++∑=

tccc tt

N

hht requires that

(23) ∑=

=N

iitc

1

0

(24) 0,0 == ttt cc

Finally, setting all variable in (19) to zero imposes the following restrictions on the bi's:

(25) ∑=

=N

iib

1

1

Hence, the equations to be estimated are defined as follows with linear restrictions on the b’s and c’s as shown above and can be either derived from the SNQ or the symmetric McFadden:

(26) tcgmgmgmbgmgmbbl

l

gm

gmhtI

N

i

N

jjiijhI

N

jjhjhN

ii

h

h

+−+==∂∂ ∑∑∑

∑ = ==

=

2

1 12

1

1

1

θ

The theoretically required convexity of the revenue function with respect to gross margins is given, if the appropriate matrix of second partial derivatives of the revenue function (19) is positive semidefinite. It can be shown that this is fulfilled if the first N x N sub-matrix of B is positive



- 22 -

semidefinite (see KOHLI p. 247). Consequently, the curvature restriction holds globally, i.e. independently of the variable values, in this case.

Gross margin elasticities i

j

j

iij l

gm

gm

l

∂∂

=ε can be calculated as: ji

ijij gm

gm

gm

gmgm

gm

∂∂

∂∂∂

=ε from (18)

and (19) which gives some nasty terms not reported in here.

The gross margin index gI was defined by using the sample mean of the level shares as weights:

(27)

∑∑

∑

=

=

t

N

iit

tit

i

l

l

1

θ

4.5.3.2 Top level system

Contrary to the cash crop system, fixed quantities (quotas and land availability) enter the top level system. Homogeneity in these fixed factors is not assumed so that normalisation with a fixed factor index is not necessary. In order to save degrees of freedom the cross-products between fixed factors were dropped because they would introduce 16 additional parameters.

Let ∑=

=N

iiiI gmgm

1

θ denote a gross margin index with pre-selected weights θi. The revenue function is

then:

(28) ∑∑ ∑∑∑∑==

+

+== ==

+++=N

iiit

N

i

MN

NkkiikI

N

i

N

jjiij

N

iii tpczgmbgmgmgmbgmbgm

11 11 12

1

1

with gm = (expected) sectoral revenue GVA (exclusive certain pre-determined activities, see above)gmi = (expected) GVA per activity unit of product i, i = 1,...,Nzk = "fixed factors", k = N+1,..., N+M (sugarbeet quota, milk quota, total land, grass land)t = a time variable subsuming other fixed factors such as labour and capitalθi = pre-selected weights for the gross margin index ∑

iii gmθ with 1=∑

iiθ

By Hotelling's Lemma, derivatives of with respect to gmi result in the following activity level equations to be estimated:

(29) Nhtczbgmgmgmbgmgmbbgm

gmht

M

NkkhkI

N

i

N

jjiijhI

N

jjhjh

h

,...,111

21

1

=∀++−+=∂∂ ∑∑∑∑

+===

θ

In the following, theoretical restrictions reducing the number of parameters to be estimated are derived. As shown above for the cash crop system, symmetry of second derivatives requires that:

(30) Njibb jiij ,...,1, =∀=

to be imposed during estimation. Due to the fact that each of the gross margins is linear dependent on all other prices and the price index, the bij parameters can only be identified if the following restrictions are introduced



- 23 -

(31) NjbN

iij ,...,10

1

=∀=∑=

As explained for the cash crop system, convexity is fulfilled if the first N x N sub-matrix of B is positive semidefinite. Elasticities can be estimated as in the case of the cash crop system.

4.6 Model Specification: Expectation Model

4.6.1 Experiences from the First Project Phase

At the time where the production process is initiated, gross margins of the different products are not known to the producer with certainty. Therefore, the gross margins used in the estimations must represent expected ones. During the first project phase (BRITZ & HECKELEI, 1998), the following expectation models were tested:

(1) Auto-regressive expectations on gross margins of the general form:

(32)∑

∑=

= −

ii

iiti

*t

1w.t.s

gmwgva

This includes naive expectations, Nerlove partial adjustment formulations and other variations.

As a specific approach, a modified Nerlove model analogous to the one applied in the MFSS was chosen which includes naive expectations as well. It is defined as follows:

(33)( )( ) ( )( )

( ) ( ) ( )324t

323t

22t1t

3

1t

t14

3

1t

t1t

*

aa3a31gvaaa2agvaaagvaagva

a1a1gvaa1agvagva

−+−++−+−+=

−−+

−=

−−−−

−

−=

−−

−

−=

− ∑∑

where the Nerlove parameter was set equal for all gross margins in the system. The estimation results were not very promising. High yearly fluctuation of yields - at least in crop production -probably prohibit plausible expectations of this form. We therefore turned relatively soon to a formulation where trend yields entered the expectation model.

(2) Expectation using trend yields and auto-regressive expectations on prices:

(34)

∑

∑=

−

= −

ii

ti

ititt

wts

cpwygva

1..

**

where t = current year, y* = trend yields, p = product prices and c = variable costs minus premiums.

This approach is more in line with simulation runs of the MFSS where yield fluctuations are excluded. Furthermore, it should better capture the typical planning situation in cash crops with the land allocation being based on expected yields of the form:



- 24 -

(35) )(* tfyt =

The trend function were estimated as linear or quadratic functions over the full sample. Although it may look it bit awkward to use ex-ante information to estimate expected yields ex-post, alternatively employed rolling trends have a tendency to be unrealistically jumpy. Therefore, the simple solution according to (35) was chosen.

Inputs and premiums were kept at realised values of the current year. In crop production, the SPEL/EU-BS implies - besides a uniform correction factor for all activities - a linear relationship between trend yield and input coefficients. Insofar, the combination of trend yield with realised costs is in line with the data generation process.

The situation in animal activities is surely a bit more complicated due to the impact of the feed distribution algorithm. Feed input coefficients are generated by a linear program to minimise deviations between the current and last year distribution of the quantities fed to animals under restrictions based on requirement functions and some a-priori bounds on input coefficients. However, costs per activity unit resulting from the algorithm are quite stable, so that (34) was used to estimate the top level system.

Plant by-products (straw etc.) were not yield corrected in (34) in order to keep the estimation equations as simple as possible. The income contribution of the by-products on cash-crops can be neglected.

The effect of different expectation models is visualised in Figure 1 taking oilseeds (rape, sunflower, soya) in France as an example.

The graph shows quite clearly that given the non-stationary nature of the deflated gross margins, auto-regressive expectations yield systematic overestimation (underestimation) of observed gross margins in periods of decreasing (increasing) gross margins. The bigger the weight of earlier gross margins in the expectation model, the higher is the over/underestimation of the gross margin for the current period. Another important effect can be seen looking at expectation models as (34) where auto-regressive price expectations are used: the drastic switch from price to direct income support in oilseeds due to the CAP reform in 1992 leads to an unrealistic overestimation during the first years after the reform.



- 25 -

Figure 1 Comparison of different expectation models for gross margins of oilseeds in France

2000

3000

4000

5000

6000

7000

8000

1975

1977

1979

1981

1983

1985

1987

1989

1991

1993

1995

con

stan

t n

atio

nal

cu

rren

cy

Gross margin

Yield(trend)*Price(Nerlove,0,55)-Costs+Premiums

Nerlove gross margin (a=0.55)

Naiv

Certainly, it cannot be ultimately decided whether the involved systematic error is a bad reflection of producers expectation. If gross margin development over time involves a stable trend component the systematic error has only little effect on the estimation results. If the direction and magnitude of the trend component changes in shorter time periods (like in the example for oilseeds in France), sluggish adjustment of expectations might not be so unrealistic. However, at least for the price effects of the CAP reform, the auto-regressive price expectation model seems unrealistic, given that reduced support prices were known to producers before their land allocation decision. Since estimation results in this project still strongly depended on the employed expectation model (see also, BRITZ & HECKELEI 1998) further time was invested in alternative formulations. Two of the explored additional approaches for exogenously formulated expectation models are mentioned here:

1. Instead of using past observed prices, market support prices can be employed as expected prices for such activities where the price component is determined mainly exogenously by market interventions (cereals). The drawback of this approach is the need for additional data which are currently not incorporated in the SPEL/EU-Data base. On the other hand, simulation runs with the SPEL/EU-MFSS are normally based on politically determined intervention prices in these markets. In order to test this approach for effects on estimation results, intervention prices for cereals in Germany have been collected and manually edited for the sample period (from BMLELF, Agrarberichte, different years). It turned out that the resulting expectation model for gross margins yielded at least better results than alternative expectation models (see below in



- 26 -

results section 6.1.4).

2. Incorporation of price or gross margin trend component in the expectation model to capture longer-term shift factors in the gross margin developments. Here, we experimented with a trend based shift for the expected gross margin plus weighted first differences.

In general, the fit, parameter values and standard errors showed substantial differences depending on the employed expectation models. The evaluation of the results from the Translog-specification showed, for example, a clear dependency between the variance of the expected gross margins and the magnitude of the elasticities: expectation models which create high variances in the expected gross margins lead to small elasticities and vice versa.

4.6.2 Endogenous Estimation of Gross Margin Expectations

Due to the generally observed dependency of the estimation results on the employed expectation model, a simultaneous estimation of the expectation model was investigated. Because of the sample size, the number of additional estimated parameters was limited, so that this approach was only explored for a Nerlove partial adjustment model with different coefficients for each gross margin (or price in specifications according to (34)) in the cash crop system. However, a consistent direct estimation of this system is not easily possible, since the predetermined gross margin index gmI

needs to be calculated based on expected gross margins. To embed the relationship in the equations would lead to rather complex non-linear system of equations to estimate.

Therefore, in order to maintain the homogeneity property of the underlying revenue function an iterative estimation procedure was employed where the Nerlove coefficients were first estimated simultaneously based on a pre-determined index. Then index gmI was recalculated based on the estimated expected gross margins and the whole model was estimated again. These steps were repeated until convergence of the results. It turned out that this procedure converged easily, but the iteration had only limited effects on the parameter values.

The simultaneously estimated Nerlove coefficients were usually in the range between 0.4 and 0.6. The overall estimation results, however, were not any more promising than for previously tested exogenous expectation models.

One last remark: HAZELL and NORTON (1986, p.288 ff.) discuss the effect of covariances between yields and prices created by the market mechanism. If these covariances are high, expectation models which use trend yields and weighted realised prices lead to a systematic error in the expectation. The following Table 1 reveals, however, that correlations between yield fluctuation and prices fluctuations (measured as first differences) are relatively weak so that we decided to neglect the problem. Problems, however, could occur depending on the expectation model and the specific Member State in the case of pulses and potatoes.



- 27 -

Table 1 Correlation between price and yield fluctuations (first differences) (France, 1975-1996)WheatD(Y1)

BarleyD(Y2)

Other CerealsD(Y3)

MaizeD(Y4)

PulsesD(Y5)

PotatoesD(Y6)

OilseedsD(Y7)

D(P1) -0.339628 -0.340075 -0.463387 0.105468 -0.207978 -0.104312 -0.459855

D(P2) -0.398661 -0.508096 -0.636184 0.012298 -0.270284 -0.263176 -0.501947

D(P3) -0.142653 -0.067469 -0.353764 -0.305306 -0.428281 -0.228334 -0.240675

D(P4) -0.233788 -0.121798 -0.291291 -0.345408 -0.112479 -0.111340 -0.218330

D(P5) -0.177739 -0.269835 -0.474736 -0.229050 -0.787879 -0.504169 0.050213

D(P6) -0.262223 -0.398692 -0.654194 -0.452674 -0.693008 -0.736165 -0.050056

D(P7) -0.157389 -0.368653 -0.427382 -0.214047 -0.119309 -0.489659 -0.274811

4.7 Estimation Approach

4.7.1 SUR and 3-SLS as Estimators

Both for the cash crop (26) and the top level system (29) the same parameters occur in several equations which makes a system estimation necessary to impose these parameter restrictions across equations.

The error terms of the estimated levels or level share equations are most likely contemporaneously correlated, because of the interrelatedness of the level determination for the different production activities and due to the data generation process of the independent variables in the algorithm of the SPEL/EU-BS. In this case, the Seemingly Unrelated Regression (SUR) estimator is an efficient estimator and was employed for the cash crop system.

In the case of the top level system, a problem exists concerning the milk quota which was introduced in 1983. It was assumed that sales of milk (“TRAPMILK”) is a good proxi for the quota level after 1983. However, using milk sales as an independent variable before 1983 is not possible, because then it was obviously an endogenous outcome of the producer supply decisions and might yield simultaneous equation bias of the parameter estimates. Hence, 3-Stage Least Squares was applied and the milk sales were instrumented based on the trend for the years before 1983.

4.7.2 Recovering Missing Parameters

Based on linear restrictions, certain parameters had been substituted from the equation, e.g. (compare e.g. equation (23))

(36) ∑∑−

==

=⇔=1

11

0N

iitNt

N

iit ccc

These parameters must be recovered after the estimation. Let Pr denote the vector of estimated parameters and R a matrix which represents the linear relation between the estimated coefficient and the full parameter vector P including the substituted ones. The full vector of parameters together



- 28 -

with its covariances can then be calculated as follows:

(37)( ) ( ) 'RPCOVRPCOV

RPPr

r

=

=

4.7.3 Imposing Curvature Restrictions: Bayesian Approach

Whereas homogeneity in prices is already ensured by the chosen functional form and, symmetry and additivity can be achieved by appropriately restricting the relevant parameters (see equations (21)-(24)), curvature restrictions are more difficult to impose during estimation. As explained above, a necessary and sufficient condition for convexity in gross margins is that the gross margin related part of the B matrix in (18) is positive-semidefinite. DIEWERT & WALES (1987) therefore propose matrix decomposition techniques to ensure positive semi-definiteness of the related submatrix of B. However, these approaches lead to highly non-linear estimation models. In addition, the effect of this restriction on the parameter values cannot be tested easily.

Instead, we employ a Bayesian approach to impose curvature restrictions or to check to what extent the data interpreted through the model without curvature supports the validity of this additional restriction. The general idea behind the Bayesian approach is to combine information on the parameters δ from the model - expressed through the likelihood function of the parameters, ( )YL δ ,

where Y represents the data - with a-priori information on the parameters expressed through a prior density function, p(δ). This combination is done - consistent with probability calculus - by Bayes's Law which implies that

(38) ( ) ( ) ( )YLpYh δδ∝δ

where h(δ|Y) is called the posterior distribution of the parameters δ. It describes all the information available on the parameters. The mean of the posterior distribution usually serves as a point estimate of the parameters which is motivated by minimising a quadratic loss function (see JUDGE et.al. 1988, pp. 135f.).

In our context, the prior distribution is related to the convexity of the revenue functions. Positive-semidefiniteness is here tested by checking positiveness of the eigenvalues of the relevant submatrix of B. This prior information truncates the posterior distribution of the regression coefficients. In order to obtain means of this truncated posterior density, an importance sampling approach is employed. It basically samples from the posterior density of the regression coefficients without curvature imposed (assuming prior ignorance for the covariance matrix of the residuals), calculates eigenvalues of the relevant B-submatrix and accepts all samples with only positive eigenvalues. Coefficient estimates (posterior means) are then calculated from the accepted samples (This description is somewhat simplified, ignoring an adjustment necessary for the fact that sampling from the correct posterior density is not possible). For a detailed description of this approach in the context of Seemingly Unrelated Regression systems we refer to CHALFANT, GREY & WHITE (1991).

Apart from producing coefficient estimates that satisfy curvature restrictions, this procedure also allows to assess to what extent the estimated model supports the correct curvature. Generally, the larger the share of accepted samples the less contradiction between the model and the curvature restrictions exist. In fact, one can infer from the share of accepted samples the probability of the curvature restrictions being satisfied based on the estimated model.



- 29 -

In our application, most of the models violated the curvature restriction severely, so that often not a single sample of coefficients satisfied the restriction. One possibility would be to ignore the problem and use the estimates which violate the curvature restriction. Another possibility is to conclude that the estimation does not make sense from the viewpoint of micro-economic theory and to reject the methodological approach of this study. However, none of these extreme positions were chosen. Instead, we employed two different approaches depending on the estimation results:

1. Only positive own gross-margin elasticities were imposed.

2. A concept of "normalised" eigenvalues to reflect the "degree of curvature violation".

The concept of “normalised” eigenvalues

Let B denote a symmetric N x N matrix of full rank. Each element ei of the N eigenvalues e satisfies the condition that the determinant of a modified matrix B* where ei is subtracted from the diagonal elements from B is zero:

(39) 0

1

111

=−

−−

iNNN

ijj

Ni

ebb

eb

beb

LMM

L

In order for the matrix B to be positive-definite, all eigenvalues must be positive. Hence, the curvature restriction is violated if the smallest one is negative.

Due to the fact that the magnitude of the eigenvalues relates to the magnitude of the diagonal elements of B, any normalisation which seems appropriate for the elements of B may be used for its eigenvalues, too. Analogous to the concept of elasticities, the following concept of “normalised second derivatives” nij is proposed for a matrix of second derivatives B of a function x=f(Y):

(40) yy

x/

yy

xy

x

ybn

iji

iijij ∂

∂∂∂

∂=

∂∂

=

If the factors yx

yi

∂∂

are suitable for a normalisation of B, they may be applied to the eigenvalues,

too. Based on the smallest eigenvalue min(e) and n normalisation factors, we obtain a vector of “normalised curvature violation” e* which are calculated as follows:

(41) yy

x/)emin(e

i

*i ∂

∂=

In order to abstract from the N elements of e*, the mean is used as a measurement and termed “normalised eigenvalue”:

(42) **ne ie=

The effect of the normalisation is shown in the following two tables for the example of a Cobb-Douglas production function. Whereas the eigenvalues clearly depend on the magnitude of the second derivatives (which are in the example a function of y2), the normalised eigenvalue is relatively stable – as we would expect if we take the constant sum of the production elasticities α as an indicator for the curvature violation.



- 30 -

Table 2 Eigenvalues (ei) and “normalised eigenvalue (en)” of second derivatives of a Cobb-

Douglas production function ( ∏=

=n

ii

iyx1

α ) with n=2, y1=1, α1=0.55, α2=0.49 and

increasing y2

Y2 1 2 3 4 5 6 7 8 9 10

E1 -0.447229 -0.374124 -0.691606 -1.788485 -5.614816 -20.14721 -80.07316 -345.9078 -1603.918 -7911.231

E2 0.011886 0.015019 0.023848 0.047014 0.111027 0.304203 0.943224 3.247627 12.23814 49.90545

En 0.042237 0.040139 0.039406 0.039195 0.039141 0.039134 0.039140 0.039149 0.039158 0.039166

Table 3 Eigenvalues (ei) and “normalised eigenvalue” (en) of second derivatives of a Cobb-

Douglas production function ( ∏=

=n

ii

iyx1

α ) with n=2, y1=1, α1=0.80, α2=0.49 and

increasing y2

Y2 1 2 3 4 5 6 7 8 9 10

E1 -0.439889 -0.514726 -1.268130 -4.540720 -20.79785 -114.3511 -726.8849 -5211.951 -41431.44 -360491.2

E2 0.127435 0.162800 0.335960 0.956654 3.462602 15.16595 77.78878 456.4064 3009.639 22001.09

En 0.427067 0.312000 0.280751 0.272408 0.271111 0.271993 0.273434 0.274888 0.276186 0.277294

The normalised eigenvalues for the cash crop systems were normally smaller than the results in Table 2 for the Cobb-Douglas-function with slightly increasing returns of scales. Insofar, we conclude that the curvature for the cash crop is not violated too strong. In case of the top level system, however, the normalised eigenvalues were quite big.

The concept of normalised eigenvalues now allows to restrict the coefficient estimates to a small degree of curvature violation if a full restriction is not feasible. Experiences show that smaller violations are often coupled to smaller magnitudes of absolute cross-gross margin elasticities. Intuitively, we expect those to be smaller than the own gross margin elasticities in absolute terms.

4.7.4 Interpretation of the Results

For most estimation results, tables are presented showing the fit of the individual equations as well as parameter estimates and standard errors. For a better intuitive understanding gross margin elasticities are listed. A closer look reveals that cross gross margin elasticities are often larger than own gross margin elasticities. One may at first glance judge that such elasticities are not plausible.

This intuitive rule may however be misleading due to the aggregation problem in sectoral estimations. In some of our estimation results, cross-elasticities of "rest of cereals" to wheat or barley were relatively strong. After some discussions, we concluded that these results cannot be rejected a priori. In marginal areas, gross margin differences between these low yield cereals and wheat or barley are small and they can be found together in rotations whereas on a major part of the area the difference in gross margins high so that the low yield cereals are excluded from the rotation



- 31 -

(at least under the price and costs relations which prevailed over the estimation period). For the major part of the area, we have hence no cross effects at all, but sharp effects in marginal areas. Under these circumstances, the effect of a change of, for example, the wheat gross margin on the land allocated to other low yield cereals can be much sharper then on the wheat level itself.

The intuition of rather small cross-elasticities is probably also influenced by the idea of constant elasticities. This concept might be defendable if the range of land adjustment is within magnitudes of adjustment observed ex-post and if the products considered are produced on a significant share of total land. Marginal products like rye, oats and other cereals, however, have very small shares compared to, for example, wheat and barley in most European countries, such that a higher percentage reaction to changing gross margins can be expected. The functional form employed in this analysis accommodates for this effect. The elasticities reported are not constant but instead depend on the share of total land of the respective product.

4.7.5 Multicollinearity in the Independent Variables ?

Problems arise concerning the identification of the parameters if the independent variables are collinear. The following table reports correlations between the gross margins divided by the gross margin index (see above) and the trend variable for France (1975-1996). Generally, correlations are relatively small.

This is a somewhat surprising result given that one may expect high correlations both in between prices and in between yields and across the two groups. As Table 5 and Table 6 reveal, the sectoral correlations between yield differences - even inside the cereal complex (activities with the numbers 1-4) - are generally low, although some higher coefficients exist. The same is true for price differences. The correlations for yields and prices are calculated for differences to remove the trend related correlation between the series. The trend effect in the gross margins has been removed by dividing through the gross margin index.

Table 4 Correlation between gross margins divided by gross margin index and trend for the cash crop production activities (France, 1975-1996)

WheatG1/GI

BarleyG2/GI

Other CerealsG3/GI

MaizeG4/GI

PulsesG5/GI

PotatoesG6/GI

OilseedsG7/GI T

G1/GI 1.000000 0.482341 0.363589 0.220840 0.403741 -0.728711 0.005348 -0.488021

G2/GI 0.482341 1.000000 0.496921 0.511919 0.186225 -0.679575 0.294189 0.323942

G3/GI 0.363589 0.496921 1.000000 0.346706 -0.201426 -0.369076 0.079145 0.014602

G4/GI 0.220840 0.511919 0.346706 1.000000 0.407953 -0.728537 0.217018 0.304599

G5/GI 0.403741 0.186225 -0.201426 0.407953 1.000000 -0.650971 0.141826 -0.186835

G6/GI -0.728711 -0.679575 -0.369076 -0.728537 -0.650971 1.000000 -0.433034 -0.011076

G7/GI 0.005348 0.294189 0.079145 0.217018 0.141826 -0.433034 1.000000 0.491247

T -0.488021 0.323942 0.014602 0.304599 -0.186835 -0.011076 0.491247 1.000000



- 32 -

Table 5 Correlation between first differences of yield and trend (France, 1975-1996)

D(Y1) D(Y2) D(Y3) D(Y4) D(Y5) D(Y6) D(Y7) T

D(Y1) 1.000000 0.857349 0.650582 0.023051 0.270959 0.355610 0.534626 -0.056862

D(Y2) 0.857349 1.000000 0.780365 0.082893 0.271938 0.523995 0.625017 -0.023787

D(Y3) 0.650582 0.780365 1.000000 0.493901 0.375419 0.624774 0.562687 0.051090

D(Y4) 0.023051 0.082893 0.493901 1.000000 0.071949 0.551521 0.179128 -0.044381

D(Y5) 0.270959 0.271938 0.375419 0.071949 1.000000 0.613337 0.022832 -0.148113

D(Y6) 0.355610 0.523995 0.624774 0.551521 0.613337 1.000000 0.321331 -0.091392

D(Y7) 0.534626 0.625017 0.562687 0.179128 0.022832 0.321331 1.000000 -0.054977

T -0.056862 -0.023787 0.051090 -0.044381 -0.148113 -0.091392 -0.054977 1.000000

Table 6 Correlation between first differences of prices and trend (France, 1975-1996)

D(P1) D(P2) D(P3) D(P4) D(P5) D(P6) D(P7) T

D(P1) 1.000000 0.868748 0.274271 0.305318 0.196658 0.183109 0.251306 -0.075351

D(P2) 0.868748 1.000000 0.424385 0.380022 0.244411 0.332928 0.326486 -0.123522

D(P3) 0.274271 0.424385 1.000000 0.521558 0.319971 0.379492 -0.049431 -0.146925

D(P4) 0.305318 0.380022 0.521558 1.000000 0.165550 0.107845 -0.150939 -0.206509

D(P5) 0.196658 0.244411 0.319971 0.165550 1.000000 0.865158 0.006120 0.028319

D(P6) 0.183109 0.332928 0.379492 0.107845 0.865158 1.000000 0.211209 0.023455

D(P7) 0.251306 0.326486 -0.049431 -0.150939 0.006120 0.211209 1.000000 -0.213918

T -0.075351 -0.123522 -0.146925 -0.206509 0.028319 0.023455 -0.213918 1.000000

Depending on the expectation model and the respective Member State, the actual correlation between the independent variables varied slightly. Generally, we judged the problem of multi-collinearity as not relevant for the estimation.

4.7.6 R2 as the Measurement of Fit ?

Table 7 below shows twice the fit measured as R2 for the same pure trend based estimation of the shares of wheat, barley, maize, other cereals, oilseeds and pulses for France in the first two columns. However, in the second column, the fit is reported relative to the first differences. Both estimations yield exact the same parameter vector.

First of all, the fit of the shares for all products besides wheat and maize is relatively high. Due to the fact that the trend and a constant are included in our estimation models as well, the use of R² as a measurement of fit might therefore be misleading. A large part of the variance of the dependent variable is already explained by the time variable. If we add gross margins as additional explanatory variables, their contribution to an improvement of the fit measured on the shares can only be relatively small.



- 33 -

The picture is however quite different if we look at the fit in relation to first differences. Not surprising, the trend explains about nothing (apart from maize) of the yearly changes. One may wonder about negative R² in the absence of parameter restrictions. However, subtracting the lagged share on the right hand side is equivalent to adding a new independent with its parameter restricted to unity.

Table 7 Comparison of R² based on shares and on first differences (France, 1979-1996)

Activity R² on shares:

tiii utcbl ++=

R² on first differencesof shares:

tt

iiit

it

i ultcbll +−+=− −− 11

R² on first differencesof shares,

corrected for autocorrelation :

111 arultcbll t

tiii

ti

ti ++−+=− −−

Wheat 6.22E-05 -0.124384 0.251842

Barley 0.907099 -0.773709 0.140476

Other cereals 0.891850 -0.181705 0.234838

Maize 0.111210 0.412577 0.333676

Pulses 0.830428 -1.166582 -0.144117

Potatoes 0.768579 -0.173976 0.343483

Based on the evaluation, we propose to check the contribution of gross margins to the explanation of changes in the dependent variables of our models using at least additionally if not solely R2

related to first differences.

As a further step, an auto-regressive term is added to the trend equation because some of the gross margins models presented below include auto-regressive terms as well. Here, a comparison of the fit of the economic models with the pure time series model is an indicator for the relevance of the additional variables in the economic model.

It should be noted that the model with the auto-regressive term naturally has a better fit across all equations compared to the pure trend model. The three systems above have been estimated using the SUR estimator, but a difference in the parameter compared to OLS occurs in the model, only, where a common autocorrelation coefficient is used.

For the cash crop system where one of the equation must be omitted because the dependent variables represent shares and are therefore linear dependent, it is not possible to estimate separate autocorrelation coefficients in the equations without getting parameter estimates which depend on the omitted equation.



- 34 -

5 Technical Solution

5.1 Data Aggregation and Import into EViews

During the first project phase, technical solutions were tested in order to aggregate production activity related information from the SPEL/EU-Data base, to export the aggregated data to an econometric package and performing there the estimations. Based on the evaluation of the first project phase, the following guide-lines were laid down in co-operation with EUROSTAT:

1. The econometric work will continue to be based on the econometric package EViews. Although other packages could probably be used, there are no imperative reasons to switch in the current project phase. Econometric Views has proven to be an efficient tool, and the developing circle for new programs is short compared to typical large-scale packages as SPSS or SAS. On top, some shortcomings of EViews mentioned in the first report are now healed in the new Version EViews 3.1.

2. The data treatment will be based on FORTRAN where in the first project phase GAMS was employed, a widespread package for economic modelling which is currently not licensed by EUROSTAT. The comparative advantage of GAMS lays in its straightforward way optimisation problems can be formulated and its coupling to a number of well-known solver (e.g. MINOS, CPLEX). Although numerical operations can be performed quickly and defined easily in GAMS, they can naturally be based on other packages, too. The drawback of GAMS are relatively high license costs, and for the project at hand, the need to use - besides existing software from the SPEL project and Eviews, a third software package. Due to the fact that EUROSTAT does not posses a GAMS license, the use of GAMS was terminated for this project in accordance with Mr. G. Weber.

Therefore, in order to substitute the GAMS part, a FORTRAN based solution was chosen, based on the existing Graphical User Interface (GUI) (GREUEL & ZINTL 1995) used by the SPEL and further projects by EuroCARE and the Institute of Agricultural Policy, Bonn. SPEL users are already familiar with the user interface of the new tool, e.g. by having used DAOUT. Additionally, as laid down in the following, the new tool can be used in a much wider context as just the current project.

In order to do the estimation, income indicators and activity levels of some activities from the SPEL/EU-Data base must be aggregated and the result exported in an appropriate format which can be read by EViews, e.g. comma separated. The existing GUI features a spreadsheet-like object named EDTPAC which allows to show a multi-dimensional matrix on screen, turn the dimensions, select specific elements from each dimension and export the result either to the clipboard or to file in different formats. Most users of the SPEL/EU-Data base had already contact via DAOUT with that object. If the aggregated data needed for the estimation would be loaded in, the connection to EViews is solved automatically because the object can write data in CSV-format directly.

5.2 Aggregation over Activities and Products as a More General Task

Although activity levels and income indicators must be aggregated in a flexible way for the current project, only, others users or projects may need information aggregated for activities/products from the SPEL/EU-Data base as well. It was therefore decided to widen the scope for the newly developed FORTRAN program as to allow user defined aggregations concerning activities (and the connected products) of all positions of the SPEL tables.



- 35 -

The task fulfilled by CAPAGT, the new program, are:

• Read in a user set selection of SPEL tables from a table file

• Define the aggregation rules for the activities

• Aggregates the tables

• And put the result in the spreadsheet object EDCPAC

The resulting tool can be characterised as a DAOUT for SPEL tables embedding an aggregation routine working with user defined aggregates. The aggregation algorithm uses the current activity levels, quantities and prices as weights.

CAPAGT features six menus:

1. File<Open, where “Input file (tab)” defines the table file where the data are read from. Typically, that would be the current data base created by the SPEL/EU-BS, the so-called SPEL-SYS.TAB, distributed by EUROSTAT via CD, too.

2. Data<Selection, where the regions, years etc. can be set. In the case of our estimation, data for one Member States (e.g. D) were chosen and the year 1975 up to 1996. Data were annual ones (Periodicity 00) from the SPEL/EU-BS (Sub-region 00, base year NN, type BASB, model area E).

3. Data<Aggregates Act., where each input field defines the name of an aggregate of activities and lists the SPEL activities to be aggregated to it, e.g. CERE SWHE-PARI. The name of the aggregates can be freely chosen by the user, however, no duplicates are allowed.

4. Data<Aggregates pro., where aggregates for all products not implicitly covered by the activity aggregate definition can be set. Usually, this are by-products and derived ones.

5. Data<Aggregates inp., allows the definition of aggregates of inputs, e.g. INPP NITF-PLAP.

6. Data<Aggreg. Modus, defines the aggregation rule:

Keep physical values and activity levels

Convert physical values to constant prices

Convert activity levels to main product

Convert physical values and activity levels

In order to put the results of the aggregation into EViews, the transposing/merging dialogue of the spreadsheet object should be used to move the years in the screen columns and the SPEL-table columns and rows merged together in the screen rows. Afterwards, all time series can be directly exported from the spreadsheet object as a comma separated file (English CSV format). Empty rows should not be exported.

The CSV-file can then be read by the import command of EViews (File>Import>Read Text-Lotus-Excel), Data order: in rows, Number of series: 1200, rows to skip 8. For the rest, default values may be used. EViews will then create more series as needed, named SER01 etc. which can be deleted



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from the EViews workfile.

5.3 Definition of the System to Estimate

First experiences on defining systems to estimate exist already from the first project phase. EViews is generally designed as a window driven system where the user communicates with the program by the mouse and a command line.

In order to define a system of equations, each of these must be usually edited manually in a specific window. The proceeding is naturally error prone. Additionally, EViews does not allow to write equality restrictions on the parameters separately, but forces the user to substitute the left hand side of such a restriction manually in all equations, a difficult task in a complex system estimation.

In the first project phase, the substitution was arranged in an EViews program using the string handling facilities of EViews. The experiences with this kind of macro programming in EViews were however not very promising. The programs are very hard to maintain and any adjustments to other functional forms etc. would be quite a demanding task.

Programmable text editors are much better designed to handle strings. Due to the fact that EViews allows to paste the content of the clipboard in the system definition window, the system can be defined outside in an appropriate editor and copied over the clipboard.

In our case, Kedit for Windows was used, the editor already in use in the SPEL group in Luxembourg. The equations were first entered without any linear restrictions on parameters taken into account. Appropriate replace statements where then defined as KEXX-macros (SYM.KEX and ADDI.KEX). If wished, the gross margin expectation can be estimated simultaneously (NERL.KEX). Due to the fact that the expression tend to grow longer, the file must be opened with the maximum record length “x basic.txt (width 32000” and margins must be adjusted “set margins 1 *” accordingly. After the all the macros had been used, each single equation must be converted in one record “FLOW *” because EViews treats each record as a separate equation. The result may then be copied over the clipboard to EViews.

The handling of linear restrictions of parameter and the missing possibility to write complex system in matrix notation are severe limitations of EViews which are hopefully addressed in future versions. Currently, we would choose another package if we would attack a similar project.

5.4 Technical Integration in SPEL/EU-MFSS

Due to the fact that the general methodological structure – two-stage decision model – was not changed in the current project, the integration of the results in the SPEL/EU-MFSS is straightforward. The estimated elasticities can directly replace the set used so far. Additionally, shift factors for the levels must be introduced based on the estimated parameters. Such shift factors had been partially been included in the past but where based so far on trend analysis of the ex-post development coupled with a careful tuning of the overall model behaviour.

It would be advisable, however, to invest the time to replace the linearisation of elasticities as currently applied in the SPEL/EU-MFSS by the use of the estimated functions directly.

Some minor technical changes in the FORTRAN programs of SPEL/EU-MFSS are necessary in order to account for changes in the expectation model (see above). However, the modules dealing with the expectation model had been already designed in a way which accounted for further



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changes, especially for activity and country specific parameters.

However, the technical integration is surely the easier part of an integration in the context of a complex model as SPEL/EU-MFSS where both the regional components, i.e. the supply models for the Member States, interact which each other and with the demand component. On top, due to its recursive-dynamic character, changes to individual component affect the time path of reactions in the model.

5.5 Conclusions for the Application to Other Member States

Based on the flexible functional form employed and the existing EViews and FORTRAN programs, estimation for a new Member State can be initiated relatively easily. However, the real time-consuming process consists in experimenting with different separability structures and expectation models.

Currently, for the new Member States (Austria, Sweden and Finland) not enough observations are available for estimation purposes. The Member States which joined in the mid eighties, at least the first years in the data base tend to comprise a certain extent of estimated instead of official data and are therefore sometimes doubtful. Here, degrees of freedom problems could also arise if these observations are excluded.



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6 Results

The estimation results presented in this section for different Member States and system levels are usually one set of a considerable (!) amount of results from other specifications, with types of variations explained in earlier sections of this report. They have been selected based on subjective judgement. The main criteria have been the maximum consistency of the estimation results to the underlying theoretical model, the fit of the level share equations in first differences, significance values of gross margin effects, and the plausibility of resulting elasticity estimates.

6.1 Results for Cash Crop Systems

In the following, results will be presented for cash crop systems of France, Italy, Spain and Germany. Without going into detail here, we obtained at least plausible gross margin elasticities for some of the reported cash crop systems. However, the elasticities are generally very unstable regarding the employed expectation model and regarding the in- or exclusion of observations. The probability that curvature restrictions, or even only positive own gross margin elasticities hold are generally very low. Also, the problem of serially autocorrelated errors prevailed in all of the different model specifications explored. We will discuss the results for France in more detail and summarise results for the three remaining countries.

6.1.1 France

In the case of France we experimented longer than in case of the other Member States, i.e. a greater variety of expectation models, separability structures etc. were tested.

Two sets of estimated parameter and elasticities are shown, both based on the same Nerlove like expectation model, however with different Nerlove parameters for cereals. Expected gross margins for the cereal complex were based on price expectation, trend yields and realised costs and premiums (compare equation (34)), whereas naive expectations on the gross margins were used for pulses, potatoes and oilseeds. For pulses and potatoes, the correlation between price and yield is quite high whereas in oilseeds, prices dropped dramatically with the 92 CAP reform so that for these three groups of activities trend yields multiplied with autoregressive price expectations as an indicator for the market income seemed not very realistic. The estimations have been corrected for first order residual autocorrelation, using the standardised procedure in EViews.

Three different sets of estimation results are reported:

• with no inequality restrictions imposed

• with positive own-gross margin elasticities imposed

• with correct curvature imposed.

First, Table 8 below shows the fit of the models without imposing positive own gross margin elasticities or curvature. Based on the explained variance of first differences, there is no obvious reason to pick one of both.



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Table 8 R² squared of first differences of level shares, cash crop system for France(1981-1996), a priori ignorance

Activity Nerlove parameter = 0.3 Nerlove parameter = 0.55

Wheat 0.428646 0.388736

Barley 0.212282 0.222157

Other cereals 0.209197 0.297362

Maize 0.603392 0.536258

Pulses 0.175516 0.085094

Potatoes 0.293864 0.238781

Table 10 below shows the parameter estimates and related test statistics for the first model which yielded more plausible results. Whereas the auto-regressive term, the constants in the level share equations and most of the trend parameters have high t-values, most gross margin related parameters are not significant at the 5% level (Probabilities above 0.05). This is a typical finding for the different cash crop models tested for France and for most specifications for other Member States.

Table 9 shows elasticities based on the estimated parameters of Table 10 below. For these unrestricted estimation results, own gross margin elasticities for barley, other cereals and pulses are negative. In general, the absolute values of the elasticities are rather small. On top, certain cross effects are doubtful, for example wheat reacts stronger to changes of the maize gross margin (-0.12) then to its own (+0.08). Similar examples can be found in the case of pulses and potatoes.

Table 9 Elasticities for the cash crop system, France (1981-1996), Nerlove parameter = 0.3.,

Wheat Barley Other cereals Maize Pulses Potatoes Oilseeds

Wheat 0.075501 -0.015978 0.003705 -0.118805 0.017944 0.039525 -0.001892

Barley -0.061574 -0.016353 0.008505 0.192129 0.047025 -0.079665 -0.090066

Other cereals 0.060062 0.035777 -0.007609 -0.049168 0.030883 0.035749 -0.105695

Maize -0.211572 0.088784 -0.005401 0.113101 0.121246 -0.100289 -0.005869

Pulses 0.085968 0.058459 0.009127 0.326177 -0.006519 0.034650 -0.507862

Potatoes 0.243251 -0.127225 0.013572 -0.346590 0.044512 0.072092 0.100388

Oilseeds -0.003656 -0.045165 -0.012600 -0.006369 -0.204862 0.031523 0.241131

A Bayesian approach was used to impose positive gross margin elasticities. The probability that positive gross margin elasticities hold was 15,5%. The resulting elasticities, presented in Table 11, show quite different magnitudes compared to the elasticities without the inequality constraint imposed.



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Table 10 Parameter estimates and statistics of the cash crop system for France (1981-1996), Nerlove parameter = 0.3

Coefficient Std. Error t-Statistic Probability

Auto-regressive term

A(1) 0.472259 0.108472 4.353737 0.0000

Constants

B(1) 0.399257 0.033217 12.01957 0.0000

B(2) 0.263435 0.021259 12.39189 0.0000

B(3) 0.088177 0.008891 9.917014 0.0000

B(4) 0.170966 0.017672 9.674509 0.0000

B(5) -0.062077 0.029226 -2.124020 0.0373

B(6) 0.020232 0.002068 9.785189 0.0000

Gross margin parameters

B1(1) 0.246692 0.140764 1.752526 0.0842

B1(2) -0.125343 0.084000 -1.492166 0.1403

B1(3) -0.025125 0.030968 -0.811326 0.4200

B1(4) -0.092501 0.042539 -2.174513 0.0331

B1(5) -0.001177 0.011431 -0.102930 0.9183

B2(2) 0.059103 0.059343 0.995960 0.3228

B2(3) 0.022274 0.019134 1.164102 0.2485

B2(4) 0.042709 0.024066 1.774659 0.0804

B2(5) 0.011847 0.006979 1.697533 0.0942

B3(3) 0.002586 0.010860 0.238115 0.8125

B3(4) 0.006192 0.009980 0.620418 0.5371

B3(5) 0.000943 0.002755 0.342210 0.7332

B4(4) 0.059075 0.020628 2.863834 0.0056

B4(5) 0.000308 0.009078 0.033957 0.9730

B5(5) 0.005270 0.006254 0.842609 0.4024

Trend parameters

C(1) 0.001206 0.001706 0.706868 0.4821

C(2) -0.006591 0.001158 -5.688890 0.0000

C(3) -0.002332 0.000477 -4.885228 0.0000

C(4) -0.000961 0.001073 -0.895214 0.3738

C(5) 0.002656 0.000684 3.883823 0.0002

C(6) -0.000326 0.000133 -2.443175 0.0172



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Table 11 Elasticities for the cash crop system, France (1981-1996), Nerlove parameter = 0.3, positive own gross margin elasticities imposed (15,5% probability)


Wheat 0.160067 -0.055713 -0.014177 -0.087202 -0.016722 0.024998 -0.011251

Barley -0.200858 0.107244 0.001719 0.055432 0.100698 -0.051647 -0.012588

Other cereals -0.214153 0.007203 0.101836 0.078466 0.099403 0.020843 -0.093599

Maize -0.163744 0.028871 0.009754 0.106533 0.096822 -0.090400 0.012163

Pulses -0.081098 0.135461 0.031915 0.250071 0.117597 0.022057 -0.476003

Potatoes 0.163270 -0.093564 0.009012 -0.314434 0.029705 0.057535 0.148476

Oilseeds -0.023591 -0.007321 -0.012993 0.013582 -0.205800 0.047667 0.188455

Finally, full curvature is imposed using the Bayesian Approach. The probability that the true parameters are in line with the assumed micro-economic theory is less then 1%. Differences to the two sets above are remarkable (see Table 12) . The absolute magnitudes of the elasticities has considerably increased. It also should be noted that the fit of the land share equations based on the coefficients satisfying curvature restrictions is very weak.

Table 12 Elasticities for the cash crop system, France (1981-1996), Nerlove parameter = 0.3, full curvature restriction imposed (0.6% probability)


Wheat 0.303804 -0.143892 -0.013486 -0.162536 -0.009302 0.030037 -0.004624

Barley -0.528127 0.218418 0.050702 0.330337 0.096808 -0.075822 -0.092316

Other cereals -0.208413 0.213481 0.025246 0.053143 -0.002640 0.104762 -0.185579

Maize -0.329116 0.182245 0.006963 0.359486 0.024767 -0.065279 -0.179066

Pulses 0.475242 -1.347621 0.008729 -0.624938 1.094050 -1.136332 1.530870

Potatoes 0.207396 -0.142640 0.046808 -0.222598 0.153566 0.029238 -0.071769

Oilseeds -0.006276 -0.034134 -0.016297 -0.120012 -0.040662 -0.014106 0.231486

Alternative results with a slightly different expectation model

The following four tables are not commented on in detail. They underline the importance of the expectation model for the parameter estimates. The only difference to the last four tables is a change of the Nerlove parameter for the price expectation in cereals from 0.3 to 0.55. As shown above, the fit of the two models is comparable. Concerning the t-values of the parameters they differ, but none of the two models is definitively better than the other.

Nevertheless, the results are quite different concerning the magnitude of the individual parameters, the resulting elasticities as well as concerning the stability of individual parameters. Note especially that the gross margin parameters show totally different point estimates.



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Table 13 Parameter estimates and statistics of the cash crop system for France (1981-1996), Nerlove parameter 0.55/1

Coefficient Std. Error t-Statistic Probability


A(1) 0.471816 0.114038 4.137355 0.0001

Constants

B(1) 0.439787 0.022135 19.86863 0.0000

B(2) 0.231287 0.016419 14.08643 0.0000

B(3) 0.090618 0.007409 12.23011 0.0000

B(4) 0.161246 0.016961 9.506808 0.0000

B(5) -0.050238 0.028131 -1.785879 0.0786

B(6) 0.020598 0.002179 9.451893 0.0000


B1(1) 0.028067 0.083865 0.334672 0.7389

B1(2) 0.040127 0.050807 0.789790 0.4324

B1(3) -0.029042 0.022777 -1.275009 0.2066

B1(4) -0.034489 0.025906 -1.331324 0.1875

B1(5) 0.000590 0.010347 0.057065 0.9547

B2(2) -0.043879 0.040548 -1.082167 0.2830

B2(3) 0.005770 0.017700 0.326010 0.7454

B2(4) -0.004095 0.014543 -0.281577 0.7791

B2(5) 0.008099 0.006692 1.210311 0.2303

B3(3) 0.016831 0.013911 1.209886 0.2305

B3(4) 0.008487 0.007725 1.098642 0.2758

B3(5) 0.001205 0.003474 0.347033 0.7296

B4(4) 0.041580 0.017862 2.327863 0.0229

B4(5) -0.003175 0.009247 -0.343349 0.7324

B5(5) 0.005666 0.006221 0.910791 0.3656

Trend parameters

C(1) -0.000678 0.001273 -0.532472 0.5961

C(2) -0.005079 0.001003 -5.066276 0.0000

C(3) -0.002420 0.000424 -5.713482 0.0000

C(4) -0.000380 0.001055 -0.360521 0.7196

C(5) 0.003197 0.000702 4.555874 0.0000

C(6) -0.000359 0.000139 -2.585354 0.0119



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Table 14 Elasticities for the cash crop system, France (1981-1996), Nerlove parameter = 0.55


Wheat 0.058956 0.009564 -0.009592 -0.053825 -0.004171 0.028083 -0.029014

Barley 0.035745 -0.065736 0.021956 -0.012786 0.099534 -0.039182 -0.039531

Other cereals -0.154647 0.094712 0.026772 0.048444 0.014705 0.034115 -0.064102

Maize -0.094693 -0.006019 0.005286 0.061463 0.069609 -0.075430 0.039784

Pulses -0.017732 0.113220 0.003878 0.168212 0.196217 -0.029810 -0.433986

Potatoes 0.193047 -0.072067 0.014546 -0.294739 -0.048201 0.123128 0.084286

Oilseeds -0.056187 -0.020483 -0.007700 0.043792 -0.197687 0.023744 0.214520

Table 15 Elasticities for the cash crop system, France (1981-1996), Nerlove parameter = 0.55, positive own gross margin elasticities imposed (5,3% probability)


Wheat 0.078065 -0.003196 -0.017238 -0.041733 -0.011014 0.015005 -0.019889

Barley -0.011585 0.047772 -0.023965 -0.012325 0.066555 -0.031885 -0.034567

Other cereals -0.266029 -0.102049 0.236808 0.036261 0.138210 0.120672 -0.163873

Maize -0.076028 -0.006195 0.004281 0.048243 0.054372 -0.060685 0.036013

Pulses -0.050252 0.083788 0.040861 0.136175 0.180495 0.005237 -0.396303

Potatoes 0.099176 -0.058149 0.051681 -0.220170 0.007586 0.115968 0.003907

Oilseeds -0.041558 -0.019930 -0.022188 0.041306 -0.181495 0.001235 0.222628

Table 16 Elasticities for the cash crop system, France (1981-1996), Nerlove parameter = 0.55, full curvature restrictions imposed (0.2% probability)


Wheat 0.136009 -0.019737 -0.015712 -0.053570 -0.048756 0.046650 -0.044883

Barley -0.070085 0.116349 -0.038886 0.012232 0.046676 -0.024241 -0.042046

Other cereals -0.243910 -0.169994 0.230690 0.047322 0.183430 0.048541 -0.096079

Maize -0.089472 0.005753 0.005092 0.090459 0.056563 -0.064815 -0.003580

Pulses -0.239853 0.064664 0.058130 0.166602 0.246413 -0.092714 -0.203242

Potatoes 0.326566 -0.047788 0.021890 -0.271663 -0.131932 0.237832 -0.134906

Oilseeds -0.083658 -0.022070 -0.011536 -0.003995 -0.077006 -0.035920 0.234187



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6.1.2 Italy

As mentioned above, the separability structure in the cereal complex differs from the models for other Member States: durum wheat was treated separately from soft wheat, and barley was added to other cereals. Results presented here are based on gross margin expectations with trend yields and a Nerlove based price expectation with five lags and a Nerlove parameter of 0.4. Again, the first order autocorrelation problem has been corrected. The estimated autocorrelation coefficient is 0.617298 (t-value 6.907884). As Table 17 shows, the correction rendered satisfactory Durbin Watson statistics (the absence of first order serial correlation cannot be rejected for all equations). The fit for all equations measured as R2 on the level shares is higher than 60% for all activities and around 90% for four out of six estimated equations

Table 17 R2 and Durbin-Watson Statistic for Cash crop system in Italy

R2 Durbin-Watson

Soft wheat 0.974656 1.604675

Durum wheat 0.610073 1.827381

Other cereals 0.871921 1.812236

Maize 0.632698 1.616789

Pulses 0.898952 2.006958

Potatoes 0.862532 1.961331

Table 18 below shows the elasticities for the unrestricted system. For pulses and potatoes, negative own gross margin elasticities were estimated, the Bayesian approach revealed that these elasticities are quite stable (see Table 19). The high own gross margin elasticity of soft wheat compared to other elasticities in the cereal complex is surprising. Is was not possible to draw any sample if full curvature conditions were imposed.

Table 18 Elasticities, cash crop system Italy

Soft wheat Durum wheat Other cereals Maize Pulses Potatoes Oilseeds

Soft wheat 1.047603 -0.531128 -0.124912 -0.116527 -0.135658 -0.052569 -0.086810

Durum wheat -0.330722 0.209414 0.015220 -0.010031 0.060036 -0.005539 0.061622

Other cereals -0.382511 0.074850 0.033842 0.325552 -0.022149 -0.129482 0.099900

Maize -0.067904 -0.009387 0.061951 0.045001 0.033206 0.095595 -0.158462

Pulses -0.860038 0.611250 -0.045856 0.361263 -0.201181 -0.199996 0.334559

Potatoes -0.097333 -0.016472 -0.078289 0.303739 -0.058409 -0.293616 0.240380

Oilseeds -0.102282 0.116602 0.038437 -0.320398 0.062177 0.152967 0.052497



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Table 19 Elasticities, cash crop system Italy, Positive own gross margin elasticities imposed (2,3% probability)

Soft wheat Durum wheat Other cereals Maize Pulses Potatoes Oilseeds

Soft wheat 1.392400 -0.501863 -0.181102 -0.319196 -0.363249 0.075186 -0.102177

Durum wheat -0.302937 0.160037 0.035939 -0.021081 0.071393 0.024539 0.032109

Other cereals -0.555424 0.182602 0.063918 0.281638 -0.033036 -0.074364 0.134665

Maize -0.182483 -0.019966 0.052500 0.073394 0.218960 -0.015445 -0.126959

Pulses -0.785960 0.255910 -0.023307 0.828693 0.098796 -0.434806 0.060673

Potatoes 0.128178 0.069305 -0.041337 -0.046058 -0.342590 0.048579 0.183922

Oilseeds -0.175629 0.091433 0.075474 -0.381716 0.048200 0.185439 0.156798

6.1.3 Spain

The separability structure for Spain is identical to the system estimated for France and Germany: wheat (soft and durum), barley, maize, Other cereals (oats, rye and other cereals according to SPEL definition), pulses, potatoes, oilseeds. Gross margin expectations of the results presented here were based on trend yields and a Nerlove price expectation with five lags and a Nerlove parameter of 0.55. Again, the first order autocorrelation problem has been corrected. The estimated autocorrelation coefficient is 0.774227 (t-value 9.458053). As the Durbin-Watson statistics in Table 20 below show, the correction could only partially heal the problem. The fit of the system, especially for maize, is not really convincing and worse than in the case of France and Italy.

Table 20 R2 and Durbin-Watson Statistic for cash crop system Spain

R2 Durbin-Watson

Soft wheat 0.848524 2.074199

Durum wheat 0.698527 2.153458

Other cereals 0.670548 2.007820

Maize 0.457756 1.933596

Pulses 0.672121 0.656526

Potatoes 0.849514 3.024312

Table 21 below shows the elasticities for the unrestricted system. The only negative own-gross margin elasticity occurs for other cereals. Compared to Italy, the magnitude of the elasticities is quite small, some cross relations (e.g. between wheat and oilseeds) are surely doubtful.



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Table 21 Elasticities, cash crop system Spain


Wheat 0.149265 -0.095056 -0.008993 -0.119961 -0.055112 -0.002053 0.131910

Barley -0.090478 0.042640 0.016846 0.074563 -0.005913 0.012765 -0.050423

Other cereals -0.042429 0.083502 -0.003748 0.035911 0.095491 0.027626 -0.196352

Maize -0.320201 0.209095 0.020316 0.158822 0.281512 -0.028569 -0.320974

Pulses -0.117880 -0.013287 0.043290 0.225583 0.049292 -0.153464 -0.033533

Potatoes -0.006109 0.039910 0.017425 -0.031852 -0.213517 0.205363 -0.011221

Oilseeds 0.171433 -0.068847 -0.054085 -0.156279 -0.020375 -0.004900 0.133055

Imposing positive own gross margin elasticities with the Bayesian approach (restriction holds with probability 14.1%) increased the magnitude of the elasticities, especially for the own gross margin elasticities, compared to the unrestricted set results. The hardly plausible positive cross elasticities between oilseeds and wheat remain nearly unchanged.

Table 22 Elasticities, cash crop system Spain, Positive own gross margin elasticities imposed (14,1% probability)


Wheat 0.376743 -0.218881 0.011116 -0.137650 -0.145441 -0.020967 0.135080

Barley -0.219289 0.141104 -0.023523 0.086835 0.052036 0.028796 -0.065959

Other cereals 0.053173 -0.112312 0.147559 0.014061 0.045513 -0.022447 -0.125546

Maize -0.377802 0.237889 0.008068 0.149682 0.286294 -0.017710 -0.286421

Pulses -0.297179 0.106128 0.019441 0.213136 0.157179 -0.123409 -0.075296

Potatoes -0.063613 0.087203 -0.014237 -0.019576 -0.183240 0.197570 -0.004107

Oilseeds 0.188925 -0.092079 -0.036708 -0.145954 -0.051539 -0.001893 0.139249

Nearly full curvature (normalised eigenvalue ≤ -107) was fulfilled with a probability of about 13,6% (see Table 23 below). Some of the own gross margin elasticities are smaller compared to the set above, but most cross effects are considerably reduced compared to the unrestricted results (including the ones between wheat and oilseeds).



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Table 23 Elasticities, cash crop system Spain, Positive own gross margin elasticities and nearly full curvature imposed (13,6% probability)


Wheat 0.276996 -0.144275 0.024900 -0.159518 -0.056929 0.026063 0.032763

Barley -0.145724 0.118884 -0.022241 0.111001 0.033234 0.021482 -0.116636

Other cereals 0.114664 -0.101403 0.105030 0.011157 -0.036308 0.016709 -0.109850

Maize -0.450495 0.310361 0.006842 0.183473 0.280782 0.044308 -0.375270

Pulses -0.130929 0.075674 -0.018133 0.228661 0.040438 -0.092521 -0.103190

Potatoes 0.078141 0.063766 0.010879 0.047039 -0.120615 0.168417 -0.247628

Oilseeds 0.039575 -0.139486 -0.028814 -0.160510 -0.054197 -0.099764 0.443195

6.1.4 Germany

The separability structure for Germany is identical to the system estimated for France and Spain: wheat(soft and durum), barley, maize, Other cereals (oats, rye and other cereals according to SPEL definition), pulses, potatoes, oilseeds. Gross margin expectations for the presented results were based on trend yields, intervention prices (BMELF, Agrarberichte, different years) for cereals and Nerlove price expectations with five lags and a Nerlove parameter of 0.55 for the other activities.

The re-unification led to high instability and drastic reactions in the former GDR especially in the years 1990 and 1991, which were therefore excluded from the sample used for estimation. This implies that sectoral reactions before and after the unification remained the same - with the exception of an adjustment period of 2 years.

Again, the first order autocorrelation problem has been corrected. The estimated autocorrelation coefficient is 0.774227 (t-value 10.38284). As Table 24 below shows, the correction rendered satisfactory Durbin Watson statistics (the absence of first order serial correlation cannot be rejected for all equations). The R2's of the first difference equations are quite high compared to other results obtained for different Member States.

Table 24 R2 and Durbin-Watson Statistic for cash crop system, Germany

R2 on first differences Durbin-Watson Statistic

Soft wheat 0.303012 2.248365

Durum wheat 0.530027 2.262298

Other cereals 0.570671 1.870260

Maize 0.471584 2.164181

Pulses 0.224063 1.490449

Potatoes 0.354785 2.058989

Table 25 below shows the elasticities for the unrestricted system. All own gross margin elasticities have the correct sign, but the magnitude and sign of certain cross-relations - e.g. between wheat, barley and other cereals - is doubtful. Especially cross-elasticities in the cereals complex are very



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high and exceed in many cases the own gross margin effect.

Table 25 Elasticities, cash crop system Germany


Wheat 0.346661 -0.408151 0.223257 -0.144014 0.007346 -0.027841 0.002742

Barley -0.563279 0.189052 -0.202463 0.547253 0.035711 -0.014461 0.008187

Other cereals 0.566442 -0.372215 0.527157 -0.656772 -0.049046 0.066829 -0.082395

Maize -0.965506 2.658481 -1.735450 0.029271 0.023134 -0.047609 0.037679

Pulses 0.099222 0.349512 -0.261107 0.046610 0.115500 -0.217160 -0.132576

Potatoes -0.077392 -0.029127 0.073221 -0.019741 -0.044692 0.075848 0.021884

Oilseeds 0.011476 0.024827 -0.135902 0.023520 -0.041075 0.032944 0.084210

Own gross margin elasticities were positive using the Bayesian approach with probability 48.8% (see Table 26 below). Compared to the unrestricted set, the magnitude of the elasticities is generally increasing, especially for the own gross margin elasticities. However, the doubtful cross effects increased in magnitude as well.

Table 26 Elasticities, cash crop system Germany, Positive own gross margin elasticities imposed (48,8% probability)


Wheat 0.403702 -0.586584 0.353129 -0.168795 0.035922 -0.034717 -0.002657

Barley -0.779717 0.545114 -0.450261 0.682160 -0.015801 0.005332 0.013172

Other cereals 0.940002 -0.901681 0.941769 -0.918532 -0.055391 0.090594 -0.096761

Maize -1.035700 3.148864 -2.117256 0.046892 0.053568 -0.123671 0.027302

Pulses 0.565271 -0.187053 -0.327449 0.137382 0.072938 -0.278089 0.017000

Potatoes -0.090300 0.010433 0.088523 -0.052426 -0.045966 0.082622 0.007114

Oilseeds -0.011309 0.042171 -0.154695 0.018936 0.004598 0.011639 0.088659

Full curvature of the underlying revenue function holds with probability of about 4% (see Table 27 below). The overall change in the magnitude of the elasticities is relatively small compared to the two sets above including the rather implausible cross elasticities.



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Table 27 Elasticities, cash crop system Germany, Positive own gross margin elasticities and full curvature imposed (4,2% probability)


Wheat 0.396691 -0.495740 0.294538 -0.188002 0.007821 -0.019238 0.003930

Barley -0.668131 0.276379 -0.275286 0.631479 0.015606 0.000834 0.019119

Other cereals 0.758178 -0.525784 0.668154 -0.840949 -0.022846 0.057083 -0.093836

Maize -1.127223 2.809305 -1.958785 0.322610 0.014482 -0.099302 0.038913

Pulses -1.154637 -1.709400 1.310258 -0.356587 0.755241 0.495004 0.660121

Potatoes -0.056088 0.001805 0.064653 -0.048286 -0.009776 0.044528 0.003163

Oilseeds 0.015031 0.054259 -0.139432 0.024824 -0.017103 0.004150 0.058271

Generally, the employment of intervention prices as expected prices for cereals yield estimation results which comply comparatively close to the full set of restrictions of the underlying theoretical model. This is true compared to other specifications for Germany as well as compared to specifications tested for other Member States. Together with the relatively good fit of the level share equations and the comparatively (!) high t-values of the estimated gross margin parameters (not reported here), this might indicate the usefulness of politically administered prices for the formulation of expected gross margins in our model context.

6.2 Results for Top Level Systems

6.2.1 France

Results for the top level system are presented for France first. The expectation is based on a Nerlove based price expectation with five lags (Nerlove parameter = 0.35) and trend yields. As explained above, the activity level of laying hens is defined as the weight of the eggs produced and the gross margin expressed per output unit. Consequently, the yield is set to unity and the expectation model works on the gross margin per output unit.

Table 28 below shows that estimates of the autocorrelation coefficient and most of the constants have low standard errors. The gross-margin parameters on the diagonal have the expected positive sign and relatively high t-values with the exception of pork (BT4(4)). Some of the cross parameters, however, show low t-values. In opposite to the cash-crop systems, the trend parameters show high standard errors, partially due to collinearity with quotas and the land variables.

Some of the fixed factor effects (1=arable land, 2=gras land, 3=sugar beet quota, 4=milk) had been excluded due to very high standard errors and plausibility reasons. Contrary to the gross margin parameter which enter all equations and are connected via linear restrictions, the fixed factor effects occur without any restriction in the individual equations and can therefore be easily excluded.



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Table 28 Parameter estimates and statistics for top-level system France

Coefficients Parameter estimate Standard error t-value Probability


ARX(1) 0.464646 0.098967 4.694948 0.0000

Constants

BT(1) -7348.771 3048.944 -2.410268 0.0187

BT(2) 8030.742 5013.058 1.601965 0.1139

BT(3) -25069.93 10948.52 -2.289801 0.0252

BT(4) 9930.522 9086.047 1.092942 0.2783

BT(5) 581.4667 150.2503 3.869987 0.0002

BT(6) 1497.635 794.7657 1.884373 0.0639

BT(7) 3835.742 23710.97 0.161771 0.8720


BT1(1) 1679.670 787.0189 2.134218 0.0365

BT1(2) -110.4954 388.2960 -0.284565 0.7769

BT1(3) 2910.364 895.5981 3.249632 0.0018

BT1(4) -1564.375 2733.573 -0.572282 0.5690

BT1(5) -485.6847 181.0874 -2.682046 0.0092

BT1(6) -301.1225 1077.495 -0.279465 0.7807

BT2(2) 916.8769 365.4424 2.508951 0.0145

BT2(3) -2157.874 677.1856 -3.186533 0.0022

BT2(4) 589.3978 1777.316 0.331622 0.7412

BT2(5) 61.77397 126.5655 0.488079 0.6271

BT2(6) 292.5834 897.5344 0.325986 0.7455

BT3(3) 5058.868 1961.125 2.579575 0.0121

BT3(4) 5476.601 3675.058 1.490208 0.1409

BT3(5) -630.6633 328.6763 -1.918797 0.0593

BT3(6) 1519.688 2197.238 0.691635 0.4916

BT4(4) 164.2271 944.5849 0.173862 0.8625

BT4(5) -1014.007 1015.865 -0.998170 0.3218

BT4(6) -7916.396 5562.297 -1.423224 0.1593

BT5(5) 139.0850 93.40289 1.489087 0.1412

BT5(6) 1581.494 645.0366 2.451789 0.0168



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Coefficients Parameter estimate Standard error t-value Probability

BT6(6) 75697.96 17054.38 4.438622 0.0000

Trend effects

CT(1) 154.9501 25.07104 6.180439 0.0000

CT(2) 13.26104 61.17647 0.216767 0.8290

CT(3) 334.8944 129.6421 2.583223 0.0120

CT(4) 361.5059 118.0839 3.061432 0.0032

CT(5) 19.06714 6.918731 2.755872 0.0075

CT(6) -41.46666 41.62461 -0.996205 0.3227

CT(7) 21.01292 292.7941 0.071767 0.9430

Fix factor effects

FT1(1) 1.009293 0.177998 5.670245 0.0000

FT1(3) 0.003736 0.003390 1.102041 0.2744

FT2(2) -0.554691 0.372271 -1.490020 0.1409

FT2(4) 0.062163 0.047155 1.318270 0.1919

FT3(2) 1.790846 0.815674 2.195540 0.0316

FT3(4) 0.240863 0.095766 2.515124 0.0143

FT4(1) 0.768498 0.412897 1.861234 0.0671

FT4(4) -0.076743 0.193485 -0.396635 0.6929

FT7(2) 0.954178 1.714971 0.556381 0.5798

The fit of the system (Table 29 below) and the Durbin-Watson test statistic are reported in the next table. Both the gross margin and the eggs production show some curious peeks which cannot be explained by the model (and not changed by excluding specific observations), so that the R2 of the eggs equation has a negative sign.

Table 29 R squared and Durbin-Watson Statistic for Top level system France

R2 Durbin-Watson

Cash crops 0.979836 1.917879

Other cows 0.983493 2.781821

Beef 0.927615 2.201191

Pork 0.961058 1.652059

Poultry 0.965131 0.991094

Eggs -19.63944 1.552824

Sheep and goat 0.709139 2.094333

Table 30 below shows the elasticities based on the parameter estimates presented above. All own



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gross margin elasticities are positive, however, some of the cross effects are higher than the diagonal ones. The magnitude of the elasticities is relatively small.

Table 30 Elasticities, top level system France

Cash crops Other cows Beef Pork Poultry Eggs Sheep & goat

Cash crops 0.089004 0.000709 0.035670 -0.001343 -0.014767 -2.28E-06 -0.001955

Other cows 0.008155 0.094609 -0.171050 0.002550 0.020040 2.52E-05 0.003777

Beef 0.213773 -0.089122 0.151264 0.009066 -0.061174 5.03E-05 -0.036893

Pork -0.046013 0.007597 0.051829 9.37E-05 -0.027916 -8.01E-05 0.004052

Poultry -0.644306 0.076019 -0.445374 -0.035550 0.326101 0.001127 0.027815

Eggs -0.489766 0.470026 1.801261 -0.501963 5.540878 0.094805 -8.210457

Sheep and goat -0.087240 0.014651 -0.274667 0.005277 0.028444 -0.001707 0.178942

Table 31 below shows elasticity estimates with positive diagonal elements imposed. The overall effect of the restriction compared to the unrestricted results above is relatively small.

Table 31 Elasticities, top level system France, positive own gross margin elasticities imposed (22,2% probability)


Cash crops 0.084993 -0.005087 0.043509 -0.004213 -0.010810 6.51E-06 0.002392

Other cows -0.067553 0.118249 -0.219916 0.002796 0.028230 5.03E-05 0.008049

Beef 0.224485 -0.085441 0.163877 0.001619 -0.052170 8.88E-05 -0.029769

Pork -0.167606 0.008375 0.012481 0.000320 0.018501 -0.000113 0.014576

Poultry -0.382482 0.075212 -0.357765 0.016456 0.233178 0.000747 -0.050399

Eggs 0.266871 0.155376 0.705507 -0.116638 0.865791 0.020347 -1.789280

Sheep and goat 0.087027 0.022051 -0.209912 0.013331 -0.051824 -0.001588 0.141148

The curvature violation of the top level systems were even more severe than in case of the cash crop system. Therefore, full curvature restriction or even nearly full curvature restriction (based on normalised eigenvalues) could not be imposed with the Bayesian approach.

6.2.2 Italy

The expectation model underlying the presented results for Italy is based on a Nerlove price expectation with five lags (Nerlove parameter = 0.4) and trend yields. The fit of the system and the Durbin-Watson test statistic are reported in the Table 32 below. Compared to France, the fit of the equations is lower and the Durbin-Watson statistics are not satisfying.



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Table 32 R2 and Durbin-Watson Statistic for Top level system Italy

R2 Durbin-Watson

Cash crops 0.871009 1.121477

Other cows 0.100693 1.358205

Beef 0.271002 1.471532

Pork 0.888282 1.947132

Poultry 0.354942 1.212804

Eggs -12.52644 1.592055

Sheep and goat 0.744293 1.913479

Table 33 below shows that most parameters have a higher standard error compared to the results for France. Especially the gross margin effects have low t-values. Four out of six directly estimated own gross margin parameters have a negative sign. Experimenting with different expectation models which usually lead to sometimes drastic changes in the parameter estimates, however, did not produce any more plausible results. The same fixed factor effects as for France (1=arable land, 2=gras land, 3=sugar beet quota, 4=milk) had been excluded.

Table 33 Parameter estimates and statistics for top-level system Italy

Parameter estimate Standard error t-value Probability


ARX(1) 0.150751 0.133812 1.126590 0.2639

Constans

BT(1) -2544.976 1322.214 -1.924783 0.0585

BT(2) 778.8882 930.9932 0.836621 0.4058

BT(3) 5902.723 2416.600 2.442574 0.0172

BT(4) 34937.59 5238.442 6.669462 0.0000

BT(5) 50.08182 254.3081 0.196934 0.8445

BT(6) -21.68069 699.4163 -0.030998 0.9754

BT(7) -6350.536 5952.117 -1.066937 0.2898

Gross margin effects

BT1(1) -8.76E-05 0.003182 -0.027533 0.9781

BT1(2) -0.498988 0.316117 -1.578492 0.1192

BT1(3) -0.075108 0.944463 -0.079525 0.9369

BT1(4) -1.752816 1.410272 -1.242892 0.2182

BT1(5) 0.236704 0.394343 0.600248 0.5504

BT1(6) -0.103185 0.731601 -0.141039 0.8883

BT2(2) 49.05037 124.7771 0.393104 0.6955



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BT2(3) 601.4435 217.9838 2.759120 0.0075

BT2(4) 272.1511 595.9058 0.456702 0.6494

BT2(5) -115.8246 70.58882 -1.640834 0.1055

BT2(6) -49.39628 328.8624 -0.150203 0.8811

BT3(3) -268.8008 758.4830 -0.354393 0.7242

BT3(4) 5768.887 1253.478 4.602304 0.0000

BT3(5) -375.7400 200.8998 -1.870286 0.0658

BT3(6) 1653.889 668.5347 2.473902 0.0159

BT4(4) -970.5303 678.9081 -1.429546 0.1575

BT4(5) -1319.234 334.4841 -3.944087 0.0002

BT4(6) 2882.933 4764.601 0.605073 0.5472

BT5(5) 208.9970 99.21331 2.106542 0.0389

BT5(6) -518.5697 325.2060 -1.594588 0.1155

BT6(6) 908.8860 10891.03 0.083453 0.9337

Trend parameters

CT(1) 18.08869 8.873235 2.038567 0.0454

CT(2) -15.71336 10.55948 -1.488081 0.1414

CT(3) -36.68690 27.88778 -1.315519 0.1928

CT(4) 87.79670 38.82951 2.261082 0.0270

CT(5) 12.03907 5.834533 2.063415 0.0430

CT(6) 2.853208 24.41047 0.116885 0.9073

CT(7) 281.0880 57.93177 4.852053 0.0000

Fix factor effects

FT1(1) 0.942061 0.157130 5.995408 0.0000

FT1(3) 0.002144 0.004706 0.455522 0.6502

FT2(2) -0.091037 0.158463 -0.574500 0.5676

FT2(4) 0.051936 0.035875 1.447683 0.1524

FT3(2) -0.137370 0.412530 -0.332995 0.7402

FT3(4) -0.010185 0.094999 -0.107217 0.9149

FT4(1) -2.943834 0.587007 -5.014989 0.0000

FT4(4) -0.160651 0.177948 -0.902794 0.3699

FT7(2) 4.317558 1.072420 4.025995 0.0001



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Table 34 below shows the elasticities based on the parameter estimates presented above. Three own gross margin elasticities have a negative sign. Given this fundamental implausibility of the results, the further curious magnitudes of some of the cross-elasticities are not surprising.

Table 34 Elasticities, top level system Italy


Cash crops 0.040556 0.001816 0.018253 0.005058 -0.028596 2.76E-05 -0.007425

Other cows 0.052579 0.040020 0.415144 0.036606 -0.512006 -5.74E-05 -0.081991

Beef 0.085251 0.066980 -0.009611 0.103621 -0.220026 0.000317 -0.109572

Pork 0.043079 0.010770 0.188961 -0.005645 -0.265263 0.000184 -0.033119

Poultry -0.129500 -0.080100 -0.213347 -0.141048 0.708421 -0.000569 0.183781

Eggs -0.358682 0.025757 -0.881280 -0.281097 1.632237 -0.000927 0.388282

Sheep and goat -0.038922 -0.014847 -0.122976 -0.020384 0.212721 -0.000157 0.043980

Given the results above, it is not surprising that positive own gross margin elasticities hold only with 0.4% probability. The result is reported here solely for completeness. Any interpretation due to the strong rejection of the restriction by the model is hardly useful.

Table 35 Elasticities, top level system Italy, positive own gross-margin elasticities imposed (0.4% probability)


Cash crops 0.056774 -0.001364 0.024750 0.005633 -0.037928 9.58E-06 -0.006327

Other cows -0.037434 0.123176 0.560607 -0.057347 -0.447713 3.41E-05 -0.050078

Beef 0.112634 0.092957 0.034332 0.089666 -0.334228 0.000301 -0.103555

Pork 0.049602 -0.018400 0.173502 0.000655 -0.240228 0.000214 -0.034766

Poultry -0.231939 -0.099756 -0.449113 -0.166824 1.300880 -0.000832 0.247767

Eggs -0.398001 -0.051670 -2.746278 -1.011530 5.651904 0.025642 -0.889029

Sheep and goat -0.032345 -0.009328 -0.116323 -0.020182 0.207121 0.000109 0.021514

6.2.3 Spain

Due to the disastrous results for Italy as a Mediterranean Member State, we took another look at the top level system in Spain. The expectation model is based on a Nerlove based price expectation with five lags (Nerlove parameter = 0.55) and trend yields. For this system results, expectation models based directly on gross margins or for other Nerlove weights between 0.35 and 0.7 for price expectations yielded similar results.

The fit of the system and the Durbin-Watson test statistic are reported in the Table 36 below. Again, the equation for eggs has a negative R2. Given the Durbin-Watson coefficients, first order autocorrelation seems to be sufficiently addressed by the employed correction procedure.



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Table 36 R2 and Durbin-Watson Statistic for Top level system Spain

R2 Durbin-Watson

Cash crops 0.950059 2.463513

Other cows 0.871727 1.947356

Beef 0.054736 1.912490

Pork 0.967261 2.345214

Poultry 0.342702 2.356475

Eggs -12.48646 2.409262

Sheep and goat 0.938101 1.603650

Table 38 below shows that most parameters have a again higher standard error compared to the results for France. Especially the gross margin effects have low t-values. One out of six directly estimated own gross margin parameters has a negative sign. As for France, some of the fixed factor effects (1=arable land, 2=gras land, 3=sugar beet quota, 4=milk) had been excluded due to very high standard error and plausibility reasons.

Table 37 below shows the elasticities based on the parameter estimates presented in Table 38 below. Two own gross margin elasticities have a negative sign. Some cross relations are quite strong compared to the own gross margin effect. Overall, as for the the other two top level system presented above, gross margin elasticities show rather small magnitudes.

Table 37 Elasticities, top level system Spain


Cash crops 0.009011 -0.000388 0.000703 0.001031 -0.002740 2.09E-05 -0.002559

Other cows -0.022509 0.170566 0.086913 -0.089971 -0.115075 0.000826 0.009366

Beef 0.275527 0.586986 0.311672 0.211416 -1.094265 0.003002 -0.555272

Pork 0.007923 -0.011910 0.004144 -0.000421 -0.001812 0.000110 -0.006796

Poultry -0.023424 -0.016954 -0.023870 -0.002017 0.081279 -0.000276 0.026007

Eggs -0.094487 -0.064206 -0.034569 -0.064711 0.145913 -0.001847 0.222363

Sheep and goat -0.004929 0.000311 -0.002729 -0.001704 0.005859 -9.49E-05 0.009287



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Table 38 Parameter estimates and statistics for top-level system Spain



ARX(1) 1.110790 0.080565 13.78753 0.0000

Constants

BT(1) -1817.824 1414.969 -1.284709 0.2033

BT(2) 1623.092 2173.717 0.746690 0.4579

BT(3) 6022.324 1743.542 3.454074 0.0010

BT(4) 2476.199 3853.874 0.642522 0.5227

BT(5) 483.6536 368.4128 1.312804 0.1937

BT(6) 817.8059 1149.827 0.711243 0.4794

BT(7) 4224.510 12099.37 0.349151 0.7281


BT1(1) 0.024648 0.008688 2.837043 0.0060

BT1(2) -0.400099 0.470781 -0.849861 0.3984

BT1(3) -1.123734 0.483620 -2.323589 0.0232

BT1(4) 0.792347 1.375018 0.576245 0.5664

BT1(5) -0.177787 0.398306 -0.446357 0.6568

BT1(6) 0.594414 1.023064 0.581013 0.5632

BT2(2) 108.0171 90.82114 1.189338 0.2385

BT2(3) 74.49012 75.25121 0.989886 0.3258

BT2(4) -516.3426 192.8302 -2.677707 0.0093

BT2(5) -21.05633 51.30678 -0.410400 0.6828

BT2(6) 295.4909 142.2023 2.077962 0.0415

BT3(3) 53.01686 105.9015 0.500624 0.6183

BT3(4) 235.9518 244.5323 0.964911 0.3381

BT3(5) -43.24758 70.22521 -0.615841 0.5401

BT3(6) 215.1301 193.2427 1.113264 0.2696

BT4(4) -178.6079 202.2557 -0.883080 0.3804

BT4(5) -33.94896 145.9020 -0.232683 0.8167

BT4(6) 2745.507 1123.773 2.443115 0.0172

BT5(5) 34.99923 50.29931 0.695819 0.4889

BT5(6) -225.9783 124.2557 -1.818656 0.0734



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BT6(6) 5093.516 3514.498 1.449287 0.1519

Trend parameters

CT(1) -66.94296 121.3322 -0.551733 0.5830

CT(2) -5.934460 132.0247 -0.044950 0.9643

CT(3) -91.11745 140.4577 -0.648718 0.5187

CT(4) 453.8521 407.7805 1.112981 0.2697

CT(5) 7.610362 64.32158 0.118317 0.9062

CT(6) -143.1440 189.7196 -0.754503 0.4532

CT(7) 2975.809 1382.968 2.151756 0.0350

Fix factor effects

FT1(1) 1.012748 0.125786 8.051330 0.0000

FT1(3) 0.005154 0.010138 0.508373 0.6129

FT2(2) -0.089742 0.158432 -0.566440 0.5730

FT2(4) -0.045854 0.115524 -0.396920 0.6927

FT3(2) -0.329255 0.125046 -2.633061 0.0105

FT3(4) -0.122871 0.088518 -1.388087 0.1697

FT4(1) 1.022730 0.292258 3.499415 0.0008

FT4(4) 0.057569 0.259153 0.222142 0.8249

FT7(2) 1.254568 0.818249 1.533236 0.1299

Based on the parameter distribution of Table 38 above, the probability that positive own gross margin elasticities hold is only 0.8% (see Table 39 below). Is it interesting to note that the magnitude of the beef elasticities drops dramatically if the restriction is imposed. However again, the strong rejection of the restriction by the estimated model makes the interpretation of the elasticities a fruitless exercise.



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Table 39 Elasticities, top level system Spain, positive own gross-margin elasticities imposed (0.8% probability)


Cash crops 0.011100 -0.001646 0.001414 0.000481 -0.004242 7.26E-06 -0.000729

Other cows -0.059237 0.180768 0.044415 -0.056815 -0.066621 1.29E-06 0.036466

Beef 0.049157 0.042882 0.077594 -0.011215 -0.201261 0.000134 -0.007108

Pork 0.002444 -0.008024 -0.001640 0.000301 0.005411 2.43E-05 -0.001022

Poultry -0.030078 -0.013121 -0.041055 0.007546 0.124661 -9.84E-05 0.001925

Eggs 0.034535 0.000170 0.018363 0.022732 -0.066020 0.000308 -0.049839

Sheep and goat -0.001698 0.002359 -0.000476 -0.000468 0.000632 -2.44E-05 0.002111



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7 Final Evaluation of the Project

In this section, a final evaluation of the project in view of the results is presented. In order to better understand some possible causes for the problems encountered, data related and theoretical issues -some of which already have been pointed out in earlier sections of this and preceding reports - are first summarised. With this background, the general characteristics of the estimation results are then reviewed. Finally, the authors present their own view on possible consequences for further estimation activities and the specification of the SPEL/EU-MFSS model.

7.1 Data Base

When evaluating the results of the projects, the nature of the data used for estimation should be kept in mind. The content of the SPEL/EU-Data base differs from many other agricultural data sources as it combines data from the Economic Accounts for Agriculture with basic physical statistics (e.g. farm and market balances, herd inventories) in a consistent framework. The current study covering several Member States, many production activities and relative long time series was only possible due to the availability of the comprehensive and consistent layout of this data base.

However, with respect to the compatibility of the employed data base with the estimation of behavioural response to changes in economic incentives carried out in the study several problematic issues possibly leading to less than satisfactory estimation results shall be pointed out:

(1) One drawback is the fact that the data generation approach leads to unit value prices for all valued positions. In opposite to observed market prices - for example reported for a specific quality, at a specific location and time - the aggregated informational content of unit values may average out certain variance elements and introduce other ones (for example the quality of the quantities differs from year to year). The resulting price variances may consequently not appropriately reflect the economic incentives for agricultural producers.

(2) Due to the internal consistency algorithm any dubious observation in an original data series usually affects a lot of other items in the data base. Most problems occur with rather small and unimportant activities and their effect can often be neglected. Nevertheless, the final impact of such correction algorithms on the variance of the dependent and independent variables are hard to evaluate. It may, for example, lead to and "artificial" simultaneous equation bias for our estimations since the time series on activity levels and output coefficients are not independent.

(3) Another important point is the use of synthetic gross margins as economic incentives in a theoretically consistent econometric model. We have considerable doubts that a set of gross margins from a sectoral data base such as the SPEL/EU-Data base can be successfully used for estimation purposes. The price components are based on unit values which were commented on above. Whereas output coefficients are partly official data and partly deduced from activity levels and production figures coming from official statistics, most input coefficients are only based on “plausible” technical information.

In the context of the SPEL/EU-Data base, most input coefficient in cash crops are based on data from the Farm Accounting Data Network (FADN) for the years 1980-1988 and Standard Gross Margin calculations which in most cases are only available for some years in the middle of the 1980’s. Problems arise due to differences in definitions and aggregation levels, high yearly fluctuations in the FADN data etc. (WOLF 1995, P. 160). As far as FADN data are concerned, coefficients are not available for individual activities (wheat, rape etc.), but only in terms of averages for groups of farm (e.g. farm specialised in cereal production). In order to exploit the



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information from FADN, data on specialised farms have been mapped to groups of activities (cp. WOLF 1995, p. 211). For example, the average costs for plant protection for a group of specialised farms from the network were taken over to individual activities. Differences in definitions and aggregation problems are a first possible source of noise in the resulting gross margins. However, for one base year, the input relations had been checked intensively in close co-operation with experts.

For all other years, a linear relation between the expected yield – determined as a linear trend of the ex-post period – and the variable inputs is assumed. Finally, an uniform correction factor for each input is subsequently applied to achieve consistency to the sectoral value. The underlying linear relation between trend yield and input coefficients is possibly a further critical point.

The situation is more complex for animal activities where the greatest part of the costs relates to feed and young animals. Both are - to a large extent - produced within the agricultural sector. Here, prices, the distribution of the feeding-stuffs to the activities, and partially output coefficients - in the case of green and dried fodder - are synthesised by the SPEL/EU-BS. W. Wolf especially stressed problems with respect to feed prices: the EAA reports only the aggregated value of all feeding-stuffs bought by the sector. The underlying methodology applied by national agencies involved is not transparent. Based on the proposal of GD VI, feed prices for marketed cereals are set equal to farm gate prices. As a consequence, all cost for transporting, mixing, marketing etc. comprised in the value of the feed aggregate are mapped into the prices for the remaining feed components. On top, price series for individual feeding-stuffs are difficult to obtain.

We conclude – also based on the outcome of the estimations - that the synthetic gross margins may be an interesting tool to reveal certain trends in the profitability of individual activities ex-post, but are probably an inappropriate basis to describe economic incentives steering the supply response at the sectoral level.

(4) Another more general comment: it would be extremely helpful to have a data base with time series on relevant political variables (administered prices, quotas, premiums, etc.) matching the definitions of the SPEL/EU-Data base for projects such as this one. The results of the cash crop system for Germany with administered prices used to formulate gross margin expectations looked considerably more promising than other approaches.

(5) It should be underlined that some doubtful reported "observations" in a data base such as the SPEL/EU-Data base are unavoidable. However, if one does not regularly deal with the raw data entering the SPEL/EU-BS and its algorithms, it is a demanding task to decide which data points should be treated as outliers. Here, an intensive feedback with the SPEL team is necessary to avoid misinterpretations. A lot of the deficiencies are known for a long time and the discussion with statistical offices is continuously going on to improve the data. In other cases, a suitable methodological solution to overcome the deficiencies is currently not available. Sometimes, analytical projects of this type may detect some problematic data points which were not known to the SPEL group up to this point. However, the time needed to detect, discuss and possibly correct data points which look not plausible must be kept in mind when planning such projects. Especially, it is advisable to base econometric work on the SPEL/EU-Data base as far as possible on such data elements which are of an official or semi-official nature in close feed back with W. Wolf and the team in Luxembourg. Without that feedback, econometric estimation results may reflect more algorithms of the SPEL/EU-BS instead of the behaviour of the economic agents.

With respect to the data base, we can conclude that the general data generation approach of the SPEL/EU-BS which is perfectly suitable and useful for an ex-post description of the agricultural



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sectors of the Member States, might create considerable problems for the estimation of product differentiated, sectoral supply response to changes in economic incentives.

Another data problem, independent from the data source, is the policy intervention affecting main agricultural markets during the observation period. They tend to considerably reduce price variation and consequently render the statistical detection of behavioural reactions difficult. Also, changes in the policy regime (for example with the CAP-reform in 1992) can cause structural breaks in behavioural reactions of producers which, due to the restrictions on the number of parameters, can only be partially reflected in the empirical model.

7.2 Theoretical Model

(1) Before the more specific parts of the theoretical model are discussed, some general points should be mentioned. The underlying micro-economic model is a great simplification in the sense that it does not explicitly account for certain aspects potentially relevant for adjustments in activity levels, for example risk behaviour and the existence of transaction-, adjustment- and information costs. In these respects our approach is not different from most empirical applications of short term, duality based approaches at the sectoral level, but nevertheless these shortcomings with potentially negative effects on the quality and interpretability of the estimation results exist.

Although the theoretical model generally allows for the effect of the primary factors labour and capital on the production decisions, they have not been explicitly introduced in the estimation but were instead subsumed under the trend variable. This may cause additional problems, although other studies show that the introduction of aggregate capital stocks and labour not necessarily have a relevant effect on other estimated parameters (see GYOMARD, BAUDRY, CARPENTIER 1996).

(2) Again, we want to point at the general deficiencies of the two-stage approach with pre-determined intensities of individual production activities mentioned in HECKELEI (1997) andreviewed in section 3 of this report. These deficiencies might play a significant role for the problems to come up with a stable set of estimated parameters. We do not want to repeat all points already mentioned, but illustrate two of the more important ones for crop production:

• Even if the two-stage decision model would be an appropriate economic model at the farm level, unrealistic assumptions on the technology are necessary to employ the model at the aggregate level. Average output and input coefficients most likely depend on the shares of the individual crop production activities. For example, different land qualities alone result in changes of average yields for a crop production activity if the land allocated to the crop changes. This point should be also considered in the context of defining sectoral shift factors for yields for simulation purposes.

• With rotational effects existing in crop production, non-jointness in variable inputs might not be a correct assumption for the underlying technology. For example, the application of certain pesticides to a certain crop might also have an impact on subsequently planted crops.

(3) The static nature of the employed theoretical model might be especially restrictive for modelling animal supply response. Variations of supply quantities for animal products depend to a large extent on past investments in production capacity. Theoretically, these dynamic effects might be to some extent implicitly captured by the autoregressive gross margin expectations employed in the estimation approach. However, estimation results for the level determination of animal production activities in the reported top level systems certainly do not give much support for the empirical validity of this potential. Another related problem is that the production cycles - and with it the



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relevant expectation formulation - for most of the animal production activities does not coincide with the yearly observations used for estimation purposes.

7.3 Parameter Estimates

The estimation results must be seen in the context of the above mentioned theoretical and empirical shortcomings of the employed approach. As with any empirical study, the number of potentially relevant deficiencies does not allow to exactly identify the reasons for observed estimation problems.

(1) The parameters related to gross margins across all countries and models tested showed relatively high standard errors. One possible reason could be multicollinearity between the gross margins, their cross-products and the trend. However, reported checks on this issue did not support this hypothesis. Therefore, it must be generally concluded that the significance of the expected gross margins for the determination of production activity levels is rather small. This is especially true for the estimated top level system, whereas some of the estimated cash crop systems showed higher significance of expected gross margins. Another effect of this finding is the drastic sensitivity of the estimated parameters to slight changes of the sample. Consequently, the estimated effects of prices (and gross margins) on the level allocation are strongly subjected to the stochastic components in the underlying data base.

(2) Another observation is the strong impact of relatively small changes in the expectation model on the parameter estimates and their standard errors. In most cases, this is also true for the resulting elasticity estimates. Especially the magnitude of the elasticities depends on the variance of the expected gross margin series. As long as no clear idea exist on the appropriate formulation of the expectation model the choice of a final specification is of mainly subjective nature and must be based on plausibility reasoning, as long as no other criteria such as coherence to the underlying theoretical model or statistical evidence allows to differentiate between the models. This issue underlines the necessity to employ the same expectation model in estimation and simulation to reduce the effect of the assumed expectation model.

Actually, there is no reason to expect that estimation results should not depend on the employed expectation model, even if no other problems with the theoretical or empirical specification existed. In comparable approaches published in the literature this issue is, however, solved by a-priori assumption and the effect of different expectation models is usually not evaluated.

A specific crop production problem related to the expectation issue is the fact that probably a major part of the variance in "observed" gross margins of activities whose outputs are sold in price supported markets (cereals) is based on product quality fluctuations between the years. Relatively good estimation results for Germany based on administered prices for cereals may underline the problem.

(3) Generally, it can be concluded that the estimation results for the cash crop systems look considerably more promising than for the top level systems where animal production activities are included. Possible reasons for this finding have already been discussed above, and we strongly suggest not to pursue subsequent estimation exercises of supply response of animal production activities based on the employed theoretical and empirical model. Alternative approaches have to take the dynamics affecting animal product supply into account and should probably leave the realm of yearly observations, at least for the case of pig meat production and eggs .

For the cash crop sector, the comparative evaluation of a "price elasticity" approach, which relaxes



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the assumption of production intensities independent from the activity level is desirable, since the estimation results of the gross margin specification are still not convincing and the underlying restrictive assumptions have been extensively discussed. Certain alternative specifications might even circumvent the problem of allocating variable inputs to individual production activities.

7.4 Application to other Member States:

Although the programs, work files etc. used in this project phase were set-up to allow a technically easy application of the approach to other Member States, the time demanding part of such an application is connected to empirical questions in the light of estimation results achieved: choosing an appropriate separability structure, evaluating a suitable expectation model, deciding upon the introduction of correction measurements for serial auto-correlation, deleting insignificant parameters from equations etc.. Here, mechanical solutions are impossible. Knowledge and experience in the fields of duality theory, econometrics and the content and set-up of the SPEL/EU-Data base are necessary to obtain appropriate model specifications within the frame of the general model layout.

7.5 Possible Consequences for the SPEL/EU- MFSS

Again, the estimation results must be seen in light of the various theoretical and empirical shortcomings of the employed approach illustrated in this and earlier sections. Due to the extensive experiments conducted in this project we have considerable doubts that an econometric estimation of gross margin elasticities using the SPEL/EU-Date base can provide an empirical validation and updating approach of the supply response specification in the SPEL/EU-MFSS model, at least for activities other than crop production activities.

If that is true, one may ask how to obtain and update the behavioural parameters for a gross-margin elasticity driven model as the SPEL-EU MFSS. Synthetic elasticities in a narrow sense cannot be used – they would need to be based on econometric work using sectoral gross margins. Apart from this project, the former study by WOLFGARTEN (1991) is the only available source, which is theoretically weakly based, uses an aggregation level different from the current SPEL/EU-Data base, and is to a certain extent outdated due to the CAP reform in 1992 (estimation period 1965-1989). In a broader sense, as proposed in WEBER (1993), price elasticities could be used as a source for gross-margin elasticities. However, most econometric estimations of price elasticities relate to output quantities and do not differentiate between yields and areas. Therefore, WEBER used price elasticities as a additional source to set bounds in the calibration process for gross margin elasticities. If price elasticities are used to define gross margin elasticities, possibly doubtful input coefficients play again a major rule in deriving the parameters.

Given the outcome of the estimations and the prevailing need for some empirical validation and update of behavioural parameters, we propose for further developments of the SPEL/EU-MFSS to consider an alternative specification of the behavioural supply model based on price elasticities. This switch would make it much easier to compare the parameter set employed in the SPEL/EU-MFSS with other modelling system and to feed the model with synthetic elasticities. Furthermore, there is some hope at least for the crop sector (and some evidence in the literature, see for example GYOMARD, BAUDRY, and CARPENTIER 1996) that an econometric estimation of price elasticities might yield more stable and plausible results than the current project. We have already initiated some explorations in this respect at the Institute of Agricultural Policy. At the same time, the data generation process employed in the SPEL/EU-BS could possibly be used to calculate gross margins for the simulation period preserving the proven advantages of using gross margins as a source of



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information to check the profitability of individual activities ex-ante and the general plausibility of simulation results.



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8 References

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CHAMBERS, R.G. (1988): “Applied Production Analysis - A dual approach”, Cambridge: Cambridge University Press.

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GYOMARD, H., BAUDRY, M., & A. CARPENTIER (1996): “Estimating crop supply response in the presence of farm programmes: application to the CAP”, European Review of Agricultural Economics 23(4):401-420.

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HECKELEI, T. (1997): “Estimation of Elasticities for SPEL/EU-MFSS: Explorative study on the

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SOEC 781400001(dated 26.3.1997), Bonn: EuroCARE 26.11.1997

HECKELEI, T., R. MITTELHAMMER & T.I.WAHL (1997): “Bayesian Analysis of a Japanese Meat

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LANSINK, A.O. & J. PEERLINGS (1996): “Modelling the new EU cereals and oilseeds regime in the Netherlands”, European Review of Agricultural Economics 23(2):161-178.

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Documents

Final report - uni-bonn.de · Based on experiences from an earlier project phase (BRITZ & HECKELEI 1998) and some further tests it was decided to abolish the model specification based