3.7 Regional Coverage for Farm Type Model
3.7.3 Extrapolation Approach
The modelling units of the farm type model EU-EFEM are single farms. In comparison to a regional model, the computational effort is substantially increased, but aggregate errors decreased especially in cases of large intraregional heterogeneity. However, a wider regional coverage is also not excluded for EU- EFEM. It thereby follows a bottom-up approach, i.e. from lower to higher regional coverage, or in the concrete case from farms to NUTS-II regions. The link between both levels is created by extrapolation.
For the extrapolation of the EU-EFEM farm results to regional level an approach is chosen that balances computational effort and aggregate error. The latter is minimised by selecting the most representative farms out of the accessed farms in the FADN accountancy dataset. In this study, this is understood to be guaranteed by falling back upon the average farms (section 3.7.1).
Technically farms are extrapolated to regions within a linear programming module based on the sector-consistent approach by KAZENWADEL (1999). The variables of the
module are of the type “positive variables”, i.e. no negative activity level is allowed. The problem to be solved can be formulated as the minimisation of the objective function (B) under certain constraints (Formula 15):
Formula 14: Objective Function (B) of Linear Extrapolation Approach
∑
∑
= =×
+
×
=
m k k k m k k knDEV
d
pDEV
c
B
1 1)
(
)
(
with the indexes:
k capacity
f farm
with the variables:
nDEV(k) negative deviation of capacity k
pDEV(k) positive deviation of capacity k
and the coefficients:
c(k),d(k) objective values of capacity k (weighting factor)
142 3- Methodology
Formula 15: Constrained Regional Capacity (regk) in Linear Extrapolation
k k n f f kf k
a
EF
nDEV
pDEV
reg
=
∑
×
+
−
=1)
(
with the variables:
EF(f) extrapolation factor of farm f
and the coefficients:
a(k,f) production capacity k of farm f
Kazenwadel inserted the weighting factors c(k) and d(k) to the objective
function (B) for the purpose of balancing regionally over-/underrepresented capacities with respect to their economic importance. He expressed economic importance of regional capacities regk by assigning them their Standard Gross
Margin (SGM). With a similar motivation, instead of minimising the positive and negative deviations, the quadratic positive and negative deviations could also be minimised. This would lead to a more equal distribution of deviations over all capacities, since high deviations were penalised over-proportionally.
With the concept of the weighting factors c(k) and d(k), the main emphasis of the
objective function can be shifted. Against the background of an economic-ecological model like EU-EFEM, the application of a pure economic weighting factor like the SGM that eclipses ecological aspects appears questionable. An example is the simulation of soil borne emissions. These depend mainly on the degree of representation of cash crops, but also on that one of total grassland and of arable land. A second problem65 lies in the determination of the SGM itself. Production factors that do not directly render a marketable good (e.g. grassland) require that a substitute value is estimated. This relatively uncertain estimate militates for an alternative weighting system.
Apart from its potential to represent (empiric) economic performance of farms, the extrapolation approach should represent (empiric) farm structure, as well. Farm structure, within the official Farm Structural Survey (FSS) for example, is understood as the number of farms per farm type. The integration of this farm structure into any linear extrapolation module faces hurdles. First, the direct integration via absolute
65 The general rules for the calculation of SGMs according to EU accords are described in Annex 1 to
3- Methodology 143
numbers of farms per farm type would mean fixing to the activity level of the farm type specific extrapolation factors (EF(f)), i.e. the value of the extrapolation factor would be predefined. Second, the share of farm types in the FSS could be fixed as a constraint for the farm types of the extrapolation approach. This is technically impossible, since the total number of farms in the solution (sum of EF(f)) is unknown
ex-ante and thus no shares can be determined.
The alternative approach used for EU-EFEM keeps the original system of weighting factors based on SGMs used by Kazenwadel and simultaneously considers the representation of farm structure. It modifies the SGMs in order to account for uncertainties in the determination of the same, and it seeks to optimise the representation of the farm structure. First, the bias from the SGM is reduced by drawing back on regional SGMs (EUROSTAT, 2003) instead of local SGMs, and second by conducting a sensitivity analysis for SGMs varied by 50%. The sensitivity analysis demands a technical solution in order to simulate the stepwise variations of the original SGMs. Out of the simulations, the ones that show an impact on the extrapolation factor (EF(f)) are preselected (first three reactions to 50% increase and to 50% decrease of SGMs). Also the reference simulation with the original SGM was preselected. Out of this pre-selection, that solution is chosen which best represents the shares of farm types given by the FSS and simultaneously shows minimal capacity deviations (nDEV(k) and pDEV(k)). In summary, the approach used for EU- EFEM, modified and expanded the original approach by Kazenwadel and by introducing trial methods, picks out from a selection of possible solutions the most appropriate one with respect to the representation of farm structure.
A deficiency of linear extrapolation approaches66 becomes manifest in case farms which are a linear combination of one other farm are extrapolated. This problem was partially by-passed by constraining the maximum activity level of the extrapolation factors. However, this is a strong intervention which should be avoided as far as possible.
66 D
E CARA and JAYET (2000) applied an alternative approach for the calibration of FADN farms
forming the basis to their LP-model. They combine Monte-Carlo methods and gradient algorithms constraining the maximal variations of calibrated parameters. In so doing, the adaptation is not in the farms, but in the activities’ coefficients. Their proceeding assumes FADN farms weighted by FADN weighting factors to perfectly represent regional production.
144 3- Methodology
3.7.4 (Calibrated) Typical Farms in the Model
In the former sections, the deduction of the average farms from the real farms contained in the FADN accountancy data was explained. In this study, “typical farms” and “calibrated typical farms” are distinguished from these average farms. Only in this section, typical farms will be discriminated against calibrated typical farms. The calibrated typical farms are the modelling units of EU-EFEM. But in order to maintain brevity, outside this section, typical farms will be referred to, although this actually means calibrated typical farms.
The first evolve from the latter by slight modifications with respect to marginal capacities of reduced expressiveness. The typical farms are further discriminated against typical calibrated farms that already reflect the adjustments for deviations of farm capacities from regional capacities. The calibrated typical farm finally represents the farm to be modelled in EU-EFEM.
The typical farms evolve from the average farms. Because of reasons (mentioned in section 3.7.1) of representation and expressiveness marginal capacities are ignored and sometimes fractions are rounded to integer numbers. From the typical farms evolve the calibrated typical farms. The extrapolation approach is applied to the typical farms. The extrapolation approach presented in the previous section leaves room for capacity deviations between regional and extrapolated farm capacities. Since the regional capacities are fixed, the capacity deviations have to be copied to the farm capacities. This is done via a calibration term that transforms the original farm capacities a(k,f) of the typical farms to the modified capacities a’’(k,f) of the calibrated typical farms. The calibration term is presented in Formula 16.
Formula 16: Adaptation of Farm Capacities to Regional Deviations
−
−
−
=
k k k k kf kfreg
SGM
pDEV
nDEV
a
a
1
'
'
The transformation from the average farm, to the region typical farm, to the calibrated region typical farm is illustrated for an example in Table 57. The first modification is to the marginal capacities and real values of average farms. It is done manually because whether a farm capacity is marginal or not depends on the
3- Methodology 145
regional capacity67. The definition of “marginal” is dependent on the region and thus would have required considerable automation effort. The second modification is to the capacities of typical farms. The modification is uniform according to the presented calibration term and thus could be automated easily.
Table 57: From Average to Calibrated Typical Farms of EU-EFEM (Example)
Before Extrapolation After Extrapolation
Item Unit ‘Average’ ‘Typical’ ‘Calibrated Typical’
Capacities
arable land (ha) 42.5 42.5 43.6
grassland (ha) 5.0 5.0 0.0
cattle (LU) 12.5 12.5 0.0
pigs (LU) 6.9 0.0 0.0
sheep (LU) 0.3 0.0 0.0
potato (ha) 5.6 5.6 1.1
sugar beet (ha) 10.1 10.1 3.1
Non Calibrated Items
diesel (l) 5,595.3 5,595.3 5,885.8
milk per cow (kg) 4,222.0 4,222.0 4,222.0
cattle premiums (€) 2,052.6 2,052.6 0.0
diesel_dev (%) 130.0 130.0 130.0
The preceding process is valid for the considered capacities. However, apart from the considered capacities, the farms simulated in EU-EFEM are also characterised by some additional items. These include diesel consumption per farm, milk yield per cow, total cattle premiums, and diesel deviation factor, representing the deviation between the theoretical diesel consumption according to the KTBL engineering data and the consumption stated in the FADN accountancy data. All these items are summarised in Table 57 under the term “Non-Calibrated Items”.
Among the Non-Calibrated items, ‘diesel’ takes an outstanding position since it should follow the capacity adaptations performed on the way from the average to the calibrated typical farm. The milk yield per cow and the cattle premiums (national ceilings would be affected if it was changed on a farm level), in contrast, should not follow the capacity deviations. Correspondingly, the diesel consumption stated for the average farms is modified proportionally to the capacities’ deviation. The modification is specific to the capacity like can be seen in Table 58. For arable land 100 l of diesel
67 Even though this procedure is executed manually it is not arbitrary, but subject to certain rules.
Grassland is modified proportionately to ruminant animals that are normally fed from grassland so as to maintain the original stocking density. Other plant production capacities are not modified since the interpretation is far less complex because of missing interrelation to other production branches.
146 3- Methodology
are added or subtracted per unit. This quantity approximately corresponds to the average consumption for normal crop mix under central European conditions. Potatoes are implicitly contained in the assumed crop mix of arable land, so that the capacity adjustment of the potato area only accounts for the difference between “usual” arable crops and potatoes (additional 25 l/ha). Grassland and livestock values are very rough estimates.
Table 58: Standard Modification of Diesel Consumption per Farm Capacity
Capacity Diesel Capacity Diesel
(l/ha) (l/LU)
arable land 100.0 cattle 100.0
grassland 25.0 pigs 20.0
sugar beets 0.0 poultry 20.0
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4 Modelling Results
In this chapter the results from several modelling exercises are presented. The exercises address economic and ecological research questions for a number of scenarios dealing ultimately either with soil carbon accumulation or biogas production.
The model is firstly validated in order to allow evaluating the expressiveness of generated scenario results and also the model’s quality. Second, a common reference, to which the scenarios can be compared, is created. This reference is free of any scenario obligations, but simulates the actual situation of agricultural production. Third and finally, scenario results are calculated and presented. Each scenario is subject to specific scenario rights and obligations that are essentially in addition to the restrictions of the reference scenario.
In terms of presentation of results, there is typically a trade-off between results’ aggregation and information content. Thus only an optimal balance between both can be sought. Data aggregation is indispensable for this study since EU-EFEM generates more than 600 values per analysed parameter (up to 4 farms for 163 NUTS-II regions68). This aggregation is mostly done to a regional level. Since also the regional level still means 163 values per analysed parameter, the presentation is in the form of GIS maps. This allows for a rapid access to the results and the identification of “hot-spots” in the EU-15. In the GIS maps however the presentation is not of numeric values and thus grouping into optically different structures is necessary. Further, on level of selected regions, also farm level results will be shown to highlight the importance of farm types to the results.