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scenario_simulation [2020/04/25 06:56] – matszscenario_simulation [2022/01/03 11:17] – [Price depending crop yields and input coefficients] himics
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 **Figure 13: Link of modules in CAPRI** **Figure 13: Link of modules in CAPRI**
-{{::figure13.png?600|Source: CAPRI Modelling System. Note: the number of regions is outdated in December 2011}} +{{::figure_13.png?600|Source: CAPRI Modelling System. Note: the number of regions is outdated in December 2011}} 
  
 =====Module for agricultural supply at regional level===== =====Module for agricultural supply at regional level=====
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 ====Detailed discussion of the equations in the supply model==== ====Detailed discussion of the equations in the supply model====
  
-The definition of the supply model can be found in //‘supply\supply_model.gms’//+The definition of the supply model can be found in //‘supply/supply_model.gms’//
  
 ===Feed block=== ===Feed block===
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 Where “asym” is the land asymptote, i.e. the maximal amount of economically usable agricultural area in a region when the agricultural land rent goes towards infinity. For an application where the land market is used see Renwick et al. (2013). Where “asym” is the land asymptote, i.e. the maximal amount of economically usable agricultural area in a region when the agricultural land rent goes towards infinity. For an application where the land market is used see Renwick et al. (2013).
  
-Set aside policies have changed frequently during CAP reforms. The recent specification is covered in the context of the premium modelling in Section [[Premium module]]. The obligatory set-aside restriction introduced by the McSharry reform 1992 and valid until the implementation of the Luxembourg compromise of June 2003 has been explicitly modelled through this equation:+Set aside policies have changed frequently during CAP reforms. The recent specification is covered in the context of the premium modelling in Section [[scenario simulation#Premium module]]. The obligatory set-aside restriction introduced by the McSharry reform 1992 and valid until the implementation of the Luxembourg compromise of June 2003 has been explicitly modelled through this equation:
  
 \begin{align} \begin{align}
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 In the case of quotas (milk, for sugar beet) the sales to the market may be bounded (noting that NETTRD = v_netPutQuant in the code): In the case of quotas (milk, for sugar beet) the sales to the market may be bounded (noting that NETTRD = v_netPutQuant in the code):
  
-{{::code_p_150.png?600|}}+{{::code_p_150.png?600}}
  
 As described in the data base chapter, the concept of the EAA requires a distinction between young animals as inputs and outputs, where only the net trade is valued in the EAA on the output side. Consequently, the remonte expressed as demand for young animals on the input side must be mapped into equivalent ‘net import’ of young animals on the output side: As described in the data base chapter, the concept of the EAA requires a distinction between young animals as inputs and outputs, where only the net trade is valued in the EAA on the output side. Consequently, the remonte expressed as demand for young animals on the input side must be mapped into equivalent ‘net import’ of young animals on the output side:
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 \end{matrix} \end{matrix}
 \right] \right]
- 
 \end{split} \end{split}
 \end{align} \end{align}
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 \end{align} \end{align}
  
-The scaling factor to map from the legal quota legalquotA (as the B quota has been eliminated in the sugar reform, it holds that \(q^A = q^{A+B}) \)to the behavioural quota qA depends on the projected sugar beet sales quantity in the calibration point \(NETTRD_{SUGB}^{cal} : For a country with a high over quota production (say 40%) we would obtain a scaling factor of 1.31, such that this producer will behave like a moderate C-sugar producer: responsive to both the C-beet prices as well as to the quota beet price (and the legal quotas). Without this scaling factor, producers with significant over quota p   roduction, like France and Germany, would not show any sizeable response to a 10% cut of either the legal quotas or the quota price (at empirically observed coefficients of variation). As it is likely that the profitability of ethanol beets benefit from cross-subsidisation from the quota beets such a zero responsiveness was considered implausible.+The scaling factor to map from the legal quota legalquotA (as the B quota has been eliminated in the sugar reform, it holds that \(q^A = q^{A+B} \) )to the behavioural quota qA depends on the projected sugar beet sales quantity in the calibration point \( NETTRD_{SUGB}^{cal} \) : For a country with a high over quota production (say 40%) we would obtain a scaling factor of 1.31, such that this producer will behave like a moderate C-sugar producer: responsive to both the C-beet prices as well as to the quota beet price (and the legal quotas). Without this scaling factor, producers with significant over quota p   roduction, like France and Germany, would not show any sizeable response to a 10% cut of either the legal quotas or the quota price (at empirically observed coefficients of variation). As it is likely that the profitability of ethanol beets benefit from cross-subsidisation from the quota beets such a zero responsiveness was considered implausible. 
  
 ===Update note=== ===Update note===
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 Y_{j,t}=Y_{j,t-1}^{[\epsilon_jlog \frac{p_o,t-1}{p_t}]} Y_{j,t}=Y_{j,t-1}^{[\epsilon_jlog \frac{p_o,t-1}{p_t}]}
 \end{equation} \end{equation}
 +
 +
 +====Annex: Land use modelling ====
  
 =====Premium module===== =====Premium module=====
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   *ceilVal = Ceiling on the total budget (envelope) spent on the scheme   *ceilVal = Ceiling on the total budget (envelope) spent on the scheme
  
-In the basic setting, the ceilings work as the old Grandes Cultures payment: if the total quantity (hectares or amount) exceeds the ceiling, then the payment to each farmer is reduced so that the ceilings are respected. This means that the marginal payment is somewhat reduced but does not become zero. For some other schemes, such as the Basic Payment Scheme of the CAP 2014-2020, there is a hard limit on the number of payment entitlements, so that the marginal payment becomes zero if the ceiling is overshot. That behaviour can be triggered by including the payment scheme set element in a special set //PSDPAY_cutEndog//, as in the following example from “pol_input\mtr_until2013.gms”.+In the basic setting, the ceilings work as the old Grandes Cultures payment: if the total quantity (hectares or amount) exceeds the ceiling, then the payment to each farmer is reduced so that the ceilings are respected. This means that the marginal payment is somewhat reduced but does not become zero. For some other schemes, such as the Basic Payment Scheme of the CAP 2014-2020, there is a hard limit on the number of payment entitlements, so that the marginal payment becomes zero if the ceiling is overshot. That behaviour can be triggered by including the payment scheme set element in a special set //PSDPAY_cutEndog//, as in the following example from “pol_input/mtr_until2013.gms”.
  
  PSDPAY_cutEndog("DPSAPS")  = YES; \\  PSDPAY_cutEndog("DPSAPS")  = YES; \\
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 **Figure 14: Example of technical implementation of a premium scheme** **Figure 14: Example of technical implementation of a premium scheme**
  
-{{:figure14.png?600|}} \\ Source: CAPRI Modelling System. Note: The parameter PPDATA_E is now called p_premDataE.+{{:figure_14.png?600|Source: CAPRI Modelling System. Note: The parameter PPDATA_E is now called p_premDataE.}}
  
-The sets of payments, exemplified by DPGRCU in the figure, and the activity groups, exemplified by PGGRCU and PGPROT are defined in the file policy\policy_sets.gms. Since this is a “static” GAMS file used in any simulation, it contains the gross list of all policies that currently can be simulated, including legacy ones. In order to work efficiently with the acronyms which define the application types, these are converted to numerical attributes as shown below (//‘policy\policy.gms’)//:+The sets of payments, exemplified by DPGRCU in the figure, and the activity groups, exemplified by PGGRCU and PGPROT are defined in the file policy/policy_sets.gms. Since this is a “static” GAMS file used in any simulation, it contains the gross list of all policies that currently can be simulated, including legacy ones. In order to work efficiently with the acronyms which define the application types, these are converted to numerical attributes as shown below (//‘policy/policy.gms’)//:
  
-{{::code_p157.png?600|}}+{{::code_p157.png?600}}
  
-CAPRI also provides the possibility to incentivise extensification or intensification via the payments. Most production activities come in technological variants, by default one higher yielding and one lower yielding one, and those variants can be eligible to different rates of premium payments. This is used for instance in the implementation of agri-environmental schemes in the file policy\rd_logic.gms as shown in the figure below. The parameter p_technFact is the standard coefficient that modifies the technology of the production activities in CAPRI. In the figure below, the two statements change the rate of premium payments for the set of currently active regions (rs), for all model activities (MPACT), for all agri-environmental schemes (psdpay_ae) with different rates for technology T1 (high yield) and T2 (low yield) in the case where T2 exists. +0.5 for T2 means that the premium payment in the model becomes the nominal rate times (1 + 0.5), i.e. 50% higher, whereas the -0.5 for T1 means that the premium payment in the model becomes the nominal rate times (1 – 0.5), i.e. 50% lower. This approximates the stylized fact that agri-environmental schemes, which in reality consist of a wide range of measures, in general favour extensive technologies (see section on Pillar II payments below).+CAPRI also provides the possibility to incentivise extensification or intensification via the payments. Most production activities come in technological variants, by default one higher yielding and one lower yielding one, and those variants can be eligible to different rates of premium payments. This is used for instance in the implementation of agri-environmental schemes in the file policy/rd_logic.gms as shown in the figure below. The parameter p_technFact is the standard coefficient that modifies the technology of the production activities in CAPRI. In the figure below, the two statements change the rate of premium payments for the set of currently active regions (rs), for all model activities (MPACT), for all agri-environmental schemes (psdpay_ae) with different rates for technology T1 (high yield) and T2 (low yield) in the case where T2 exists. +0.5 for T2 means that the premium payment in the model becomes the nominal rate times (1 + 0.5), i.e. 50% higher, whereas the -0.5 for T1 means that the premium payment in the model becomes the nominal rate times (1 – 0.5), i.e. 50% lower. This approximates the stylized fact that agri-environmental schemes, which in reality consist of a wide range of measures, in general favour extensive technologies (see section on Pillar II payments below).
  
-{{:code_p158.png?600|}}+{{:code_p158.png?600}}
  
 The general flow of logic inside of CAPRI (inside the model file capmod.gms) as regards premiums is shown in the following figure. The process starts by loading baseline data, including calibrated behavioural parameters. That data set represents an equilibrium situation for the policy (premiums) that were used in the baseline generation process. The general flow of logic inside of CAPRI (inside the model file capmod.gms) as regards premiums is shown in the following figure. The process starts by loading baseline data, including calibrated behavioural parameters. That data set represents an equilibrium situation for the policy (premiums) that were used in the baseline generation process.
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 **Figure 15: General flow of logic of CAPRI model as regards premiums** **Figure 15: General flow of logic of CAPRI model as regards premiums**
  
-{{::fiugre15.png?600|}} \\ Source: own illustration+{{::figure_15.png?600|Source: own illustration}} 
  
-Generally, all attributes for a premium scheme are mapped down in space, e.g. from EU27 to EU 27 member states, from countries to NUTS1 regions inside the country, from there to the NUTS2 regions inside the NUTS1, and from NUTS2 regions to the farm types in a NUTS2 region (see //‘policy\policy.gms’//), e.g.+Generally, all attributes for a premium scheme are mapped down in space, e.g. from EU27 to EU 27 member states, from countries to NUTS1 regions inside the country, from there to the NUTS2 regions inside the NUTS1, and from NUTS2 regions to the farm types in a NUTS2 region (see //‘policy/policy.gms’//), e.g.
  
-{{:code_p159.png?600|}}+{{:code_p159.png?600}}
  
 In order to map the premium rate as defined in a legal text into one paid out on a per-activity basis, the relevant activity based attribute matching the application type is set to a premium modification factor (“Ap_premModfFactT”) as shown below: In order to map the premium rate as defined in a legal text into one paid out on a per-activity basis, the relevant activity based attribute matching the application type is set to a premium modification factor (“Ap_premModfFactT”) as shown below:
  
-{{:code_p159_2.png?600|}}+{{:code_p159_2.png?600}}
  
 The actually declared premium per activity unit (ha, [1000] [slaughtered] heads) is then the multiplication of the premium rate and that modification factor. For crops, the unit of the resulting entries are current € per ha, for animal, it depends on the exact definition of the activity level (per [1000] [slaughtered] heads). The actually declared premium per activity unit (ha, [1000] [slaughtered] heads) is then the multiplication of the premium rate and that modification factor. For crops, the unit of the resulting entries are current € per ha, for animal, it depends on the exact definition of the activity level (per [1000] [slaughtered] heads).
  
-{{::code_p160.png?600|}}+{{::code_p160.png?600}}
  
 These declared rates can hence be aggregated to higher regional units using the activity levels as weights, e.g. from farm types to NUTS2: These declared rates can hence be aggregated to higher regional units using the activity levels as weights, e.g. from farm types to NUTS2:
  
-{{:code_p160_2.png?600|}}+{{:code_p160_2.png?600}}
  
 Before the supply module is started between iterations, the current activity levels and premiums paid out are summed up for each scheme and regional level where ceilings in levels or value are defined. If one of the aggregated sums exceeds the ceilings, all premium rates for the scheme are cut proportionally to fit under the tighter of the two envelops: Before the supply module is started between iterations, the current activity levels and premiums paid out are summed up for each scheme and regional level where ceilings in levels or value are defined. If one of the aggregated sums exceeds the ceilings, all premium rates for the scheme are cut proportionally to fit under the tighter of the two envelops:
  
-{{:code_p160_3.png?600|}}+{{:code_p160_3.png?600}}
  
 From the declared rates and these cut factors, the actually paid premiums are defined: From the declared rates and these cut factors, the actually paid premiums are defined:
  
-{{:code_p160_4.png?600|}}+{{:code_p160_4.png?600}}
  
 The indivudal premiums from each premium scheme are then added up to arrive at one average rate for each activity which enters the objective function of the supply model, the data base and post-model reporting: The indivudal premiums from each premium scheme are then added up to arrive at one average rate for each activity which enters the objective function of the supply model, the data base and post-model reporting:
  
-{{:code_p160_5.png?600|}}+{{:code_p160_5.png?600}}
  
 ====An example of a payment with a ceiling==== ====An example of a payment with a ceiling====
  
-We explain the different elements and steps in the following based on an example of the slaughter premium for adult cattle of 80 EURO per slaughtered head in Latvia, defined in 2004. The following screen shot comes from the policy file gams\pol_input\mtr_until2013.gms, with some lines hidden.+We explain the different elements and steps in the following based on an example of the slaughter premium for adult cattle of 80 EURO per slaughtered head in Latvia, defined in 2004. The following screen shot comes from the policy file gams/pol_input/mtr_until2013.gms, with some lines hidden.
  
-{{:code_p160_6.png?600|}}+{{:code_p160_6.png?600}}
  
   -The application type defines the criterion upon which the payment depends, in the case of the slaughter premium it is defined per slaughtered head.   -The application type defines the criterion upon which the payment depends, in the case of the slaughter premium it is defined per slaughtered head.
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   -Regional ceiling, expressed in maximum number of premiums paid and/or total payment in EURO. In the example with the slaughter premiums, this is used to set a national ceiling limiting the total amount spent on slaughter premiums to 9.946 million euro. There can be additional ceilings at other regional levels, and the most strongly binding is always the one that limits payments.   -Regional ceiling, expressed in maximum number of premiums paid and/or total payment in EURO. In the example with the slaughter premiums, this is used to set a national ceiling limiting the total amount spent on slaughter premiums to 9.946 million euro. There can be additional ceilings at other regional levels, and the most strongly binding is always the one that limits payments.
  
-Those four pieces of information are generally easily accessible without further processing from the regulatory texts. Starting with PRMR and APPTYPE (information pieces 1 and 2 above), it is possible to calculate (3), PRMD, the amount of premium per head or hectare that would be paid if there were no (active) ceiling. These preparatory calculations, e.g. the hierarchical break down from higher to lower regional level and from activity groups to individual activities, as well as the calculations of PRMD from PRMR (using APPTYPE) is carried out in a file called ‘//policy\policy.gms//’ as shown above.+Those four pieces of information are generally easily accessible without further processing from the regulatory texts. Starting with PRMR and APPTYPE (information pieces 1 and 2 above), it is possible to calculate (3), PRMD, the amount of premium per head or hectare that would be paid if there were no (active) ceiling. These preparatory calculations, e.g. the hierarchical break down from higher to lower regional level and from activity groups to individual activities, as well as the calculations of PRMD from PRMR (using APPTYPE) is carried out in a file called ‘//policy/policy.gms//’ as shown above.
  
 For most premiums in CAP there are ceilings, which if they are binding decrease the average amount of premiums actually paid (effective premium, PRME) per head or hectare. As discussed, due to the different kind of ceilings, the reduction of premiums and the treatment of PRME can only be done endogenously during the simulations depending on the simuled production patterns. For most premiums in CAP there are ceilings, which if they are binding decrease the average amount of premiums actually paid (effective premium, PRME) per head or hectare. As discussed, due to the different kind of ceilings, the reduction of premiums and the treatment of PRME can only be done endogenously during the simulations depending on the simuled production patterns.
  
-How is this problem solved in CAPRI? The effective premium (PRME) is exogenous during the optimisation of the supply model((There are exemptions for that rule, see below for the section on entitlements.)), but adjusted iteratively between the main model iterations. So, for most premium schemes, the premium level is constant in the objective function and hence the model does not realise that the marginal premium payment is zero as soon as the ceiling is reached. Technically, the iterative adjustment of the effective premiums PRME is handled in a file called ‘//policy\premcut.gms//’ for “premium cut”. That reasoning is correct as long as the ceiling is not farm specific.+How is this problem solved in CAPRI? The effective premium (PRME) is exogenous during the optimisation of the supply model((There are exemptions for that rule, see below for the section on entitlements.)), but adjusted iteratively between the main model iterations. So, for most premium schemes, the premium level is constant in the objective function and hence the model does not realise that the marginal premium payment is zero as soon as the ceiling is reached. Technically, the iterative adjustment of the effective premiums PRME is handled in a file called ‘//policy/premcut.gms//’ for “premium cut”. That reasoning is correct as long as the ceiling is not farm specific.
  
 In each iteration, once all regional model are solved, the program adds up total number of premium units (hectares or heads for which it is paid) that belong to each ceiling. In most cases this simply means summing up number of animals or hectares of the activities for which each premium applies. This is also multiplied with the declared amount PRMD to get the total payment which would be paid if it would not be cut. For each premium this is compared to the ceilings defined (total level with the level ceiling and total amount with the value ceiling) and a “cut factor” is calculated, which defines how much the premium has to be reduced in order to fit under all ceilings. Then PRMD is multiplied by this factor to get the effective premium (PRME) for the next iteration. In each iteration, once all regional model are solved, the program adds up total number of premium units (hectares or heads for which it is paid) that belong to each ceiling. In most cases this simply means summing up number of animals or hectares of the activities for which each premium applies. This is also multiplied with the declared amount PRMD to get the total payment which would be paid if it would not be cut. For each premium this is compared to the ceilings defined (total level with the level ceiling and total amount with the value ceiling) and a “cut factor” is calculated, which defines how much the premium has to be reduced in order to fit under all ceilings. Then PRMD is multiplied by this factor to get the effective premium (PRME) for the next iteration.
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 **Figure 16: General way of SFP implementation in CAPRI** **Figure 16: General way of SFP implementation in CAPRI**
  
-{{::figure16.png?600|}} \\ Source: own illustration+{{::figure_16.png?600|Source: own illustration}}
  
 In opposite to the reforms until Agenda 2000, there are hence in most cases not longer premium rates or individual ceilings in hectares found in legal texts. Rather, these are calculated by the model itself from the decoupled part of the “old” Mac Sharry and Agenda 2000 premiums which introduces additional complexity in the model code. In opposite to the reforms until Agenda 2000, there are hence in most cases not longer premium rates or individual ceilings in hectares found in legal texts. Rather, these are calculated by the model itself from the decoupled part of the “old” Mac Sharry and Agenda 2000 premiums which introduces additional complexity in the model code.
  
-Only an overall budget envelop is given covering all pillar I premiums of the EU CAP (“old” MacSharry and Agenda 2000 premiums, SPS premiums, article 63/68/69 premiums, etc.) per Member State nad per year on the position p_premDataE(MS,SIMY,"DPMTR","CEILVAL") in ‘//pol_input\mtr_hc.gms//’. Here MS refers to member states and SIMY to a certain year.+Only an overall budget envelop is given covering all pillar I premiums of the EU CAP (“old” MacSharry and Agenda 2000 premiums, SPS premiums, article 63/68/69 premiums, etc.) per Member State nad per year on the position p_premDataE(MS,SIMY,"DPMTR","CEILVAL") in ‘//pol_input/mtr_hc.gms//’. Here MS refers to member states and SIMY to a certain year.
  
 **Single area payment scheme (SAPS)** **Single area payment scheme (SAPS)**
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 From a technical viewpoint, the single-area premium scheme (SAPS) is the easiest to implement: From a technical viewpoint, the single-area premium scheme (SAPS) is the easiest to implement:
  
-{{::code_p165.png?600|}}+{{::code_p165.png?600}}
  
 As it defines a flat rate premiums per ha of agricultural land. The ceilings in values and thus the application rates per ha are step wise increased over time: As it defines a flat rate premiums per ha of agricultural land. The ceilings in values and thus the application rates per ha are step wise increased over time:
  
-{{:code_p165_2.png?600|}}+{{:code_p165_2.png?600}}
  
 To reach their full level in 2013 (EU 10) or 2016 (Bulgaria and Romania). To reach their full level in 2013 (EU 10) or 2016 (Bulgaria and Romania).
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 During that transition period where not yet the full EU premiums were paid out, the Member States had the right to paid up to certain limits to so-called complementary national direct payments (the list of schemes used in CAPRI was shown above). They also edited in a tabular format: During that transition period where not yet the full EU premiums were paid out, the Member States had the right to paid up to certain limits to so-called complementary national direct payments (the list of schemes used in CAPRI was shown above). They also edited in a tabular format:
  
-{{:code_p166.png?600|}}+{{:code_p166.png?600}}
  
 These top-ups have to be reduced towards the end of the period where the the  Pillar I premiums are phased in: These top-ups have to be reduced towards the end of the period where the the  Pillar I premiums are phased in:
  
-{{:code_p166_2.png?600|}}+{{:code_p166_2.png?600}}
  
 **Non-SAPS implementation** **Non-SAPS implementation**
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 The non-SAPS implementation of the Mid-Term Review package is far more demanding. First of all, the countries could, at least in the earlier years of the reform, keep certain percentages of specific premium scheme still coupled to production. These coupling factors are stored on the parameter p_couplPercent_E: The non-SAPS implementation of the Mid-Term Review package is far more demanding. First of all, the countries could, at least in the earlier years of the reform, keep certain percentages of specific premium scheme still coupled to production. These coupling factors are stored on the parameter p_couplPercent_E:
  
-{{:code_p166_3.png?600|}}+{{:code_p166_3.png?600}}
  
 The amount of payments which is not kept coupled is then paid out to different implementations of the MTR: The amount of payments which is not kept coupled is then paid out to different implementations of the MTR:
   * Regional implementation where all arable crops (PGARAB) \\   * Regional implementation where all arable crops (PGARAB) \\
-{{::code_p167.png?600|}}+{{::code_p167.png?600}}
   * And permanent grass land (PGGRAS) is eligble \\   * And permanent grass land (PGGRAS) is eligble \\
-{{:code_p167_2.png?600|}}+{{:code_p167_2.png?600}}
   * The historic implementation \\   * The historic implementation \\
-{{:code_p167_3.png?600|}}+{{:code_p167_3.png?600}}
  
 The exact set member ship depends on the year. The distribution shares which map the decoupled part of the premiums received under the Agenda package (see above) to these implementation schemes are edited on the Table “p_premToDDTarget_E” The exact set member ship depends on the year. The distribution shares which map the decoupled part of the premiums received under the Agenda package (see above) to these implementation schemes are edited on the Table “p_premToDDTarget_E”
  
-{{:code_p167_4.png?600|}}+{{:code_p167_4.png?600}}
  
-That information is the basis to define regional premium envelops (= CEILVAL) for the different Member states. That is a rather complex program (‘//policy\calc_mtr.gms//’).+That information is the basis to define regional premium envelops (= CEILVAL) for the different Member states. That is a rather complex program (‘//policy/calc_mtr.gms//’).
 A first key statement defines the //remaining budget envelops for the still coupled payments//. It takes the minimum of the existing ceiling values for that scheme (CEILVAL) or the total payments paid out times the modulation factors and multiplies it with the coupling degree. A first key statement defines the //remaining budget envelops for the still coupled payments//. It takes the minimum of the existing ceiling values for that scheme (CEILVAL) or the total payments paid out times the modulation factors and multiplies it with the coupling degree.
  
-{{:code_p167_5.png?600|}}+{{:code_p167_5.png?600}}
  
 There two other factors: There two other factors:
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 The part which is not longer coupled goes into the decoupled schemes: The part which is not longer coupled goes into the decoupled schemes:
-{{:code_p168.png?600|}}+{{:code_p168.png?600}}
  
 The total budget for the new MTR schemes is derived from the summation of all the old Agenda premiums. The total payments under a scheme such as the Grandes Cultures schemes are corrected for any possible remaining coupled payments: The total budget for the new MTR schemes is derived from the summation of all the old Agenda premiums. The total payments under a scheme such as the Grandes Cultures schemes are corrected for any possible remaining coupled payments:
  
-{{:code_p168_2.png?400|}}+{{:code_p168_2.png?400}}
  
 After that, a possible share going into the greening payment (from 2014) is deducted: After that, a possible share going into the greening payment (from 2014) is deducted:
  
-{{:code_p168_3.png?400|}}+{{:code_p168_3.png?400}}
  
 And, finally, a factor is applied which lines up the total historic payments as defined from the CAPRI data and premium schemes in that Member State with the total MTR envelop: And, finally, a factor is applied which lines up the total historic payments as defined from the CAPRI data and premium schemes in that Member State with the total MTR envelop:
  
-{{:code_p168_4.png?400|}}+{{:code_p168_4.png?400}}
  
 That sum if then distributed to the relevant MTR implementation scheme according to the distribution keys defined above: That sum if then distributed to the relevant MTR implementation scheme according to the distribution keys defined above:
  
-{{:code_p168_5.png?600|}}+{{:code_p168_5.png?600}}
  
-These calculation require that first the total premiums received in the history period are calculated which is done in ‘//policy\calc_mtr_top.gms//’.+These calculation require that first the total premiums received in the history period are calculated which is done in ‘//policy/calc_mtr_top.gms//’.
  
 ===CAP 2014-2020=== ===CAP 2014-2020===
  
-From 2014 onwards, a new agricultural policy entered into force. The key elements of the policy were (i) convergence of payment rates between member states and farmers within member states, (ii) the expansion of the option to use coupled support beyond the previous articles 68/69, and (iii) the introduction of three “greening requirements”. These elements were introduced into CAPRI, and their use can be inspected in the commonly used baseline policy file “gams\pol_input\cap_after_2014\ref.gms”, the entire content of which is shown below:+From 2014 onwards, a new agricultural policy entered into force. The key elements of the policy were (i) convergence of payment rates between member states and farmers within member states, (ii) the expansion of the option to use coupled support beyond the previous articles 68/69, and (iii) the introduction of three “greening requirements”. These elements were introduced into CAPRI, and their use can be inspected in the commonly used baseline policy file “gams/pol_input/cap_after_2014/ref.gms”, the entire content of which is shown below:
  
-{{:code_p169.png?600|}}+{{:code_p169.png?600}}
  
-Since the mechanisms behind each of the three elements is somewhat complex, the file relies on include files to define each of the three components. The include files are stored in the scenario directory (gams\scen) of the CAPRI system, and which particular include files to use is indicated by the string variables ($setGlobal) in the first three code lines. The actual logic of the policy file, also the inclusion of the indicated three files, takes place in the file included in the final line, referred to as the base scenario file.+Since the mechanisms behind each of the three elements is somewhat complex, the file relies on include files to define each of the three components. The include files are stored in the scenario directory (gams/scen) of the CAPRI system, and which particular include files to use is indicated by the string variables ($setGlobal) in the first three code lines. The actual logic of the policy file, also the inclusion of the indicated three files, takes place in the file included in the final line, referred to as the base scenario file.
  
-//Convergence// between member states is set by adjusting the total budget of the CAP first pillar. Regarding the convergence of payment values per entitlement (IUVs, for Individual Unit Values) inside countries, the regulation allows ample room for national customization. Countries define the regions within which convergence occurs, the end year by which convergence shall be achieved, any remaining maximum span for the IUVs after convergence, and the mathematical formula to use for reducing high IUVs and increasing low ones. The file gams\scen\premiums\bps_convergence.gms defines the options chosen by member states in 2014.+//Convergence// between member states is set by adjusting the total budget of the CAP first pillar. Regarding the convergence of payment values per entitlement (IUVs, for Individual Unit Values) inside countries, the regulation allows ample room for national customization. Countries define the regions within which convergence occurs, the end year by which convergence shall be achieved, any remaining maximum span for the IUVs after convergence, and the mathematical formula to use for reducing high IUVs and increasing low ones. The file gams/scen/premiums/bps_convergence.gms defines the options chosen by member states in 2014.
  
-{{:code_p169_2.png?600|}}+{{:code_p169_2.png?600}}
  
 Two different uses of the convergence mechanism are illustrated by Austria and Greece, which apply very different models. Austria applies the full convergence using a linear model over time, with the same target payment rate in all of Austria. The convergence should be complete in 2019. This is obtained by assigning all Austrian regions to one generic “BPS-region”, for convenience the first one, called “rbps1”. Since the convergence mechanism later on works per member state, it is no problem that rbps1 is also used for e.g. the Netherlands. Then, the convergence option is set to “bps_linear” and the target year to 2019. Finally, the two parameters defining the rate of the final convergence are set, or, if you like, the width at the end of the convergence funnel and the handling of payments outside of that funnel. For Austria, the parameters are both set to “1”, which means that all farms will get exactly the same payments per hectare after convergence is complete in 2019. Two different uses of the convergence mechanism are illustrated by Austria and Greece, which apply very different models. Austria applies the full convergence using a linear model over time, with the same target payment rate in all of Austria. The convergence should be complete in 2019. This is obtained by assigning all Austrian regions to one generic “BPS-region”, for convenience the first one, called “rbps1”. Since the convergence mechanism later on works per member state, it is no problem that rbps1 is also used for e.g. the Netherlands. Then, the convergence option is set to “bps_linear” and the target year to 2019. Finally, the two parameters defining the rate of the final convergence are set, or, if you like, the width at the end of the convergence funnel and the handling of payments outside of that funnel. For Austria, the parameters are both set to “1”, which means that all farms will get exactly the same payments per hectare after convergence is complete in 2019.
  
-{{:code_p169_3.png?600|}}+{{:code_p169_3.png?600}}
  
 Greece applies different models for different types of regions, depending on the character of agriculture in the region. We approximate this in CAPRI by classifying the NUTS2-regions according to the shares of arable land, grass land and permanent crops in a historical year (2008). Based on those shares, three BPS-regions are created, within each of which the same convergence model is applied. The convergence is linear, but with the additional 30-percent-rule applied, defining that no farm (supply model region) should get more than 30 percent higher payments per hectare than the average of the BPS-region. Convergence proceeds up to the year 2019, and in each year, the lower limit for convergence, expressed as a share of the averge of the BPS-region, is set to 90%. The lower limit defines whether a farm needs convergence or not. Farms above the lower limit will get the same payments per unit as before, but for farms below the limit, the final option “p_bps_tunnel_gap_closure” kicks in, and defines what share of the gap to the lower convergence limit should be closed. For Greece, this value is set to 1/3, implying that for a farm receiving less than 90% of the average payment in the BPS-region, 1/3 of the gap shall be closed. The increased premiums are financed by a linear reduction of the payments to all farms with payments above the average payment, while also capping the highest premiums to be no more than 30% higher than the regional average. Greece applies different models for different types of regions, depending on the character of agriculture in the region. We approximate this in CAPRI by classifying the NUTS2-regions according to the shares of arable land, grass land and permanent crops in a historical year (2008). Based on those shares, three BPS-regions are created, within each of which the same convergence model is applied. The convergence is linear, but with the additional 30-percent-rule applied, defining that no farm (supply model region) should get more than 30 percent higher payments per hectare than the average of the BPS-region. Convergence proceeds up to the year 2019, and in each year, the lower limit for convergence, expressed as a share of the averge of the BPS-region, is set to 90%. The lower limit defines whether a farm needs convergence or not. Farms above the lower limit will get the same payments per unit as before, but for farms below the limit, the final option “p_bps_tunnel_gap_closure” kicks in, and defines what share of the gap to the lower convergence limit should be closed. For Greece, this value is set to 1/3, implying that for a farm receiving less than 90% of the average payment in the BPS-region, 1/3 of the gap shall be closed. The increased premiums are financed by a linear reduction of the payments to all farms with payments above the average payment, while also capping the highest premiums to be no more than 30% higher than the regional average.
  
-{{:code_p170.png?600|}}+{{:code_p170.png?600}}
  
-The code implementing the logic behind these various settings is generic and found in the file “gams\policy\implement_bps.gms”. The result is a payment per region, defined using the general premium mechanism of CAPRI, that is called “dp_bps” and with the eligible activity list “pgsaps”. The application type is “perLevl” and the budget is set on national level in the base scenario file “gams\scen\base_scenarios\cap_2014_2020.gms”.+The code implementing the logic behind these various settings is generic and found in the file “gams/policy/implement_bps.gms”. The result is a payment per region, defined using the general premium mechanism of CAPRI, that is called “dp_bps” and with the eligible activity list “pgsaps”. The application type is “perLevl” and the budget is set on national level in the base scenario file “gams/scen/base_scenarios/cap_2014_2020.gms”.
  
-//Voluntary Coupled Support// is defined using the standard premium mechanisms of CAPRI, based on notifications received from the European Commission. We have interpreted the notified target activities in terms of CAPRI activities, and set budget ceilings and nominal amounts in the file “gams\scen\premiums\coupling\cap_2013_2020_vcs.gms”.+//Voluntary Coupled Support// is defined using the standard premium mechanisms of CAPRI, based on notifications received from the European Commission. We have interpreted the notified target activities in terms of CAPRI activities, and set budget ceilings and nominal amounts in the file “gams/scen/premiums/coupling/cap_2013_2020_vcs.gms”.
  
-The //Greening Measures// can be steered by the modeller. Even though the greening in itself is complex in implementation, the choices open to the CAPRI modeller are limited. The standard greening policy switches can be inspected in the file “gams\scen\premiums\greening\cap_2013_2020_greening.gms”:+The //Greening Measures// can be steered by the modeller. Even though the greening in itself is complex in implementation, the choices open to the CAPRI modeller are limited. The standard greening policy switches can be inspected in the file “gams/scen/premiums/greening/cap_2013_2020_greening.gms”:
  
-{{:code_p171.png?600|}}+{{:code_p171.png?600}}
  
 The first statement defines the share of the national pillar 1 envelope that is dedicated to the “greening top-up”. By default, this is 30%. Then, a set of active greening measures is populated. There are three options available, and by default, they are all active: The first statement defines the share of the national pillar 1 envelope that is dedicated to the “greening top-up”. By default, this is 30%. Then, a set of active greening measures is populated. There are three options available, and by default, they are all active:
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   * A share of land must be allocated to certain activities counting as “ecological set-aside”.    * A share of land must be allocated to certain activities counting as “ecological set-aside”. 
  
-The shares of activities eligible as ecological set-aside is then defined in the concluding parameter definition in the file. The set-aside rate itself is defined as a string variable “$setglobal greening_setasiderate 5”, defining it to be 5% by default. The three greening restrictions are implemented as constraints in the supply models. The greening top-up is implemented as a standard CAPRI premium called DPGREEN. The logic behind the greening restrictions is activated in the include file “//policy\define_greening_limits.gms//”.+The shares of activities eligible as ecological set-aside is then defined in the concluding parameter definition in the file. The set-aside rate itself is defined as a string variable “$setglobal greening_setasiderate 5”, defining it to be 5% by default. The three greening restrictions are implemented as constraints in the supply models. The greening top-up is implemented as a standard CAPRI premium called DPGREEN. The logic behind the greening restrictions is activated in the include file “//policy/define_greening_limits.gms//”.
    
 The CAP 2014-2020 also contains three more payment schemes: Support to young farmers, support to smaller farms (first hectares) and support to areas with natural constraints (ANC). These payment schemes, with their associated budgets, are defined in the base scenario file. The CAP 2014-2020 also contains three more payment schemes: Support to young farmers, support to smaller farms (first hectares) and support to areas with natural constraints (ANC). These payment schemes, with their associated budgets, are defined in the base scenario file.
  
-The following figure summarizes the logic of the CAP 2014-2020 reference policy as implemented in the CAPRI policy module in the policy file //pol_input\cap_after_2014\ref.gms//.+The following figure summarizes the logic of the CAP 2014-2020 reference policy as implemented in the CAPRI policy module in the policy file //pol_input/cap_after_20147ref.gms//.
  
 **Figure 17: The logic of the CAP 2014-2020 reference policy as implemented in the CAPRI policy module** **Figure 17: The logic of the CAP 2014-2020 reference policy as implemented in the CAPRI policy module**
  
-{{:figure17.png?600|}} \\ Source: own illustration+{{:figure_17.png?600|Source: own illustration}}
  
 ===Tradable Single Premium Scheme entitlements=== ===Tradable Single Premium Scheme entitlements===
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 //Switching on the entitlement trade// //Switching on the entitlement trade//
  
-The trade module is implemented in the file ‘//policy\prem_entl_trade.gms//’ which is included on demand in capmod and called in each iteration+The trade module is implemented in the file ‘//policy/prem_entl_trade.gms//’ which is included on demand in capmod and called in each iteration
  
-{{::code_p173.png?600|}}+{{::code_p173.png?600}}
  
-By default, the entitlement trade is switched OFF in the general settings file of CAPMOD, called gams\capmod\set_global_variables.gms+By default, the entitlement trade is switched OFF in the general settings file of CAPMOD, called gams/capmod/set_global_variables.gms
  
-{{:code_p173_2.png?600|}}+{{:code_p173_2.png?600}}
  
 The basic idea of the module is very simple: shift entitlements from farm type or regions which unused entitlements to other farm types or regions which have an economic rent on their entitlements. The trading entities should receive the very same premium on the entitlement for the current implementation in the code. One should hence set the trade level according to the regional level for which flat rate premiums are implemented as shown below in an example: The basic idea of the module is very simple: shift entitlements from farm type or regions which unused entitlements to other farm types or regions which have an economic rent on their entitlements. The trading entities should receive the very same premium on the entitlement for the current implementation in the code. One should hence set the trade level according to the regional level for which flat rate premiums are implemented as shown below in an example:
  
-{{:code_p173_3.png?600|}}+{{:code_p173_3.png?600}}
  
 //How the entitlement trade works// //How the entitlement trade works//
  
-The following code pieces are taken from ‘//policy\prem_entl_trade.gms//’. In a first step, the demand of entitlements is determined. The dual value does only provide an indication that entitlements are scarce, but not how many additional entitlements are needed. Accordingly, first, the average marginal value of the different type of entitlements is determined:+The following code pieces are taken from ‘//policy/prem_entl_trade.gms//’. In a first step, the demand of entitlements is determined. The dual value does only provide an indication that entitlements are scarce, but not how many additional entitlements are needed. Accordingly, first, the average marginal value of the different type of entitlements is determined:
  
-{{:code_p173_4.png?600|}}+{{:code_p173_4.png?600}}
  
 From these a maximum of 10% is defined as the demand in each iteration: From these a maximum of 10% is defined as the demand in each iteration:
  
-{{:code_p173_5.png?600|}}+{{:code_p173_5.png?600}}
  
 In order to take differences in the marginal returns into account, an indicator based on the squared value is used: In order to take differences in the marginal returns into account, an indicator based on the squared value is used:
  
-{{:code_173_6.png?600|}}+{{:code_173_6.png?600}}
  
 It serves as the distribution key of unused entitlements, which are determined as follows: It serves as the distribution key of unused entitlements, which are determined as follows:
  
-{{:code_173_7.png?600|}}+{{:code_173_7.png?600}}
  
 Next, the number of unused entitlements is stored: Next, the number of unused entitlements is stored:
  
-{{:code_p174.png?600|}}+{{:code_p174.png?600}}
  
 As seen, only 50% of the unused entitlements are released in any iteration. We next determine the size of the markets, i.e. total demand and supply: As seen, only 50% of the unused entitlements are released in any iteration. We next determine the size of the markets, i.e. total demand and supply:
  
-{{:code_174_2.png?600|}}+{{:code_174_2.png?600}}
  
 The supply is then distributed according to the squared value of the individual demanders The supply is then distributed according to the squared value of the individual demanders
  
-{{:code_p174_3.png?600|}}+{{:code_p174_3.png?600}}
  
 //An example printout// //An example printout//
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 The following code snippet shows an example for a NUTS2 regions and the related farm types for a test run for Greece without the market module: The following code snippet shows an example for a NUTS2 regions and the related farm types for a test run for Greece without the market module:
  
-{{:code_p174_4.png?600|}}+{{:code_p174_4.png?600}}
  
 As seen from above, we have two farm types in the starting situation which acts as demanders, i.e. have a marginal value on their entitlements (016 and 999). Their marginal value on the entitlement is quite high in the starting situation with > 125 € / entitlement. We have also a total of 3639 ha after the first round of unused entitlements which can be sold to the demanders. Distributing half of them (ca. 1800 ha) to the two demanders reduces the marginal value of the entitlements already below 95€, the next round distributed ca. 900 ha and brings the price down to 50€ until in the last round almost nothing is left for distribution and the value of the entitlements has dropped below 10€. The reader should note the trade is not yet taking into account in the income calculation of the farm types. As seen from above, we have two farm types in the starting situation which acts as demanders, i.e. have a marginal value on their entitlements (016 and 999). Their marginal value on the entitlement is quite high in the starting situation with > 125 € / entitlement. We have also a total of 3639 ha after the first round of unused entitlements which can be sold to the demanders. Distributing half of them (ca. 1800 ha) to the two demanders reduces the marginal value of the entitlements already below 95€, the next round distributed ca. 900 ha and brings the price down to 50€ until in the last round almost nothing is left for distribution and the value of the entitlements has dropped below 10€. The reader should note the trade is not yet taking into account in the income calculation of the farm types.
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 p_aeLfa(ms,tf8): The probability of a farm of type tf8 having agri-environmental support conditional on the farm being in an LFA region or not, computed based on the FADN sample. p_aeLfa(ms,tf8): The probability of a farm of type tf8 having agri-environmental support conditional on the farm being in an LFA region or not, computed based on the FADN sample.
    
-Then, the payment rate for each region is set in proportion to the weighted share of farms likely to have some AE support, predicted by the regional share of each land class (grass, arable) being classified as LFA in each region times the share of farms in/out of LFA having AE-support in the national FADN sample. The computation takes place in policy\rd_logic.gms:+Then, the payment rate for each region is set in proportion to the weighted share of farms likely to have some AE support, predicted by the regional share of each land class (grass, arable) being classified as LFA in each region times the share of farms in/out of LFA having AE-support in the national FADN sample. The computation takes place in policy/rd_logic.gms:
  
-{{::code_p179.png?600|}}+{{::code_p179.png?600}}
  
 Note that the code does not know how high the absolute level of payments shall be for each region, but allocates the relative levels. Then, the national ceiling for AE payments are applied to adjust all regional payments until the ceiling is respected.  Note that the code does not know how high the absolute level of payments shall be for each region, but allocates the relative levels. Then, the national ceiling for AE payments are applied to adjust all regional payments until the ceiling is respected. 
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 Finally, an extensification effect to the AE payments is introduced using the possibility to make technological variants differently eligible. Finally, an extensification effect to the AE payments is introduced using the possibility to make technological variants differently eligible.
  
-{{:code_p179_2.png?600|}} \\ +{{:code_p179_2.png?600}} 
-{{:code_p180.png?600|}}+ 
 +{{:code_p180.png?600}}
  
 ====Co-financing rates, assignment of premiums to pillars, WTO boxes and PSE-types==== ====Co-financing rates, assignment of premiums to pillars, WTO boxes and PSE-types====
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 **EU and national budget contribution** **EU and national budget contribution**
  
-The reporting part of the system was expanded to account for (co-)financing rates of the different schemes, so that contributions from EU and national budgets can be differentiated. The underlying factors are currently defined in //‘policy\policy_sets.gms’//:+The reporting part of the system was expanded to account for (co-)financing rates of the different schemes, so that contributions from EU and national budgets can be differentiated. The underlying factors are currently defined in //‘policy/policy_sets.gms’//:
  
-{{:code_p180_2.png?600|}}+{{:code_p180_2.png?600}}
  
 **PSEs** **PSEs**
  
-The mapping to the PSE-types is defined in //‘policy\policy_sets.gms’//:+The mapping to the PSE-types is defined in //‘policy/policy_sets.gms’//:
  
-{{:code_p180_3.png?600|}}+{{:code_p180_3.png?600}}
  
 **WTO boxes** **WTO boxes**
  
-In a similar fashion, the premiums are allocated to the WTO boxes. The following payments are allocated to the green box (‘//policy\policy_sets.gms’//):+In a similar fashion, the premiums are allocated to the WTO boxes. The following payments are allocated to the green box (‘//policy/policy_sets.gms’//):
  
-{{:code_p181.png?600|}}+{{:code_p181.png?600}}
  
 The blue box, i.e.g payments under supply control or only paid up to certain upper limits, is defined as along with remaining amber box payments in Norway: The blue box, i.e.g payments under supply control or only paid up to certain upper limits, is defined as along with remaining amber box payments in Norway:
  
-{{:code_p182.png?600|}}+{{:code_p182.png?600}}
  
-Currently, the following budget categories are supported (see ‘//sets.gms//’ and ‘//policy\policy_sets.gms//’):+Currently, the following budget categories are supported (see ‘//sets.gms//’ and ‘//policy/policy_sets.gms//’):
  
 {{:code_p182_2.png?600}} {{:code_p182_2.png?600}}
  
-In ‘//reports\feoga.gms//’, these categories are first aggregated for each activities from actual schemes (“PRME” = actual payment rate, p_budToPsdpay: distribution key):+In ‘//reports/feoga.gms//’, these categories are first aggregated for each activities from actual schemes (“PRME” = actual payment rate, p_budToPsdpay: distribution key):
  
 {{:code_p182_3.png?600}} {{:code_p182_3.png?600}}
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 ====Behavioural equations for supply, feed demand and land markets==== ====Behavioural equations for supply, feed demand and land markets====
  
-The definition of the market model can be found in //‘arm\market_model.gms’//+The definition of the market model can be found in //‘arm/market_model.gms’//
  
 ===Agricultural supply=== ===Agricultural supply===
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 **Figure 18: Land supply curve examples** **Figure 18: Land supply curve examples**
  
-{{::figure18.png?600|}} \\ Source: own calculations+{{::figure_18.png?600|Source: own calculations}} 
  
 In order to parameterize the land demand function, information about yield and supply elasticities is used. The marginal reaction of land to a marginal change in one of the prices is defined as the total supply effect minus the yield effect: In order to parameterize the land demand function, information about yield and supply elasticities is used. The marginal reaction of land to a marginal change in one of the prices is defined as the total supply effect minus the yield effect:
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 The following table shows the substitution elasticities used for the different product groups. Compared to most other studies, we opted for a rather elastic substitution between products from different origins, as agricultural products are generally more uniform then aggregated product groups, as they can be found e.g. in CGE models. The following table shows the substitution elasticities used for the different product groups. Compared to most other studies, we opted for a rather elastic substitution between products from different origins, as agricultural products are generally more uniform then aggregated product groups, as they can be found e.g. in CGE models.
  
-**Table 28: Substitution elasticities for the Armington CES utility aggregators((A sensitivity analysis on those elasticities is given in section [[Sensitivity analysis]]))**+**Table 28: Substitution elasticities for the Armington CES utility aggregators((A sensitivity analysis on those elasticities is given in section [[scenario simulation#Sensitivity analysis]]))**
  
 ^Product (group) ^Substitution elasticity between domestic sales and imports  ^Substitution elasticity between import flows ^ ^Product (group) ^Substitution elasticity between domestic sales and imports  ^Substitution elasticity between import flows ^
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 |Other fruits |  3 |  3  | |Other fruits |  3 |  3  |
 |Sugar| 12  | 12  | |Sugar| 12  | 12  |
-|All other products| 8 |  10  | \\Source: own calculations +|All other products| 8 |  10  |  
 +Source: own calculations
 There are some specific settings, such as a value of 2 for rice and the EU15, 2.5 respectively 5 for Japan to account for its specific tariff system, as well as some lower values for EU’s Mediterrean partner countries. There are some specific settings, such as a value of 2 for rice and the EU15, 2.5 respectively 5 for Japan to account for its specific tariff system, as well as some lower values for EU’s Mediterrean partner countries.
  
 **Figure 19: Two-stage Armington System** **Figure 19: Two-stage Armington System**
  
-{{::figure_19.png?600|}} \\ Soruce: Capri Modelling System+{{::figure_19.png?600|Source: Capri Modelling System}}
  
-The above “primal” formulation of the Armington approach in terms of quantity aggregators turned out numerically less stable in the implementaiotn than the dual representation in terms of price aggregators. The Armington approach suffers from two important shortcomings. First of all, a calibration to a zero flow is impossible so that only observed import flows react to policy changes while all others are fixed at zero level. For most simulation runs, that shortcoming should not be serious. If it is relevant, it may be overcome using the modified Armington approach as explained in Section [[Market module for agricultural outputs#Price linkages]]. +The above “primal” formulation of the Armington approach in terms of quantity aggregators turned out numerically less stable in the implementaiotn than the dual representation in terms of price aggregators. The Armington approach suffers from two important shortcomings. First of all, a calibration to a zero flow is impossible so that only observed import flows react to policy changes while all others are fixed at zero level. For most simulation runs, that shortcoming should not be serious. If it is relevant, it may be overcome using the modified Armington approach as explained in Section [[scenario simulation#Price linkages]]. 
  
 Secondly, the Armington aggregator defines a utility aggregate and not a physical quantity. That second problem is healed by re-correcting in the post model part to physical quantities. Little empirical work can be found regarding the estimation of the functional parameters of Armington systems. Hence, substitution elasticities were chosen as to reflect product properties as shown above. Secondly, the Armington aggregator defines a utility aggregate and not a physical quantity. That second problem is healed by re-correcting in the post model part to physical quantities. Little empirical work can be found regarding the estimation of the functional parameters of Armington systems. Hence, substitution elasticities were chosen as to reflect product properties as shown above.
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 \end{equation} \end{equation}
  
-{{::code_p194.png?600|}}+{{::code_p194.png?600}}
  
 The reader is reminded that currently, the PSE data are not introduced in the system with two exceptions: carbon price scenarios involve negative PSEi amounts and Swiss agricultural policies are involving land subsidies entered. The reader is reminded that currently, the PSE data are not introduced in the system with two exceptions: carbon price scenarios involve negative PSEi amounts and Swiss agricultural policies are involving land subsidies entered.
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 **Figure 20: Witzke et al. calibration, two-goods case** **Figure 20: Witzke et al. calibration, two-goods case**
  
-{{::figure20.png?600|}} \\ Source: Witzhe et al 2005+{{::figure_20.png?600|Source: Witzhe et al 2005}}
  
 The additional commitment parameter involves another degree of freedom that needs to be eliminated with additional information. During the calibration this is provided by the expected imports from region 2 at the second hypothetical set of relative prices. Following the dual approach, the lower Armington nest is represented with Armington share-equations and with equations for the composite price indexes: The additional commitment parameter involves another degree of freedom that needs to be eliminated with additional information. During the calibration this is provided by the expected imports from region 2 at the second hypothetical set of relative prices. Following the dual approach, the lower Armington nest is represented with Armington share-equations and with equations for the composite price indexes:
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 **Code implementation in the CAPRI market model** **Code implementation in the CAPRI market model**
  
-The Witzke et al. approach is implemented in a modular fashion in the CAPRI market model. The calibration of the modified Armington lower nest can be switched on or off through a designated button on the CAPRI GUI  (see the next Figure). In order not to interfere with the work of other CAPRI users, a specific GUI is created for the project that can be started by running GUI\capri64modarm.bat.+The Witzke et al. approach is implemented in a modular fashion in the CAPRI market model. The calibration of the modified Armington lower nest can be switched on or off through a designated button on the CAPRI GUI  (see the next Figure). In order not to interfere with the work of other CAPRI users, a specific GUI is created for the project that can be started by running GUI/capri64modarm.bat.
  
 **Figure 21: GUI Option for the non-homothetic Armington system** **Figure 21: GUI Option for the non-homothetic Armington system**
  
-{{::figure21.png?600|}}+{{::figure_21.png?600}}
  
-The calibration of the non-homothetic Armington demand system does not require a full re-calibration of the complete CAPRI modelling system; it can be found under the workstep “Run scenario”, task: “Run scenario with market model”. Technically, the calibration modifies the simini\sim_ini.gdx file that contains the necessary starting parameters for a CAPRI simulation: if the above GUI option is selected then the existing sim_ini.gdx file is automatically deleted and the create_sim_ini CAPRI module is called. This is all steered in the main capmod.gms file by a specific GAMS setglobal variable called modArmington:+The calibration of the non-homothetic Armington demand system does not require a full re-calibration of the complete CAPRI modelling system; it can be found under the workstep “Run scenario”, task: “Run scenario with market model”. Technically, the calibration modifies the simini/sim_ini.gdx file that contains the necessary starting parameters for a CAPRI simulation: if the above GUI option is selected then the existing sim_ini.gdx file is automatically deleted and the create_sim_ini CAPRI module is called. This is all steered in the main capmod.gms file by a specific GAMS setglobal variable called modArmington:
  
-{{:code_p196.png?600|}}+{{:code_p196.png?600}}
  
-The calibration model itself is called directly by the arm\market1.gms file:+The calibration model itself is called directly by the arm/market1.gms file:
  
-{{:code_p196_2.jpg?600|}}+{{:code_p196_2.jpg?600}}
  
-The file arm\modArmington.gms file contains the definition of the calibration model and executes the calibration itself. The calibration model simply consists of Armington share equations (importShares_) and price index equations (arm2PriceAgg _), following the approach presented above.+The file arm/modArmington.gms file contains the definition of the calibration model and executes the calibration itself. The calibration model simply consists of Armington share equations (importShares_) and price index equations (arm2PriceAgg _), following the approach presented above.
  
-{{:code_p197.jpg?600|}}+{{:code_p197.jpg?600}}
  
-The share- and price index equations of the calibration model are similar to those in the CAPRI market model, but extended with an additional dimension called ‘cal_points’. The additional dimension indicates whether the equations correspond to the observed or the expected calibration points. The arm\modArmington.gms file calculates the expected price/quantity framework necessary for the Witzke et al. approach. The data input for this calculation is currently implemented in the scenario file in order to allow for a compact definition of baseline and scenario assumptions. The test scenario for the Witzke et al. demand system assumes the following expected EU poultry imports from the US under a hypothetical import price:+The share- and price index equations of the calibration model are similar to those in the CAPRI market model, but extended with an additional dimension called ‘cal_points’. The additional dimension indicates whether the equations correspond to the observed or the expected calibration points. The arm/modArmington.gms file calculates the expected price/quantity framework necessary for the Witzke et al. approach. The data input for this calculation is currently implemented in the scenario file in order to allow for a compact definition of baseline and scenario assumptions. The test scenario for the Witzke et al. demand system assumes the following expected EU poultry imports from the US under a hypothetical import price:
  
-{{:code_p197_2.jpg?600|}}+{{:code_p197_2.jpg?600}}
  
 The calibrated share equations and the commitment terms are then stored in the appropriate parameters and later picked up by the market model. The relevant equations of the market model, therefore, also had to be modified. For example, the Armington share equations of the CAPRI market model are extended with the commitment term (p_arm2Commit = \(\mu\)): The calibrated share equations and the commitment terms are then stored in the appropriate parameters and later picked up by the market model. The relevant equations of the market model, therefore, also had to be modified. For example, the Armington share equations of the CAPRI market model are extended with the commitment term (p_arm2Commit = \(\mu\)):
  
-{{:code_p197_3.jpg?600|}}+{{:code_p197_3.jpg?600}}
  
-The calibration of the full market model is tested by solving the model at trend values in the CAPRI module arm\prep_market.gms. This module also had to be modified in order to initialize the modified Armington system appropriately. The modifications mostly affect the trade flows, import prices and trade policy instruments.+The calibration of the full market model is tested by solving the model at trend values in the CAPRI module arm/prep_market.gms. This module also had to be modified in order to initialize the modified Armington system appropriately. The modifications mostly affect the trade flows, import prices and trade policy instruments.
  
 If properly calibrated, the modified Armington system with the test reference scenario should replicate the standard baseline results. It means, for example, that emerging trade flows being zero in the baseline will remain zero in the reference run and only become positive under specific scenario assumptions. If properly calibrated, the modified Armington system with the test reference scenario should replicate the standard baseline results. It means, for example, that emerging trade flows being zero in the baseline will remain zero in the reference run and only become positive under specific scenario assumptions.
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 **Figure 22: Construction of the ethanol market implemented in CAPRI** FIXME **Figure 22: Construction of the ethanol market implemented in CAPRI** FIXME
  
-{{::figure_22.png?600|}} \\ Soruce: Capri Modelling System+{{::figure_22.png?600|Source: Capri Modelling System}}
  
 Basically two biofuel product markets are covered in the model; Ethanol (BIOE) and Biodiesel (BIOD). For total domestic ethanol production, three technology pathways are covered; 1st generation ethanol (BIOFE) - differentiated in wheat, barley, rye, oats, maize, other cereals, sugar and table wine, 2nd generation ethanol (SECG), and non-agricultural ethanol (NAGR).  Basically two biofuel product markets are covered in the model; Ethanol (BIOE) and Biodiesel (BIOD). For total domestic ethanol production, three technology pathways are covered; 1st generation ethanol (BIOFE) - differentiated in wheat, barley, rye, oats, maize, other cereals, sugar and table wine, 2nd generation ethanol (SECG), and non-agricultural ethanol (NAGR). 
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 **Figure 23: Construction of the biodiesel market implemented in CAPRI** **Figure 23: Construction of the biodiesel market implemented in CAPRI**
  
-{{:figure_23.png?600|}} \\ Soruce: Capri Modelling System+{{:figure_23.png?600|Source: Capri Modelling System}} 
  
 The figure below provides a schematic diagram of the process of 2nd generation biofuel production in CAPRI. Two different product aggregates are introduced in the CAPRI product list to cover feedstock for 2nd generation biofuel processing: The figure below provides a schematic diagram of the process of 2nd generation biofuel production in CAPRI. Two different product aggregates are introduced in the CAPRI product list to cover feedstock for 2nd generation biofuel processing:
Line 1301: Line 1305:
 **Figure 24: Consideration of 2nd generation biofuel production and related feedstock** **Figure 24: Consideration of 2nd generation biofuel production and related feedstock**
  
-{{::figure_24.png?600|}} \\ Soruce: own illustration+{{::figure_24.png?600|Source: own illustration}} 
  
 ===Biofuel supply and feedstock demand=== ===Biofuel supply and feedstock demand===
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 **Figure 25: Biofuel supply function in France** **Figure 25: Biofuel supply function in France**
  
-{{::figure_25.png?600|}} \\ Source: own calculations+{{::figure_25.png?600|Source: own calculations}} 
  
 The supply of by products is directly linked to the first generation biofuel output: The supply of by products is directly linked to the first generation biofuel output:
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 **Figure 25: Biofuel demand share function in France** **Figure 25: Biofuel demand share function in France**
  
-{{::figure_26.png?600|}} \\ Source: own calculations+{{::figure_26.png?600|Source: own calculations}}
  
 Total biofuel demand (\(d_{r,xb}\)) is then derived by multiplying this share to the exogenous total fuel demand (\(d_{r,f}\)): Total biofuel demand (\(d_{r,xb}\)) is then derived by multiplying this share to the exogenous total fuel demand (\(d_{r,f}\)):
Line 1419: Line 1423:
 **Table 29: Overview of pillar II measures modelled in CAPRI** FIXME **Table 29: Overview of pillar II measures modelled in CAPRI** FIXME
  
-{{::table_29.png?350|}} \\ Source: Own calculation based on PRIMES 2009+{{::table_29.png?350|Source: Own calculation based on PRIMES 2009}} 
  
 **Biofuel Trade** **Biofuel Trade**
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 ===Calibration of the biofuel system=== ===Calibration of the biofuel system===
  
-So far, only the general form of the biofuel supply and demand functions where derived, but without any adjustments, they won’t reproduce the biofuel price-quantity framework of our baseline. Therefore both behavioural functions are due to a calibration process which takes place in ‘//gams\biofuel\def_biofuel_params.gms//’.+So far, only the general form of the biofuel supply and demand functions where derived, but without any adjustments, they won’t reproduce the biofuel price-quantity framework of our baseline. Therefore both behavioural functions are due to a calibration process which takes place in ‘//gams/biofuel/def_biofuel_params.gms//’.
  
 Firstly, the demand system is calibrated. We here assume that only the part of the observed biofuel demand share in total fuel demand that is above the quota obligations is the result of a consumer decision and thus a result of the flexible parts on the demand equations. To calibrate the demand functions to the observed combination of the price ratio bio- to fossil fuel and demand share in total fuel consumption, we chose the two parameters \(X^1\) and \(X^2\) such that: Firstly, the demand system is calibrated. We here assume that only the part of the observed biofuel demand share in total fuel demand that is above the quota obligations is the result of a consumer decision and thus a result of the flexible parts on the demand equations. To calibrate the demand functions to the observed combination of the price ratio bio- to fossil fuel and demand share in total fuel consumption, we chose the two parameters \(X^1\) and \(X^2\) such that:
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 **Figure 28: Endogenous administrative stocks in CAPRI** **Figure 28: Endogenous administrative stocks in CAPRI**
  
-{{::figure_28.png?600|}} \\ Source: own illustration+{{::figure_28.png?600|Source: own illustration}}
  
 **Purchases to intervention stocks** //v_buyingToIntervStock// depend on the probability of the current market price //v_marketPrice// to undercut the administrative price //padm// and a calibration parameter \(\gamma^p\), assuming a normally distributed market price with standard deviation //stddev// and maximal amounts of purchases //INTM//: **Purchases to intervention stocks** //v_buyingToIntervStock// depend on the probability of the current market price //v_marketPrice// to undercut the administrative price //padm// and a calibration parameter \(\gamma^p\), assuming a normally distributed market price with standard deviation //stddev// and maximal amounts of purchases //INTM//:
Line 1488: Line 1492:
  
 \begin{equation} \begin{equation}
-intd_{i,r} = (intk_{i,r}+intp__{i,r}) errf \left ( \left( uvae_{i,r} - pmrk_{i,r} + \gamma_{i,r}^p\right ) / stddev_{i,r} \right )+intd_{i,r} = (intk_{i,r}+intp_{i,r}) errf \left ( \left( uvae_{i,r} - pmrk_{i,r} + \gamma_{i,r}^p\right ) / stddev_{i,r} \right )
 \end{equation} \end{equation}
  
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 **Figure 29: Quota underfill regime** **Figure 29: Quota underfill regime**
  
-{{:figure_29.png?600|}} \\ Source: own illustration+{{:figure_29.png?600|Source: own illustration}}
  
 **Quota binding, i.e. exactly filled**: the in-quota tariff is applied. The willingness to pay of consumers and thus the price paid is somewhere between the border plus the in-quota tariff and the border price plus the MFN tariff. The difference between the price in the market and the border price plus the in-quota tariff establishes a quota rent. Depending on property rights on the quota and the allocation mechanism, the quota rent is shared in different portions by the producers, importing agencies, the domestic marketing chain or the administration. Typically, the quota rent can neither be observed nor is their knowledge about distribution of the rent. **Quota binding, i.e. exactly filled**: the in-quota tariff is applied. The willingness to pay of consumers and thus the price paid is somewhere between the border plus the in-quota tariff and the border price plus the MFN tariff. The difference between the price in the market and the border price plus the in-quota tariff establishes a quota rent. Depending on property rights on the quota and the allocation mechanism, the quota rent is shared in different portions by the producers, importing agencies, the domestic marketing chain or the administration. Typically, the quota rent can neither be observed nor is their knowledge about distribution of the rent.
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 **Figure 30: Quota binding regime** **Figure 30: Quota binding regime**
  
-{{:figure_30.png?600|}} \\ Source: own illustration+{{:figure_30.png?600|Source: own illustration}} 
  
 **Quota overfill**: the higher MFN-tariff is applied. The quota rent is equal to the difference between the MFN and the in-quota tariff. Again, how the quota rent is distributed to agents is typically not known. **Quota overfill**: the higher MFN-tariff is applied. The quota rent is equal to the difference between the MFN and the in-quota tariff. Again, how the quota rent is distributed to agents is typically not known.
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 **Figure 31: Quota overfill regime** **Figure 31: Quota overfill regime**
  
-{{:figure_31.png?600|}} \\ Source: own illustration+{{:figure_31.png?600|Source: own illustration}}
  
 The fill rate for global TRQs is defined in the code as follows, adding all imports which are not under no duty/not quota access (p_doubleZero), not from the same trade block and not prohibited. A special case provides a bi-lateral quota, here, only import quantities beyond the allocated quota quantity enter the global one. The fill rate for global TRQs is defined in the code as follows, adding all imports which are not under no duty/not quota access (p_doubleZero), not from the same trade block and not prohibited. A special case provides a bi-lateral quota, here, only import quantities beyond the allocated quota quantity enter the global one.
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 **Figure 32: Variable levies** **Figure 32: Variable levies**
  
-{{:figure_32.png?600|}} \\ Source: own illustration+{{:figure_32.png?600|Source: own illustration}} 
  
 In CAPRI, the system is implemented as follows: In CAPRI, the system is implemented as follows:
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 **Figure 33: EU entry price system for fruits and vegetables** **Figure 33: EU entry price system for fruits and vegetables**
  
-{{:figure_33.png?600|}} \\ Source: own illustration+{{:figure_33.png?600|Source: own illustration}} 
  
 In order to implement the system, first the difference beween 96% of the entry price and the cif in relation to the triggerprice is defined, times a possible factor to ease solution. In order to implement the system, first the difference beween 96% of the entry price and the cif in relation to the triggerprice is defined, times a possible factor to ease solution.
  
-{{::code_p213.png?600|}}+{{::code_p213.png?600}}
  
 That factor is the fed into a modified sigmoid function which as a result approximates the relations in the graphic shown above: That factor is the fed into a modified sigmoid function which as a result approximates the relations in the graphic shown above:
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 **Figure 34: Tariff computation in the model** **Figure 34: Tariff computation in the model**
  
-{{::figure_34.png?600|}} \\ Source: own illustration+{{::figure_34.png?600|Source: own illustration}} 
  
 ====Welfare-consistent tariff aggregation module ==== ====Welfare-consistent tariff aggregation module ====
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 The only source of trade policy data at the tariff line level in the current CAPRI system is the AMAD database. AMAD is not anymore updated by OECD, and in many respect contains outdated policy information. According to the Technical Specification, the current study relies on the AMAD data, and does not include and update of trade policies at the tariff line level. This is a clear limitation that should be improved on in the future. It is very likely that a combination of additional trade policy databases need to be added to CAPRI for a correct and comprehensive representation of global trade policies at the tariff line level. MAcMap  is one of the candidates to be included, containing global trade protection measures at HS6 level. MAcMap, however, contains TRQs already in a converted tariff-equivalent form, and is therefore insufficient to provide policy data for the explicit TRQ mechanism in the new tariff aggregation module.  The only source of trade policy data at the tariff line level in the current CAPRI system is the AMAD database. AMAD is not anymore updated by OECD, and in many respect contains outdated policy information. According to the Technical Specification, the current study relies on the AMAD data, and does not include and update of trade policies at the tariff line level. This is a clear limitation that should be improved on in the future. It is very likely that a combination of additional trade policy databases need to be added to CAPRI for a correct and comprehensive representation of global trade policies at the tariff line level. MAcMap  is one of the candidates to be included, containing global trade protection measures at HS6 level. MAcMap, however, contains TRQs already in a converted tariff-equivalent form, and is therefore insufficient to provide policy data for the explicit TRQ mechanism in the new tariff aggregation module. 
  
-The code implementation of the UN-COMTRADE data processing is modular, i.e. it can be switched on and off upon demand. A dedicated option in the GUI activates the data processing algorithms in the global part of CAPRI (see below). Technically, the extended GAMS routines create an additional intermediate dataset (‘//\global\tariff_aggregation.gdx//’) that is a direct input of the tariff aggregation module in subsequent steps. The .gdx file contains bilateral trade and tariff information at the tariff line level, already mapped into the CAPRI regional nomenclature.+The code implementation of the UN-COMTRADE data processing is modular, i.e. it can be switched on and off upon demand. A dedicated option in the GUI activates the data processing algorithms in the global part of CAPRI (see below). Technically, the extended GAMS routines create an additional intermediate dataset (‘// /global/tariff_aggregation.gdx//’) that is a direct input of the tariff aggregation module in subsequent steps. The .gdx file contains bilateral trade and tariff information at the tariff line level, already mapped into the CAPRI regional nomenclature.
  
 **Figure 35: Tariff computation in the model** **Figure 35: Tariff computation in the model**
  
-{{:figure_35.jpg?600|}} \\ Source: CAPRI Modelling System+{{:figure_35.jpg?600|Source: CAPRI Modelling System}} 
  
 The different tasks implemented in the aggreg_tariffs.gms tariff aggregation module includes: The different tasks implemented in the aggreg_tariffs.gms tariff aggregation module includes:
  
-  * Defining nomenclatures and sets for the UN-COMTRADE dataset (‘global\comtrade_sets.gms’)+  * Defining nomenclatures and sets for the UN-COMTRADE dataset (‘global/comtrade_sets.gms’)
   * Processing, filtering and mapping UN-COMTRADE data in order to align it with the CAPRI database   * Processing, filtering and mapping UN-COMTRADE data in order to align it with the CAPRI database
   * Aggregate tariffs to the CAPRI regional nomenclature. The aggregation follows the standard CAPRI approach; the only difference is that tariffs are not aggregated over tariff lines.   * Aggregate tariffs to the CAPRI regional nomenclature. The aggregation follows the standard CAPRI approach; the only difference is that tariffs are not aggregated over tariff lines.
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 **Figure 36: Activation of the tariff aggregation module on the GUI** **Figure 36: Activation of the tariff aggregation module on the GUI**
  
-{{:figure_36.jpg?600|}} \\ Source: CAPRI Modelling System+{{:figure_36.jpg?600|Source: CAPRI Modelling System}} 
  
 The tariff aggregation module takes over the appropriate tariff cuts from the scenario file and applies them at the tariff line level. The module then feeds back an aggregate tariff equivalent of the resulting (cut) tariffs. The tariff aggregation module takes over the appropriate tariff cuts from the scenario file and applies them at the tariff line level. The module then feeds back an aggregate tariff equivalent of the resulting (cut) tariffs.
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 Generally, tariff cuts have to be defined in a specific format in the CAPRI scenario file. A simple example is illustrated in hte following, where ad-valorem and specific tariffs are cut relative to their initial level and TRQ thresholds are increased. Generally, tariff cuts have to be defined in a specific format in the CAPRI scenario file. A simple example is illustrated in hte following, where ad-valorem and specific tariffs are cut relative to their initial level and TRQ thresholds are increased.
  
-{{::code_p220.png?600|}}+{{::code_p220.png?600}}
  
-{{::code_p220_2.png?600|}}+{{::code_p220_2.png?600}}
  
 **Reporting (GUI tables)** **Reporting (GUI tables)**
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 The GUI has been extended with tables under 'Trade|Advanced tariff aggregators' that collect the results of the tariff aggregation module:  The GUI has been extended with tables under 'Trade|Advanced tariff aggregators' that collect the results of the tariff aggregation module: 
  
-{{:gui_p220.png?600|}} \\ Source: CAPRI Modelling System+{{:gui_p220.png?600|Source: CAPRI Modelling System}}
  
 The MacMap-type aggregators are calculated both with respect to bilateral trade relations and with respect to a total ('from World') measure of tariff/TRQ restrictions. In the above calculation of total aggregate measures, imports from other countries are neglected; an assumption that can be easily relaxed if relevant policy and trade data will be available in future applications. MacMap-type trade weighted aggregators give the following results. The MacMap-type aggregators are calculated both with respect to bilateral trade relations and with respect to a total ('from World') measure of tariff/TRQ restrictions. In the above calculation of total aggregate measures, imports from other countries are neglected; an assumption that can be easily relaxed if relevant policy and trade data will be available in future applications. MacMap-type trade weighted aggregators give the following results.
  
-{{:gui_p221.png?600|}}+{{:gui_p221.png?600}}
  
 TRI estimates are also reported in a specific GUI table. By definition the TRI indicies are defined for all trade relations only (not a bilateral index): TRI estimates are also reported in a specific GUI table. By definition the TRI indicies are defined for all trade relations only (not a bilateral index):
  
-{{:gui_p221_2.png?600|}}+{{:gui_p221_2.png?600}}
  
 The Anderson tariff combination is presented next. The current implementation is an extension of the original approach, including correction factors for TRQs (Himics and Britz, 2014): The Anderson tariff combination is presented next. The current implementation is an extension of the original approach, including correction factors for TRQs (Himics and Britz, 2014):
  
-{{:gui_p221_3.png?600|}}+{{:gui_p221_3.png?600}}
  
 The Bach and Martin (2001) approach, i.e. a combination of an aggregator for the expenditures and another one for the tariff revenues, is also implemented and reported in a designated GUI table: The Bach and Martin (2001) approach, i.e. a combination of an aggregator for the expenditures and another one for the tariff revenues, is also implemented and reported in a designated GUI table:
  
-{{:gui_p222.png?600|}}+{{:gui_p222.png?600}}
  
 ====Overview on a regional module inside the market model==== ====Overview on a regional module inside the market model====
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 **Figure 37: Graphical presentation for one region of a spatial market system ** **Figure 37: Graphical presentation for one region of a spatial market system **
  
-{{:figure_37.png?600|}} \\ Source: CAPRI modelling system +{{:figure_37.png?600|Source: CAPRI modelling system }} 
  
 ====Basic interaction inside the market module during simulations==== ====Basic interaction inside the market module during simulations====
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 Simultaneously, impacts on market for others products will occur. Depending on the size of the cross price elasticities, demand for other products will drop with falling prices for a substitute. At the same time, reduced prices will stimulate supply of other products. The resulting imbalances will hence force downwards price adjustments in other markets as well. Simultaneously, impacts on market for others products will occur. Depending on the size of the cross price elasticities, demand for other products will drop with falling prices for a substitute. At the same time, reduced prices will stimulate supply of other products. The resulting imbalances will hence force downwards price adjustments in other markets as well.
 +
 +=====Solving the market model=====
 +
 +The solution of the market model with its close to 750.000 equations of which some are highly non-linear poses a serious challenge for any non-linear solver. CAPRI applies CONOPT which has proven quite stable and fast to solve both constrained system and optimization problems. However, even CONOPT would spend quite some time when trying to solve the full market model in one block after a larger shock is introduced.
 +
 +Therefore, a sequence of pre-solves is introduced (see //‘arm/simu_prestep.gms’//). Firstly, single commodity models are defined by only allowing changes of the endogenous variables of one commodity in the equation template. Cross prices and their effects on quantities for variables related to the current market are hence fixed. These relatively small models can typically be solved rapidly by the solver, and are solved in parallel based on the so-called “grid solve option” in GAMS. That process is repeated a few times, each time updating the cross prices, to let differences between the single models and the full system decrease.
 +
 +As a next step, the single products are clustered to groups where larger cross price effects can be expected, such as all cereals or all oilseeds. Again, these groups are solved repeatedly, in each round with updated cross-prices, to close in to the final solution. The full system is only solved at the very end.
 +
 +Heuristics track the time needed for these solves and determine if it looks promising to skip solving single commodity and start with solving the groups or even the full model directly. The solution time of the model clearly depends on the hardware platform the models runs, but the heuristics do not take that into account. Accordingly, it cannot be guaranteed that the model finds exactly the same solution in a scenario on different machines.
 +
 +Another problem possible problem beside long solution times is the occurrence of infeasibilities. Bounds are generally introduced for all endogenous variables to avoid numerical errors such as a division by zero. Bounds also help the solver in the solution process. However, they might also restrict the solution space so that no feasible solution exists. The CES functions for the Armington might as a response to a larger price shocks – e.g. provoked by removal of very large tariffs – drive trade flows almost to zero towards their lower bounds. Once that bounds are hit, the equation system is not longer symmetric as a new constraint becomes binding, and typically, the system will become infeasibility. If one would have the time to inspect the solution, one might perhaps accept that if the infeasibility is small and found only for that CES share equation. It is however generally impossible to leave it up to the model user to decide if she accepts infeasibility solutions or not, simply as there is simply not enough time to check these infeasibilities.
 +
 +Fortunately, CONOPT helps us with in that case as it uses a gradient approach to reduce the sum of infeasibilities. It therefore introduces an objective into our problem, does also adding dual values to the constraints. We hence can inspect automatically the solution to find out which bounds carry a shadow values – removing these bounds will reduce the sum of infeasibilities. There is hence code (‘//arm/widen_bounds.gms//’) which in case of a infeasible solution will check which bounds carry dual values and will expand those stepwise. That proceeding generally guarantees that for most shocks, the market model finds a feasible solution.
 +
 +=====Linking the different modules – the price mechanism =====
 +
 +====Iterative solution method====
 +
 +As hinted at above several times, the market modules and the regional programming models interact with each other in an iterative way. Basically, the market modules deliver prices to the supply module, and the supply module information to update the supply and feed demand response from the market models.
 +
 +For the market module for agricultural outputs, the update of the supply and feed demand response is put to work by changing the constant terms in the behavioural equations such that supply and demand quantities simulated at prices used during the last iteration in the supply module would be identical to the quantities obtained from the market module at that prices. However, the “functional form” of the regional programming models is unknown but certainly differs from the one in the market model which necessitates an iterative update. In order to speed up convergence, the supply side uses a weighted average of prices of the last iterations.
 +
 +Convergence is achieved faster if supply has the same price responsiveness in the market model as in the regional programming models. To achieve this at least approximately, a set of price elasticities is generated from the regional programming models and is used to calibrate the parameters of the market model.  This also applies to young animals which are “netputs” that are only traded between European regions with regional supply models.
 +
 +===Price linkage in the sugar sector===
 +
 +Whereas the linkage of prices from the market model to the supply model is usually a proportional one, the price linkage in the sugar sector is specific for ethanol beets. Sugar and ethanol beets are considered two products with independent proportional linkage applied to each of them. Their prices may move independently therefore and European beet producers respond to both prices. 
 +
 +=====Sensitivity analysis=====
 +
 +The CAPRI model results depend on a large number of parameters, some of which are more uncertain than others. In order to analyze how model results depend on uncertain parameters, a set of sensitivity analyses were carried out in the context of an analysis of the climate impact of EU coupled support((Blanco, G., R. Gerlagh, J. Barrett, S. Suh, H.C. de Coninck, C.F. Diaz Morejon, R. Mathur, N. Nakicenovic, A. Ofosu Ahenkora, H. Pathak J. Pan, J. Rice, R. Richels, S.J. Smith, D.I. Stern, F.L. Toth, and P. Zhou. 2014. Drivers, Trends and Mitigation. In //Climate Change 2014: Mitigation of Climate Change. Contribution of Working Group III to the Fifth Assessment Report,// eds. Edenhofer et al. Cambridge and New York: Cambridge University Press.)) . In that study, a baseline scenario for 2030 representing the CAP 2014-2020 was compared to a scenario where the voluntary coupled support was removed. This resulted in less production of e.g. beef in the EU, and less GHG emissions there. Due to inelastic demand for food, trade flows changed, so that less beef was exported from the EU and more imported, and thus carbon leakage arose. We carried out sensitivity analyses to investigate how carbon leakage depend on the model parameters. 
 +
 +We selected four types of parameters that were assumed to be most critical to emissions leakage, and varied those in three levels: “low” (lo), “high” (hi) and “most likely” (ML). The groups of parameters subjected to the sensitivity analyses are as follows:
 +
 +  * The elasticities of supply (SupElas) of ruminants in the EU are influenced by the slope of the marginal cost function((CAPRI contains quadratic cost functions in the tradition of Positive Mathematical Programming (PMP). In the sensitivity analyses, we varied the coefficient of the quadratic term.)). Higher slope means lower supply elasticity and vice versa. The slope was varied +/- 50% to create the lo and hi scenario variants.
 +  * The elasticities of demand (DemElas) for meat and dairy products. We recalibrated the demand systems for all countries so that the own-price demand elasticities would be as close as possible to +/- 50% of the standard value, while observing relevant regularity conditions for demand systems.
 +  * Substitution elasticities (CES) between imports and domestic products and between different import sources were also set to +/- 50% of the standard values. The standard values differ per product, ranging from 2 to 10.
 +  * GHG emission factors (EF) per commodity outside of the EU. Emissions leakage depends more on the relationship between EF in the EU to those outside the EU than on the absolute level. Therefore, we chose to vary only the factors outside of the EU. Since, in general, N<sub>2</sub>O factors are considered less certain than emissions of CH<sub>4</sub>, which in turn are less certain than CO<sub>2</sub>, we chose to apply the uncertainty ranges of the IPCC (Blanco et al. 2014) to construct the hi and lo scenarios. The ranges used were +/- 60% for N<sub>2</sub>O and +/- 20% for CH<sub>4</sub>.
 +
 +We do not know the covariance of the uncertain parameters across countries and products. In order to avoid running a very large number of simulation experiments, we chose to implement only the most extreme variants given by setting all parameters of the same type to lo/ML/hi simultaneously (e.g., elasticities of supply of all ruminants in all countries being hi, ML or lo simultaneously, etc.). We thus obtained 3×3×3×3 = 81 result sets; this should span the extremes of the result space.
 +
 +The manuscript was submitted to a journal. Therefore, this section does not yet contain any results from this exercise, but it will be completed as soon as the review process of the manuscript has been completed.
  
  
scenario_simulation.txt · Last modified: 2023/09/08 12:07 by massfeller
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