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— | scenario_simulation [2022/01/17 09:28] – [Annex: Land supply and land transitions in the supply part of CAPRI] matsz | ||
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+ | ======Scenario simulation====== | ||
+ | =====Overview of the system===== | ||
+ | |||
+ | The CAPRI simulation tool is composed of a supply and market modules, interlinked with each other. | ||
+ | |||
+ | In the //supply module//, regional or farm type agricultural supply of crops and animal outputs is modelled by an aggregated profit function approach under a limited number of constraints: | ||
+ | |||
+ | In the //first stage//, producers determine //optimal variable input coefficients// | ||
+ | |||
+ | In the //second stage, the profit maximising mix of crop and animal activities// | ||
+ | |||
+ | A cost function covering the effect of all factors not explicitly handled by restrictions or the accounting costs –as additional binding resources or risk ensures calibration of activity levels and feeding habits in the base year and plausible reactions of the system. These cost function terms are estimated from ex post data or calibrated to exogenous elasticities. | ||
+ | |||
+ | Fodder (grass, straw, fodder maize, root crops, silage, milk from suckler cows or mother goat and sheep) is assumed to be non-tradable, | ||
+ | |||
+ | The market module breaks down the world into 40 country aggregates or trading partners, each one (and sometimes regional components within these) featuring systems of supply, human consumption, | ||
+ | |||
+ | In the market module, special attention is given to the processing of dairy products. First, balancing equations for fat and protein ensure that these make use of the exact amount of fat and protein contained in the raw milk. The production of processed dairy products is based on a normalised quadratic function driven by the regional differences between the market price and the value of its fat and protein content. Then, for consistency, | ||
+ | |||
+ | The market module comprises of a bilateral world trade model based on the Armington assumption (Armington, 1969). According to Armington’s theory, the composition of demand from domestic sales and different import origins depends on price relationships according to bilateral trade flows. This allows the model to reflect trade preferences for certain regions (e.g. Parma or Manchego cheese) that cannot be observed in a net trade model. | ||
+ | |||
+ | The // | ||
+ | |||
+ | The implementation in CAPRI is based on a core module file // | ||
+ | |||
+ | **Figure 13: Link of modules in CAPRI** | ||
+ | {{:: | ||
+ | |||
+ | =====Module for agricultural supply at regional level===== | ||
+ | |||
+ | ====Basic interactions between activities in the supply model==== | ||
+ | |||
+ | There are two sources for interactions between activities in simulation experiments: | ||
+ | |||
+ | \begin{equation} | ||
+ | Rev_j = Cost_j+ac_j+\sum_k bc_{j, | ||
+ | \end{equation} | ||
+ | |||
+ | The left hand side (//Rev//) shows the marginal revenues, which are typically equal to the fixed prices times the fixed yields plus premiums. The right hand side shows the different elements of the marginal costs. Firstly, the variable or accounting costs (//Cost//) which are fix as they are based on the Leontief assumption. The term \( (ac_j+\sum_k bc_{j, | ||
+ | |||
+ | The remaining term \( (\sum_i^m\lambda_ia_{ij}) \) captures the marginal costs linked to the use of exhausted resources and is equal to the sum of the shadow prices \lambda multiplied the per unit demand of resource //i// for activity //j//; the matrix **//A//** being again based on Leontief technology. The shadow values of binding resources hence are the drivers linking the activities. | ||
+ | |||
+ | The land balance plays a central role in the CAPRI supply model. The land shadow price appears as a cost in all crop activities including fodder producing ones, so that animals are indirectly affected as well. The second major link is the availability of not-marketable feeding stuff, and finally, less important, organic fertiliser. | ||
+ | |||
+ | The basic effects are best discussed with a simple example. Assume an increase of a per hectare premium for soft wheat, all other things unchanged. | ||
+ | |||
+ | * //What will happen in the model//? The increased premium will lead to an imbalance between marginal revenues (= yield times prices plus premium) and marginal costs (=accounting costs, ‘resource use cost’, non-linear costs). In order to close the gap, as marginal revenues are fixed, the area under soft wheat will be increased until marginal costs of producing soft wheat have increased to a point where they are again equal to marginal revenues. As the marginal costs linked to the non-linear cost function \( (ac_j+\sum_k bc_{j, | ||
+ | * //What will be the impact on animal activities//? | ||
+ | |||
+ | To summarize the supply response, increasing premiums for a crop will hence increase the cropping share of that crop, reduce the share of other crops, increase the shadow price of land, lead to less fodder production, higher fodder costs and thus reduced herd size of animals. | ||
+ | |||
+ | * //What will be the impacts covered by the market//? The changes in hectares will lead to increased supply of the crop with the higher premium and less supply of all other crops at given prices, i.e. one upward and many downward shifts of the supply curves. Equally, supply curves for animal products will shift downwards. On the other hand, some feed demand curve will shift as well, some upward, other downward. These shifts will move the market module away from the former fixed points where market balances were closed. For the crop product with the increased premiums, increased supply plus some changes in feed will most probably lead to lower prices, whereas prices of other crops will most probably increase. That will require new adjustments during the next iteration where the supply models are solved, with to a certain extent countervailing effects. | ||
+ | |||
+ | **Table 25: Overview on a regional aggregate programming model** | ||
+ | |||
+ | | | Crop Activities | ||
+ | |**Objective function**| + Premium \\ – Acc.Costs \\ – variable cost function terms |+ Premium \\ – Acc.Costs \\ – variable cost function terms | - variable cost function \\ terms for feeding | + Price| | ||
+ | |**Output**| | ||
+ | |**Area **| | ||
+ | |**Set aside**| | ||
+ | |**Quotas**| | ||
+ | |**Fertilizer needs**| | ||
+ | |**Feed requirements**| | | ||
+ | |||
+ | ====Detailed discussion of the equations in the supply model==== | ||
+ | |||
+ | The definition of the supply model can be found in // | ||
+ | |||
+ | ===Feed block=== | ||
+ | |||
+ | The feed block ensures that the requirements of the animal processes in terms of feed energy and protein are met and links these to the markets and crop production decisions. | ||
+ | |||
+ | \begin{equation} | ||
+ | \overline{AREQ}_{r, | ||
+ | \end{equation} | ||
+ | |||
+ | The left hand side captures the daily animal requirements (//AREQ//) for each region //r//, animal activity //act// and requirement //AREQ// multiplied with the days (//DAYS//) the animal is in the production process. Both are parameters fixed during the solution of the modelling system. The right hand side ensures that the requirement content of the actual feed mix represented by the feeding (//FEDNG//) of certain type of feed to the animals multiplied with the requirement content (// | ||
+ | Total feed use (// | ||
+ | |||
+ | \begin{equation} | ||
+ | FEDUSE_{r, | ||
+ | \end{equation} | ||
+ | |||
+ | Total feed use might be either produced regionally in the case of fodder assumed not tradable (grass, fodder root crops, silage maize, other fodder from arable land), or bought from the market at fixed prices. | ||
+ | |||
+ | ===Land balances and set-aside restrictions=== | ||
+ | |||
+ | The model distinguishes arable and grassland and comprises thus two land balances: | ||
+ | |||
+ | \begin{equation} | ||
+ | \overline{LEVL}_{r," | ||
+ | \end{equation} | ||
+ | |||
+ | \begin{equation} | ||
+ | \overline{LEVL}_{r," | ||
+ | \end{equation} | ||
+ | |||
+ | Both land balances might become slack if marginal returns to land drops to zero. For arable land, idling land not in set-aside (activity //FALL//) is a further explicit activity. For the grassland, the model distinguishes two types with different yields (//GRAE//: grassland extensive, //GRAI//: grassland intensive) so that idling grassland can be expressed of an average lower production intensity of grassland by changing the mix between the two intensities. | ||
+ | |||
+ | The model comprises a land use module with two major components: | ||
+ | |||
+ | - Imperfect substitution between arable and grass lands depending on returns to the two types of agricultural land uses. | ||
+ | - A land supply curve which determines the land available to agriculture as a function to the returns to land. | ||
+ | |||
+ | There are hence two further equations: | ||
+ | |||
+ | \begin{equation} | ||
+ | \overline{LEVL}_{r," | ||
+ | \end{equation} | ||
+ | |||
+ | And a further one which prevents numerical problems with the terms relating to land supply in the objective function | ||
+ | |||
+ | \begin{equation} | ||
+ | \overline{LEVL}_{r," | ||
+ | \end{equation} | ||
+ | |||
+ | 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 [[scenario simulation# | ||
+ | |||
+ | \begin{align} | ||
+ | \begin{split} | ||
+ | & | ||
+ | & | ||
+ | \end{split} | ||
+ | \end{align} | ||
+ | |||
+ | LEVL_{r," | ||
+ | |||
+ | The equation above is replaced for years where the Luxembourg compromise of June 2003 is implemented by a Member State, where the level of obligatory set-aside is fixed instead to the historical obligations. | ||
+ | |||
+ | For certain years of the McSharry reform, the total share of set-aside – be it obligatory or voluntary – on a list of certain crops was not allowed to exceed a certain ceiling. That restriction is captured by the following equation: | ||
+ | |||
+ | \begin{align} | ||
+ | \begin{split} | ||
+ | & | ||
+ | & \le \sum_{arab \wedge SETF_{r, | ||
+ | \end{split} | ||
+ | \end{align} | ||
+ | |||
+ | ===Fertilising block=== | ||
+ | |||
+ | As of CAPRI Stable Release 2.1, the fertilizer allocation was modified, and this section of the documentation updated. Notation has changed compared with previous versions of the model and documentation. Here, we represent the equations in more general mathematical notation, avoiding the long GAMS code names of the source code, in order to save space. | ||
+ | |||
+ | We distinguish the three macro-nutrients N, P and K. The supply and uptake of those nutrients are modelled in a uniform way, save for the fact that there is fixation and atmospheric deposition only of N. | ||
+ | |||
+ | Each crop has a requirement per hectare, calculated based on the yield. Yields are exogenous from the vantage point of the producer, but there are alternative technologies available for each cropping activity, and a separable, i.e. handled outside of the optimization model, relation between prices and optimal yields. | ||
+ | |||
+ | From the basic nutrient requirement we first deduct the rate of biological fixation (only for nitrogen and selected crops). The remainder is inflated by a (calibrated) factor and additive term of over-fertilization, | ||
+ | |||
+ | Nutrient supply, shown on the right handside, comes from mineral fertilizer, manure, crop residues and atmospheric deposition. Mineral fertilizer may have ammonia losses during application. For manure, there are both losses and inefficiencies. When manure is applied to crops, there is an efficiency factor applied to the nutrient content (denoted by ϕ_(r," | ||
+ | |||
+ | \begin{align} | ||
+ | \begin{split} | ||
+ | & | ||
+ | & = fmine_{rni}(1-loss_{rn}) +fexcr_{rni} \phi_{r, | ||
+ | & + isPerm_j | ||
+ | & \forall r,n,j | ||
+ | \end{split} | ||
+ | \end{align} FIXME | ||
+ | |||
+ | Indices: | ||
+ | |||
+ | \(r\) = region \\ | ||
+ | \(i\) = crop \\ | ||
+ | \(j\) = crop group \\ | ||
+ | \(k\) = technological crop option (high/low yield) \\ | ||
+ | \(n\) = nutrient (N/P/K) \\ | ||
+ | \(isPerm_j\) = indicates that crop group \(j\) contains permanent crops | ||
+ | |||
+ | Endogenous choice variables: | ||
+ | |||
+ | \(levl_{rik}\) = Area (ha) of each crop \(i\) and technology \(k\) in region \(r\). | ||
+ | \(fmine_{rnj}\) = Application of mineral fertilizer \(n\) to crop group \(j\) in region \(r\). | ||
+ | \(fexcr_{rnj}\) = Application of manure \(n\) to crop group \(j\) in region \(r\). | ||
+ | \(fcrex_{rnj}\) = Allocation of crop residue \(n\) to crop group \(j\) in region \(r\). | ||
+ | |||
+ | Parameters: | ||
+ | \(ret_{rni}\) = Retention (uptake) of nutrients by the crop \\ | ||
+ | \(res_{rni}\) = Crop residues output \\ | ||
+ | \(biofix_{rni}\) | ||
+ | \(λ_{rnik}^{prop} \) = Over-fertilization factor, calibrated \\ | ||
+ | \(λ_{rni}^{const} \) = Over-fertilization term, calibrated \\ | ||
+ | \(soil_{rn}\) = Soil factor \\ | ||
+ | \(yf_{rnik}\) = Yield factor for technologies \\ | ||
+ | \(loss_{rn}\) = Loss rate \\ | ||
+ | \(ϕ_{r", | ||
+ | \(ϕ_{r," | ||
+ | |||
+ | The reader may have noted that there is no loss rate for manure in the Equation 96 FIXME . CAPRI does contain such loss rates, but they are specific for each animal type and therefore happens on the manure supply side of the regional manure balance (see section on input allocation). | ||
+ | |||
+ | The model contains three types of manure: N-manure, P-manure and K-manure. From an agricultural point of view this may seem odd. It might be more intuitive to think of one type of manure per animal category. The motivation is to keep the system simple and flexible. With the present representation, | ||
+ | |||
+ | The supply of each manure type is collected in a “pool” for each regional farm model, i.e. for each NUTS2 region. Regions within a member state may trade manure, subject to a cost. The supply in the pool plus the traded quantities has to be distributed to the crops in the region, i.e. there is an equality-restriction in place. This is handled in the equations “FertDistExcr_” and “ManureNPK_”. Note that fertilizer flows are measured in //tons//, for the sake of scaling, whereas other total quantities in CAPRI are measured in 1000 tons. Hence the factors 1000 and 0.001. | ||
+ | |||
+ | \begin{equation} | ||
+ | \sum_j fexcr_{rnj}= 1000 v\_ManureNPK_{rn} | ||
+ | \end{equation} | ||
+ | |||
+ | \begin{equation} | ||
+ | v\_ManureNPK_{rn} + \sum_s T_{rs}nutshr_{rn} = 0.001 \sum_{i\in Anim_j,k} levl_{rik}o_{rnik}(1-loss_{rin}) \quad \forall r, n | ||
+ | \end{equation} | ||
+ | |||
+ | where \\ | ||
+ | \(o_{rnik}\) is the output of manure nutrient \(n\) from animal type \(i\) using technology \(k\) in region \(r\), \\ | ||
+ | \(nutshr_{rn}\) is the average content of each nutrient in the regional manure pool, \\ | ||
+ | \(T_{rs}\) is the quantity of manure traded from \(r\) to \(s\), \\ | ||
+ | \(isAnim_{i}\) indicates that activity \(i\) is an animal production activity | ||
+ | |||
+ | Equation “FertDistMine_” allocates total mineral fertilizer sales to the crops / group of crops. | ||
+ | |||
+ | \begin{equation} | ||
+ | \sum_j fmine_{rnj} = -netPutQuant_{rn} | ||
+ | \end{equation} | ||
+ | |||
+ | Finally, crop residues and atmospheric definition are distributed in equation “FertDistCres_”. | ||
+ | |||
+ | \begin{equation} | ||
+ | \sum_j fcers_{rnj} = \sum_{i \notin isPerm_j,k} levl_{rik}res_{rni}(techf_{rink}+1) | ||
+ | \end{equation} | ||
+ | |||
+ | One flow from a source s={" | ||
+ | |||
+ | To resolve the ill-posedness of the fertilizer distribution, | ||
+ | |||
+ | To develop this probabilistic model, we assume that the decisions of the farmer are separable and taken in two steps: first, the farmer decides about the cropping plan and just ensures that the total amount of fertilizer available is sufficient. This is called the outer model. Then, a statistical model is solved that finds the most probable fertilizer flows out of the continuum of possible ones. This is called the inner model. The structure with outer and inner models makes the problem a bi-level programming one. | ||
+ | |||
+ | To implement the bi-level programming problem in a way that does not change the present structure of the model (with just one optimization solve of the representative farm model) we implement the inner model by its optimality conditions. By carefully choosing the proper probability density functions we ensure that no complementary slackness conditions are needed, so that the inner model is simple to solve. For this the gamma density function is very suitable, as it has a support from zero to infinity, with a probability that goes towards zero as the random variable goes to zero. | ||
+ | |||
+ | The parameters of the gamma function are determined in the calibration step, described further below, and then kept constant in simulation. The gamma density function for some random variable x has the form | ||
+ | |||
+ | \begin{equation} | ||
+ | p(x|\alpha, | ||
+ | \end{equation} | ||
+ | |||
+ | where Γ(α) is the gamma function, and α and β are parameters that determine the shape of the density function. The gamma density is nonlinear, and the joint density, being the product of the densities of all nutrient flows, is even more so. In order to reduce nonlinearity we note that are interested in finding the highest posterior density, i.e. maximizing a joint density function, and since the maximum is invariant to monotonous positive transformations we compute the logarithm of the joint density, which will be the sum of terms like the following (the constant term has been omitted since it also does not influence the optimal solution for x): | ||
+ | |||
+ | \begin{equation} | ||
+ | log \, p(x|\alpha, | ||
+ | \end{equation} | ||
+ | |||
+ | Maximization of the logged density under the constraints that the nutrient balance restrictions of the supply modes have to be met gives a set of equations that define explicit and unique fertilizer flows, where v are the Lagrange multipliers of the source-pool restrictions and u the Lagrange multipliers of the nutrient balance equation. | ||
+ | |||
+ | \begin{equation} | ||
+ | \text{FOC w.r.t. manure use:} \\ | ||
+ | \frac {\alpha_{r, | ||
+ | \end{equation} | ||
+ | |||
+ | \begin{equation} | ||
+ | \text{FOC w.r.t. crop residues use:} \\ | ||
+ | \frac {\alpha_{r, | ||
+ | \end{equation} | ||
+ | |||
+ | \begin{equation} | ||
+ | \text{FOC w.r.t. mineral feritilzer use:} \\ | ||
+ | \frac {\alpha_{r, | ||
+ | \end{equation} | ||
+ | |||
+ | The system of FOC contains expressions of the type \(1/fmine\) which is likely to impair performance as the second derivatives are not constant (CONOPT computes second derivatives). Therefore, the first term in each FOC was turned into a new variable \(z\) defined as \( z_{r," | ||
+ | |||
+ | ===Balancing equations for outputs=== | ||
+ | |||
+ | Outputs produced must be sold – if they are tradable across regions – or used internally, as in the case of young animals or feed. | ||
+ | |||
+ | \begin{equation} | ||
+ | \sum_{act}Levl_{r, | ||
+ | \end{equation} | ||
+ | |||
+ | 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): | ||
+ | |||
+ | {{:: | ||
+ | |||
+ | 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, | ||
+ | |||
+ | \begin{equation} | ||
+ | \sum_{aact}Levl_{r, | ||
+ | \end{equation} | ||
+ | |||
+ | In combination with the standard balancing equation shown above, the NETTRD variable for young animals on the output side becomes negative if the YANUSE variable for a certain type of young animals exceeds the production inside the region. | ||
+ | |||
+ | ===The objective function=== | ||
+ | |||
+ | The objective function is split up into the linear part, the one related to the quadratic cost function for activities, and the quadratic cost function related to the feed mix costs: | ||
+ | |||
+ | \begin{equation} | ||
+ | OBJE=\sum_r LINEAR_r+QUADRA_r+QUADRF_r | ||
+ | \end{equation} | ||
+ | |||
+ | The linear part comprises the revenues from sales and the costs of purchases, minus the costs of allocated inputs not explicitly covered by constraints (i.e. all inputs with the exemptions of fertilisers, | ||
+ | |||
+ | \begin{equation} | ||
+ | LINEAR_r= \sum_{io} NETTRD_{r, | ||
+ | \end{equation} | ||
+ | |||
+ | The quadratic cost function relating to feed is defined as follows: | ||
+ | |||
+ | \begin{equation} | ||
+ | QUDRAF_r = \sum_{aact, | ||
+ | \begin {matrix} | ||
+ | LEVL_{r, | ||
+ | (a_{r, | ||
+ | \end{matrix} | ||
+ | \right] | ||
+ | \end{equation} | ||
+ | |||
+ | The marginal feed costs per animal increase hence linearly with an increase in the feed input coefficients per animal. It should be emphasised that this is the main mechanism that “stabilises” the feed allocation by animals. The two balances on feed energy and protein alone would otherwise leave the feed allocation indeterminate and give a rather “jumpy” simulation behaviour. | ||
+ | |||
+ | There is another more complex PMP term (equation quadra_ in supply_model.gms, | ||
+ | |||
+ | A final term relates to the entitlements introduced with the 2003 Mid Term reviews. If those entitlements are overshot, a penalty term equal to the premium paid under the respective scheme (regional, historical etc.) is subtracted to the objective. Accordingly, | ||
+ | |||
+ | ===Sugar beet (M. Adenäuer, P. Witzke)=== | ||
+ | |||
+ | The Common Market Organisation (CMO) for sugar regulates European sugar beet supply with a system of production quotas, even after the significant reforms of 2006, up to year 2017 when the quota system expired. Before that reform, two different quotas had been established subject to different price guarantee (A and B quotas, qA and qB). Beet prices were depending on intervention prices and levies to finance the subsidised export of a part of the quota production to third countries. Sugar beets produced beyond those quotas (so called C beets) were sold as sugar on the world market at prevailing prices, i.e. formally without subsidies. However, a WTO panel initiated by Australia and Brazil concluded that the former sugar CMO involved a cross-subsidisation of C-sugar from quota sugar such that all exports of C sugar was also counted in terms of the EU’s limits on subsidised exports. As a consequence, | ||
+ | * A-beets receiving the highest price derived from high sugar prices (and before the 2006 reform less a small levy amount) | ||
+ | * B-beets receiving a lower price as the applicable levies were higher before the reform. However, the 2006 reform eliminated the distinction of A and B quotas. Furthermore, | ||
+ | * C-beets receiving the lowest price, formerly derived from world market sugar prices, now derived from ethanol prices. | ||
+ | |||
+ | The high price sector covers for farmers at least the farm level quota endowment. However, the sugar industry may grant high prices also for a limited, “desirable” over-quota production, for example to avoid bottlenecks in sugar or ethanol production. This has been the case in some EU countries before the reform (so-called “C1 beets”) and it is also current practice (see, for example [[http:// | ||
+ | |||
+ | Considering a kinked demand curve and in addition yield uncertainty renders the standard profit maximisation hypothesis inappropriate for the sugar sector (at least). The CAPRI system therefore applies an expected profit maximisation framework that takes care for yield uncertainty (see Adenäuer 2005). The idea behind this is that observed C sugar productions in the past are unlikely to be an outcome of competitiveness at C beet prices rather than being the result of farmers’ aspirations to fulfil their quota rights even in case of a bad harvest. This approach essentially assumes that the “behavioural quotas” of farmers may exceed the “legal quotas” (derived from the sugar CMO) by some percentage. This percentage reflects in part the pricing behaviour of the regional sugar industry, but it may also depend on farmers expectations on the consequences of an incomplete quota fill. These aspects may be captured with the following specification of expected sugar beet revenues that substitute for the expression \(NETTRD_{r, | ||
+ | |||
+ | |||
+ | \begin{align} | ||
+ | \begin{split} | ||
+ | SegbREV_r & = p^A NETTRD_{r, | ||
+ | & - \left( p^A-p^B\right) \left [ | ||
+ | \begin{matrix} | ||
+ | (1-CDFSugb(q^A))(NETTRD_{r, | ||
+ | + (\sigma^S)^2 PDFSugb(q^A) | ||
+ | \end{matrix} | ||
+ | \right] \\ | ||
+ | & -\left(p^B-p^C\right) \left [ | ||
+ | \begin{matrix} | ||
+ | (1-CDFSugb(q^A+B))(NETTRD_{r, | ||
+ | + (\sigma^S)^2 PDFSugb(q^A+B) | ||
+ | \end{matrix} | ||
+ | \right] | ||
+ | \end{split} | ||
+ | \end{align} | ||
+ | |||
+ | Where \(PDFSugb_r\) and \(CDFSugb_r\) are the probability res. cumulated density functions of the NETTRD variable with the standard deviation \(\sigma^S\). \(\sigma^S\) is defined as \(NETTRD_{r, | ||
+ | |||
+ | |||
+ | \begin{align} | ||
+ | \begin{split} | ||
+ | p^A &= legalqout^A \cdot scalefac \\ | ||
+ | & = legalqout^A \cdot \left(\frac{NETTRD_{SUGB}^{cal}}{legalqout^A} \right )^{0.8} | ||
+ | \end{split} | ||
+ | \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 | ||
+ | |||
+ | |||
+ | ===Update note=== | ||
+ | |||
+ | A number of recent developments are not covered in the previous exposition of supply model equations | ||
+ | |||
+ | -A series of projects have added a distinction of rainfed and irrigated varieties of most crop activities which is the core of the so-called “CAPRI-water” version of the system((A more complete presentation is given in [[https:// | ||
+ | -Several projects have added endogenous GHG mitigation options((These are most completely included in the “trunk” version of the CAPRI system. For details, see, for example, [[http:// | ||
+ | -Several new equations serve to explicitly represent environmental constraints deriving from the Nitrates Directive and the NEC directive((These are most completely included in the “trunk” version of the CAPRI system but developments are still ongoing.)). | ||
+ | -A complete area balance monitoring the land use changes according to the six UNFCCC land use types (cropland, grassland, forest land, wetland, settlements, | ||
+ | |||
+ | ====Calibration of the regional programming models==== | ||
+ | |||
+ | Since the very first CAPRI version, ideas based on Positive Mathematical Programming were used to achieve perfect calibration to observed behaviour – namely regional statistics on cropping pattern, herds and yield – and data base results as the input or feed distribution. The basic idea is to interpret the ‘observed’ situation as a profit maximising choice of the agent, assuming that all constraints and coefficients are correctly specified with the exemption of costs or revenues not included in the model. Any difference between the marginal revenues and the marginal costs found at the base year situation is then mapped into a non-linear cost function, so that marginal revenues and costs are equal for all activities. In order to find the difference between marginal costs and revenues in the model without the non-linear cost function, calibration bounds around the choice variables are introduced. | ||
+ | |||
+ | The reader is now reminded that marginal costs in a programming model without non-linear terms comprise the accounting cost found in the objective and opportunity costs linked to binding resources. The opportunity costs in turn are a function of the accounting costs found in the objective. It is therefore not astonishing that a model where marginal revenues are not equal to marginal revenues at observed activity levels will most probably not produce reliable estimates of opportunity costs. The CAPRI team responded to that problem by defining exogenously the opportunity costs of two major restrictions: | ||
+ | |||
+ | ====Estimating the supply response of the regional programming models==== | ||
+ | |||
+ | The development, | ||
+ | |||
+ | The two possible competitors are standard duality based approaches with a following calibration step or estimates based directly on the Kuhn-Tucker conditions of the programming models. Both may or may not require a priori information to overcome missing degrees of freedom or reduce second or higher moments of estimated parameters. The duality based system estimation approach has the advantage to be well established. Less data is required for the estimation, typically prices and premiums and production quantities. That may be seen as advantage to reduce the amount of more or less constructed information entering the estimation, as input coefficients. However, the calibration process is cumbersome, and the resulting elasticities in simulation experiments will differ from the results of the econometric analysis. | ||
+ | |||
+ | The second approach – estimating parameters using the Kuhn-Tucker-conditions of the model – leads clearly to consistency between the estimation and simulation framework. However, for a model with as many choice variables as CAPRI that straightforward approach may require modifications as well, e.g. by defining the opportunity costs from the feed requirements exogenously. | ||
+ | |||
+ | The dissertation work of Torbjoern Jansson (Jansson 2007) focussed on estimating the CAPRI supply side parameters. The results have been incorporated in the current version. The milk study (2007/08) contributed additional empirical evidence on marginal costs related to milk production (Kempen et al. 2011) | ||
+ | |||
+ | ====Price depending crop yields and input coefficients ==== | ||
+ | |||
+ | Let Y denote yields and j production activities. Yield react via iso-elastic functions to changes in output prices | ||
+ | |||
+ | \begin{equation} | ||
+ | log(Y_j)=\alpha_j+\epsilon_j \, log(p_o) | ||
+ | \end{equation} | ||
+ | |||
+ | The current implementation features yield elasticities for cereals chosen as 0.3, and for oilseeds and potatoes chosen as 0.2. These estimates might be somewhat conservative when compared e.g. with Keeney and Hertel (2008). However, in CAPRI they relate to small scale regional units and single crops, and to European conditions which might be characterized by a combination of higher incentive for extensive management practises and dominance of rainfed agriculture where water might be a yield limiting factor. | ||
+ | |||
+ | Currently, the code is set up as to only capture the effect of output prices. However, in order to spare calculation of the constant terms α, the actual code implemented in ‘// | ||
+ | |||
+ | \begin{equation} | ||
+ | Y_{j, | ||
+ | \end{equation} | ||
+ | |||
+ | |||
+ | ====Annex: Land supply and land transitions in the supply part of CAPRI==== | ||
+ | |||
+ | **Introduction** | ||
+ | |||
+ | This technical paper explains how the most aggregate level of the CAPRI area allocation in the context of the supply models has been re-specified in the TRUSTEE project((https: | ||
+ | )) and subsequently adopted in the CAPRI trunk. The former specification for land supply and transformation functions focused on agricultural land use and the transformation of agricultural land between arable land and grass land((See https:// | ||
+ | )). | ||
+ | |||
+ | During the subsequent period, CAPRI was increasingly adapted to analyses of greenhouse gas (GHG) emission studies. Examples include CAPRI-ECC, GGELS, ECAMPA-X, AgCLim50-X, (European Commission, Joint Research Centre), ClipByFood (Swedish Energy Board), SUPREMA (H2020). This vein of research is very likely to gain in importance in the future. | ||
+ | |||
+ | In order to improve land related climate gas modelling within CAPRI, it was deemed appropriate to (1) extend the land use modelled to //all// available land in the EU (i.e. not only agriculture), | ||
+ | )), but as always, an operational version emerged only after integrating efforts by researchers in several projects working at various institutions. | ||
+ | |||
+ | This paper focusses on the theory applied while data and technical implementation are only briefly covered. | ||
+ | |||
+ | **A simple theory of land supply** | ||
+ | |||
+ | Recall the dual methodological changes attempted in this paper: | ||
+ | |||
+ | - Extend land use modelling to the entire land area, and | ||
+ | - Explicitly model transitions between each pair of land uses | ||
+ | |||
+ | In order to keep things as simple as possible, we opted for a theory where the decision of how much land to allocate to each use is independent of the explicit transitions between classes. This separation of decisions is simplifying the theoretical derivations, | ||
+ | |||
+ | The land supply and transformation model developed here is a bilevel optimization model. At the higher level (sometimes termed the //outer problem//), the land owner decides how much land to allocate to each aggregate land use based on the rents earned in each use and a set of parameters capturing the costs required in order to ensure that the land is available to the intended use. At the lower level (sometimes termed the //inner problem//), the transitions between land classes are modelled, with the condition that the total land needs of the outer problem are satisfied. The inner problem is modelled as a stochastic process involving no explicit economic model. | ||
+ | |||
+ | For the outer problem, i.e. the land owner’s problem, we propose a quadratic objective function that maximizes the sum of land rents minus a dual cost function. The parameters of the dual cost function were specified in two steps: | ||
+ | |||
+ | - A matrix of land supply elasticities was estimated (by TRUSTEE partner Jean Saveur Ay, CESEAR, Dijon (JSA). This estimation might be updated in future work or replaced with other sources for elasticities. | ||
+ | - The parameters of the dual cost function are specified so that the supply behaviour replicates the estimated elasticities as closely as possible while exactly replicating observed/ | ||
+ | |||
+ | The model is somewhat complicated by the fact that land use classes in CAPRI are defined somewhat differently compared to the UNFCCC accounting and also in the land transition data set. Therefore, some of the land classes used in the land transitions are different from the ones used in the land supply model. In particular, “Other land”, “Wetlands” and “Pasture” are differently defined. To reconcile the differences, | ||
+ | |||
+ | **Inner model – land transitions** | ||
+ | |||
+ | A vector of supply of land of various types could result from a wide range of different transitions. The inner model determines the matrix of land transitions that is “most likely”. The concept of “most likely” is formalized by assuming a joint density function for the land transitions, | ||
+ | |||
+ | Since each transition is non-negative, | ||
+ | |||
+ | {{: | ||
+ | |||
+ | Figure 1: Gamma density graph for mode=1 and various standard deviations. “acc”=" | ||
+ | |||
+ | Let $i$ denote land use classes in CAPRI definition, whereas //l// and //k// are land uses in UNFCCC classification. Let $\text{LU}_{k}$ be total land use after transitions and $\text{LU}_{l}^{\text{initial}}$ be land use before transitions. Furthermore, | ||
+ | |||
+ | $${\max_{T_{\text{lk}}}{\log{\prod_{\text{lk}}^{}{f\left( T_{\text{lk}}|\alpha_{\text{lk}}, | ||
+ | |||
+ | $$\Rightarrow \max_{T_{\text{lk}}}\sum_{\text{lk}}^{}\left\lbrack \left( \alpha_{\text{lk}} - 1 \right)\log T_{\text{lk}} - \beta_{\text{lk}}T_{\text{lk}} \right\rbrack$$ | ||
+ | |||
+ | subject to | ||
+ | |||
+ | $$\text{LU}_{k} - \sum_{l}^{}T_{\text{lk}} = 0 \; \left\lbrack \tau_{k} \right\rbrack$$ | ||
+ | |||
+ | $$\text{LU}_{l}^{\text{initial}} - \sum_{k}^{}T_{\text{lk}} = 0\; | ||
+ | |||
+ | $$\text{LU}_{k} - \sum_{i}^{}{\text{shar}e_{\text{ki}}\text{LEV}L_{i}} = 0$$ | ||
+ | |||
+ | The last equation is needed to convert land use in UNFCCC classification to land use in CAPRI classification, | ||
+ | |||
+ | $$\ \left( \alpha_{\text{lk}} - 1 \right)T_{\text{lk}}^{- 1} - \beta_{\text{lk}} + \tau_{k}^{} + \tau_{l}^{\text{initial}} = 0$$ | ||
+ | |||
+ | The parameters $\alpha$ and $\beta$ of the gamma density function were computed by assuming that (i) the observed transitions are the mode of the density, and (ii) the standard deviation equals the mode. Then the parameters are obtained by solving the following quadratic system: | ||
+ | |||
+ | $$\text{mode} = \frac{\alpha - 1}{\beta}$$ | ||
+ | |||
+ | $$\text{variance} = \frac{\alpha}{\beta^{2}}$$ | ||
+ | |||
+ | **Land use transitions as implemented in CAPRI** | ||
+ | |||
+ | The implementation in CAPRI differs from the above general framework in that it explicitly identifies the //annual// transitions in year t $T_{\text{lk}}^{t}$ from the initial $\text{LU}_{l}^{\text{initial}}$ land use to the final land use $\text{LU}_{k}$. This is necessary to identify the annual carbon effects occurring only in the final year in order to add them to the current GHG emissions, say from mineral fertiliser application in the final simulation year. If the initial year is the base year = 2008 and projection is for 2030, then the carbon effects related to the change from the 2008 $\text{LU}_{l}^{\text{initial}}$ to the final land use $\text{LU}_{k}$ (=$T_{\text{lk}}$in the above notation, without time index) refer to a period of 22 years that cannot reasonably be aggregated with the “running” non-CO2 effects from the final year 2030. Furthermore the historical time series used to determine the mode of the gamma density for the transitions also refer to annual transitions. | ||
+ | |||
+ | Initially the problem to link total to annual transitions has been solved by assuming a linear time path from the initial to the final period, but this was criticised as being an inconsistent time path (by FW). Ultimately the time path has been computed therefore in the supply model in line with a static Markov chain with constant probabilities $P_{\text{lk}}$ such that both land use $\text{LU}_{l}^{t}$ as well as transitions $T_{\text{lk}}^{t}$ in absolute ha require a time index (e_luOverTime in supply_model.gms). | ||
+ | |||
+ | $$\text{LU}_{k}^{t} - \sum_{l}^{}{P_{\text{lk}}\text{LU}_{l}^{t - 1}} = 0\ ,\ t = \{ 1,\ldots s\}$$ | ||
+ | |||
+ | Where $\text{LU}_{k}^{s}$ is the final land use in the simulation year s and $\text{LU}_{k}^{0} = \text{LU}_{k}^{\text{iniital}}$ is the initial land use. The transitions in ha in any year may be recovered from previous years land use and the annual (and constant) transition probabilities (e_LUCfromMatrix in supply_model.gms). | ||
+ | |||
+ | $$T_{\text{lk}}^{t} = P_{\text{lk}}*\text{LU}_{l}^{t - 1}$$ | ||
+ | |||
+ | The absolute transitions may enter the carbon accounting (ignored here) and if we substitute the last period’s transitions we are back to the condition for consistent land balancing in the final period from above: | ||
+ | |||
+ | $$\text{LU}_{k}^{s} = \sum_{l}^{}{P_{\text{lk}}\text{LU}_{l}^{s - 1}} = \sum_{l}^{}T_{\text{lk}}^{s}$$ | ||
+ | |||
+ | When using the transition probabilities in the consistency condition for initial land use we obtain | ||
+ | |||
+ | $$\text{LU}_{l}^{\text{initial}} - \sum_{k}^{}T_{\text{lk}}^{1} = 0$$ | ||
+ | |||
+ | $$\Longleftrightarrow \text{LU}_{l}^{\text{initial}} = \sum_{k}^{}{P_{\text{lk}}^{}\text{LU}}_{l}^{\text{iniital}}$$ | ||
+ | |||
+ | $$\Leftrightarrow 1 = \sum_{k}^{}P_{\text{lk}}$$ | ||
+ | |||
+ | So the simple condition is that probabilities have to add up to one (e_addUpTransMatrix in supply_model.gms). In this form the model is currently implemented in CAPRI. | ||
+ | |||
+ | **Outer model – land supply** | ||
+ | |||
+ | The outer problem is defined as a maximization of the sum of land rents minus a quadratic cost term, subject to the first order optimality conditions of the inner problem: | ||
+ | |||
+ | $$\max{\sum_{i}^{}{\text{LEV}L_{i}r_{i}} - \sum_{i}^{}{\text{LEV}L_{i}c_{i}} - \frac{1}{2}\sum_{\text{ij}}^{}{\text{LEV}L_{i}D_{\text{ij}}\text{LEV}L_{j}}}$$ | ||
+ | |||
+ | subject to, | ||
+ | |||
+ | $$\text{LU}_{k} - \sum_{i}^{}{\text{shar}e_{\text{ki}}\text{LEV}L_{i}} = 0$$ | ||
+ | |||
+ | $$\text{LU}_{k} - \sum_{l}^{}T_{\text{lk}} = 0\; | ||
+ | |||
+ | $$\text{LU}_{l}^{\text{initial}} - \sum_{k}^{}T_{\text{lk}} = 0\; | ||
+ | |||
+ | $$\ \left( \alpha_{\text{lk}} - 1 \right)T_{\text{lk}}^{- 1} - \beta_{\text{lk}} + \tau_{k}^{} + \tau_{l}^{\text{initial}} = 0$$ | ||
+ | |||
+ | The parameters of the inner model **α** and **β// | ||
+ | |||
+ | There are a few methodological and numerical challenges to overcome. In particular, we need to (i) analytically derive $\mathbf{\eta}\left( \mathbf{c}, | ||
+ | |||
+ | $$\sum_{i}^{}{\text{LEV}L_{i}} - \sum_{l}^{}{LU_{l}^{\text{initial}}} = 0$$ | ||
+ | |||
+ | Note that the second sum is a constant. This simplification is based on the observation that the land transitions don’t appear in the objective function of the outer problem, so that all solutions to the inner problems are equivalent from the perspective of the outer problem, and that any land use vector that preserves the initial land endowment is a feasible solution to the inner problem. | ||
+ | |||
+ | Next, we formulate the first order condition (FOC) of the modified outer problem to obtain land use as an implicit function of the parameters, $F\left( LEVL, | ||
+ | |||
+ | The first order conditions, and the implicit function, become | ||
+ | |||
+ | $$F\left( LEVL, | ||
+ | \frac{\partial\mathcal{L}}{\partial LEVL_{i}} = & r_{i} - c_{i} - \sum_{j}^{}{D_{\text{ij}}\text{LEV}L_{j}} - \lambda & = 0 \\ | ||
+ | \frac{\partial\mathcal{L}}{\partial\lambda} = & \sum_{i}^{}{\text{LEV}L_{i}} - \sum_{l}^{}{LU_{l}^{\text{initial}}} & = 0 \\ | ||
+ | \end{bmatrix}$$ | ||
+ | |||
+ | In order to apply the implicit function theorem((Recall that the implicit function theorem states that if F(x,p) = 0, then dx/dp = -[dF/ | ||
+ | )) we need to differentiate the FOC once w.r.t. the variables $\text{LEV}L_{i}$ and $\lambda$ and once with respect to the parameter of interest, $r_{j}$, invert the former and take the negative of the matrix product. If (currently) irrelevant parameter are omitted, the following matrix of $(N + 1) \times (N + 1)$ is obtained (the “+1” is the uninteresting derivative of total land rent $\lambda$ with respect to individual land class rent $r_{i}$) | ||
+ | |||
+ | $$\left\lbrack \frac{\partial LEVL}{\partial r} \right\rbrack = - \left\lbrack D_{LEVL, | ||
+ | |||
+ | $$\begin{bmatrix} | ||
+ | \frac{\partial LEVL}{\partial r} \\ | ||
+ | \frac{\partial\lambda}{\partial r} \\ | ||
+ | \end{bmatrix} = - \begin{bmatrix} | ||
+ | \frac{\partial F}{\partial LEVL} & \frac{\partial F}{\partial\lambda} \\ | ||
+ | \end{bmatrix}\left\lbrack \frac{\partial F}{\partial r} \right\rbrack$$ | ||
+ | |||
+ | Carrying out the differentiation specifically for land rent // | ||
+ | |||
+ | $$\begin{bmatrix} | ||
+ | \frac{\partial LEVL_{i}}{\partial r_{j}} \\ | ||
+ | \frac{\partial\lambda}{\partial r_{j}} \\ | ||
+ | \end{bmatrix} = - \begin{bmatrix} | ||
+ | \left\lbrack {- D}_{\text{ij}} \right\rbrack & - 1 \\ | ||
+ | - 1' & 0 \\ | ||
+ | \end{bmatrix}^{- 1}\begin{bmatrix} | ||
+ | I \\ | ||
+ | 0 \\ | ||
+ | \end{bmatrix}$$ | ||
+ | |||
+ | Discarding the last row of the resulting $(N + 1) \times N$ matrix finally lets us compute the elasticity as | ||
+ | |||
+ | $$\left\lbrack \eta_{\text{ij}} \right\rbrack = \left\lbrack \frac{\partial LEVL_{i}}{\partial r_{j}} \right\rbrack\left\lbrack \frac{r_{j}}{\text{LEV}L_{i}} \right\rbrack$$ | ||
+ | |||
+ | In the estimation, we assumed that the prior elasticity matrix is the mode of a density where each entry were independently distributed. Furthermore, | ||
+ | |||
+ | $$\max_{\eta, | ||
+ | |||
+ | subject to | ||
+ | |||
+ | $$\left\lbrack \frac{\partial LEVL_{i}}{\partial r_{j}} \right\rbrack = - \begin{bmatrix} | ||
+ | \left\lbrack {- D}_{\text{ij}} \right\rbrack & - 1 \\ | ||
+ | - 1' & 0 \\ | ||
+ | \end{bmatrix}^{- 1}\begin{bmatrix} | ||
+ | I \\ | ||
+ | 0 \\ | ||
+ | \end{bmatrix}$$ | ||
+ | |||
+ | $$\left\lbrack \eta_{\text{ij}} \right\rbrack = \left\lbrack \frac{\partial LEVL_{i}}{\partial r_{j}} \right\rbrack\left\lbrack \frac{r_{j}}{\text{LEV}L_{i}} \right\rbrack$$ | ||
+ | |||
+ | $$\begin{matrix} | ||
+ | & r_{i} - c_{i} - \sum_{j}^{}{D_{\text{ij}}\text{LEV}L_{j}} - \lambda & = 0 \\ | ||
+ | & \sum_{i}^{}{\text{LEV}L_{i}} - \sum_{l}^{}{LU_{l}^{\text{initial}}} & = 0 \\ | ||
+ | \end{matrix}$$ | ||
+ | |||
+ | and the curvature constraint using a stricter variant of the Cholesky factorization | ||
+ | |||
+ | $$D_{\text{ij}}\left( 1 - \delta I_{\text{ij}} \right) = \sum_{k}^{}{U_{\text{ki}}U_{\text{kj}}}$$ | ||
+ | |||
+ | where $\delta$ is a small positive number and $I_{\text{ij}}$ entries of the identity matrix such that the factor $(1 - \delta I_{\text{ij}})$ shrinks the diagonal of the D-matrix, ensuring //strict// positive definiteness instead of // | ||
+ | |||
+ | **Prior elasticities and area mappings** | ||
+ | |||
+ | The empirical evidence obtained in the TRUSTEE project applied to prior elasticities for land categories based on Corine Land Cover (CLC) data. These categories are also covered in the CAPRI database based on various sources (see the database section in the CAPRI documentation): | ||
+ | |||
+ | The introduction has mentioned already three systems of area categories that need to be distinguished. The first one is the set of area aggregates with good coverage in statistics that has been investigated recently by JS Ay (2016), in the following “JSA”: | ||
+ | |||
+ | $$\text{LEVL} = \left\{ \text{ARAC}, | ||
+ | |||
+ | Where | ||
+ | |||
+ | ARAC = arable crops | ||
+ | |||
+ | FRUN = perennial crops | ||
+ | |||
+ | GRAS = permanent grassland | ||
+ | |||
+ | FORE = forest | ||
+ | |||
+ | ARTIF = artificial surfaces (settlements, | ||
+ | |||
+ | OLND = other land | ||
+ | |||
+ | The above categories are matching reasonably well with the definitions in JSA. A mismatch exists in the classification of paddy (part of ARAC in CAPRI but in the perennial group in JSA) and terrestrial wetlands (part of OLND in CAPRI and a separate category in JSA). Inland waters are considered exogenous in CAPRI and hence not included in the above set LEVL. | ||
+ | |||
+ | For carbon accounting we need to identify the six LU classes from IPCC recommendations and official UNFCCC reporting: | ||
+ | |||
+ | $$LU = \left\{ \text{CROP}, | ||
+ | |||
+ | which is typically indexed below with “l” or “k” ∈ LU and where | ||
+ | |||
+ | CROP = crop land (= sum of arable crops and perennial crops) | ||
+ | |||
+ | GRSLND = grassland in IPCC definition (includes some shrub land and other “nature land”, hence GRSLND> | ||
+ | |||
+ | WETLND = wetland (includes inland waters but also terrestrial wetlands) | ||
+ | |||
+ | RESLND = residual land is that part of OLND not allocated to grassland or wetland, hence RESLND< | ||
+ | |||
+ | FORE = forest | ||
+ | |||
+ | ARTIF = artificial surfaces | ||
+ | |||
+ | In the CAPRI database, in particular for its technical base year, we have estimated an allocation of other land OLND into its components attributable to the UNFCCC classes GRSLND, | ||
+ | |||
+ | $$\text{OLND}^{0} = {\text{OLND}G}^{0} + {\text{OLND}W}^{0} + {\text{OLND}R}^{0}$$ | ||
+ | |||
+ | Lacking better options to make the link between sets LEVL (activity level aggregates) and LU (UNFCCC classes, technically in CAPRI code: set “LUclass”) we will assume that these shares are fixed and may estimate the “mixed” LU areas from activity level aggregates as follows | ||
+ | |||
+ | ^// | ||
+ | |WETLND | ||
+ | |RESLND | ||
+ | |||
+ | which means that the mapping from set LEVL to set LU only uses some fixed shares of LEVL areas that are mapped to a certain LU: | ||
+ | |||
+ | $$LU_k=\sum_i{\text{share}_{\text{i, | ||
+ | |||
+ | where 0 ≤ // | ||
+ | |||
+ | **Technical implementation** | ||
+ | |||
+ | The key equations corresponding to the approach explained above are collected in file supply_model.gms or the included files supply/ | ||
+ | |||
+ | The new land supply specification is only activated if the global variable %trustee_land%==on which may be set via the CAPRI GUI. In order to store the results of the calibration in a compact way that is compatible with the existing code, the existing parameter files “pmppar_XX.gdx” was used. The parameters of the land supply functions, called “c” and “D” above, were stored on two parameters “p_pmpCnstLandTypes” and “p_pmpQuadLandTypes”. As a new symbol (p_pmpCnstLandTypes) is introduced in an existing file, the first run of CAPRI after setting %trustee_land%==on may give errors if the file exists already but has been used with the previous land supply specification before. In this case it helps to delete or rename the old pmppar files. | ||
+ | |||
+ | At this point, it should also be explained that rents for non-agricultural land types were entirely based on assumptions (a certain ratio to agricultural rents). As there were no plans to run scenarios with modified non-agricultural rents, these land rents //r// used in calibration for those land types were subtracted from the “c-paramter”, | ||
+ | |||
+ | Furthermore, | ||
+ | |||
+ | More detailed explanations on the technical implementation are covered elsewhere, for example in the “Training material” included in the EcAMPA-4 deliverable D5. | ||
+ | |||
+ | =====Premium module===== | ||
+ | |||
+ | ====Overview==== | ||
+ | |||
+ | For the European Union, the CAPRI programming models cover in rich detail the different coupled and de-coupled subsidies of the so-called first Pillar 1 of the CAP, as well as major ones from Pillar 2 (i.e., Less Favoured Area support, agri-environmental measures, Natura 2000 support). The interaction between premium entitlements and eligible hectares for the Single Farm Payment (SFP) of the CAP is explicitly considered, as are the different national SFP implementations, | ||
+ | |||
+ | Decoupled payments – as with other premium schemes of the CAP from the present and past – are simulated in CAPRI relatively closely to their definition in existing legislation. The rather high dis-aggregation of the model template regarding production activities and the resolution by farm types inside of NUTS 2 regions clearly eases that task. Currently, 260 different voluntary coupled support schemes are implemented, | ||
+ | |||
+ | The payments – both in reality and in the model – tend to be defined in a cumulative manner. In 1992, the direct payments were introduced based on the previous price support levels multiplied by regional historic reference yields. The payments therefore became regionally differentiated. In the subsequent decoupling under Agenda 2000 and the following reforms, the single farm payments were defined based on the payments that each farm had previously received. The payments got very different expressed per hectare for farms in high yield regions versus low yield regions and for farms that had held animal payments versus arable farms. Then, the 2013 reforms introduced convergence of payment rates, both across farms (internal convergence) and between member states (external convergence). CAPRI reflects these incremental reforms, so that the payment rates in the most recent reform are based on coupled payments from MacSharry times. | ||
+ | |||
+ | Given that each reform has added complexity to the previous system, so too has the premium module of CAPRI grown to maintain the capacity to model previous reforms while allowing novel features such as greening to be introduced. Nevertheless, | ||
+ | |||
+ | ====Basic concept==== | ||
+ | |||
+ | In the CAPRI supply module, premiums are always paid per activity level (per hectare or per animal) basis. They can be differentiated by the low and high yield variant of each crop activity. The premiums are calculated in the premium module from different premium schemes. | ||
+ | |||
+ | A premium scheme (such as DPGRCU for the Grandes Cultures premiums after the Fischler reform) is a logical entity which encompasses: | ||
+ | - A specific application type (defining the basis for the payment amount) | ||
+ | - a region or regional aggregate to which it is applied, | ||
+ | - Possible ceilings in entitlements (CEILLEV) and in value (CEILVAL) | ||
+ | - Payment rates for possibly several lists of activities (such as PGGRCU for all types of Grandes Cultures or PGPROT for protein crops). | ||
+ | - Optionally an indication of the marginal payment when a ceiling is reached | ||
+ | - Optionally a modifier for different amounts per technology | ||
+ | |||
+ | |||
+ | The schemes provide many-to-many mappings between policy instruments and agricultural activities: each scheme can apply to many different activities – with possibly differentiated rates – and each activity can draw support from different schemes. | ||
+ | |||
+ | The application type defines how the nominal amount (called PRMR) is applied. Currently, the following application types are supported: | ||
+ | |||
+ | * perLevl = per ha or head | ||
+ | * perSlgtHd = per slaughtered head | ||
+ | * perYield = per unit of main output | ||
+ | * perHistY = per historic yield | ||
+ | * perLiveStockUnit = per livestock unit | ||
+ | * noDirPay = Norwegian direct payment | ||
+ | * noPriceSup = Norwegian price support | ||
+ | |||
+ | The application type points to a factor by which the nominal amount PRMR (for PRemiuM in Regulation) is converted to a declared value per hectare or head (PRMD). For perLevl, the factor is unity (it is already per hectare), but for instance for perYield, the amount is interpreted as a payment per unit of main output. That is used for the Nordic Aid Scheme for dairy cows in the northmost parts of Europe and for coupled payments in Norway. | ||
+ | |||
+ | Each payment is defined for one or seveal //groups// of activities, functioning as lists of eligible activities. Additionally, | ||
+ | |||
+ | Each premium scheme also has up to two ceiling values: | ||
+ | |||
+ | *ceilLev = Ceiling on LEVL, i.e. the number of hectares or heads | ||
+ | *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, | ||
+ | |||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | |||
+ | The following figure shows the technical implementation at an example: | ||
+ | |||
+ | **Figure 14: Example of technical implementation of a premium scheme** | ||
+ | |||
+ | {{: | ||
+ | |||
+ | 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/ | ||
+ | |||
+ | {{:: | ||
+ | |||
+ | 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/ | ||
+ | |||
+ | {{: | ||
+ | |||
+ | 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. | ||
+ | |||
+ | After loading data, the file with declarations of all available premium schemes et cetera (policy_sets.gms) is loaded. The particular policy to use in the present simulation is contained in the //policy file// with the name defined by the placeholder (environment/ | ||
+ | |||
+ | |||
+ | The premiums defined in the policy file is processed by the file policy.gms. That processing implies a translation of the regulation-like definitions used in the policy file to parameters useful for CAPRI. | ||
+ | |||
+ | Within the simulation algorithm itself, a special file called prmcut.gms is called repeatedly, with the purpose to cut effective premium rates paid in case any ceiling is overshot, so that budgets are respected. | ||
+ | |||
+ | **Figure 15: General flow of logic of CAPRI model as regards premiums** | ||
+ | |||
+ | {{:: | ||
+ | |||
+ | 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 // | ||
+ | |||
+ | {{: | ||
+ | |||
+ | 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: | ||
+ | |||
+ | {{: | ||
+ | |||
+ | 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). | ||
+ | |||
+ | {{:: | ||
+ | |||
+ | These declared rates can hence be aggregated to higher regional units using the activity levels as weights, e.g. from farm types to NUTS2: | ||
+ | |||
+ | {{: | ||
+ | |||
+ | 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: | ||
+ | |||
+ | {{: | ||
+ | |||
+ | From the declared rates and these cut factors, the actually paid premiums are defined: | ||
+ | |||
+ | {{: | ||
+ | |||
+ | 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: | ||
+ | |||
+ | {{: | ||
+ | |||
+ | ====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/ | ||
+ | |||
+ | {{: | ||
+ | |||
+ | -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 regulation premium rate (PRMR) is the default (maximum, uncut) amount of the premium according to regulatory texts, for all activities coverd by the premium group (here PGMEAT) and regions for which the premium is defined. In the example, this means that it is 80 EURO for the group of activities PGMEAT, which is dairy cows, suckler cows, male adult cattle and fattened heifers, in Latvia (LV000000). This is defined in a hierarchical way: if it is set to 80 EURO for the EU and not set at all at lower regional level, the 80 EURO are mapped down to all sub regions by the program. The program also lets you define groups of activities that are linked to the premium. In this case a group PGMEAT has been defined which contains the relevant animals (set s_PSGRP(*) in the file // | ||
+ | -The declared amount in the activity definition of CAPRI (per ha, per head, per 1000 heads) way that the amount PRMR should be applied or declared in CAPRI is called declared premium (PRMD) and applies per head or hectare. In our example, the regulation says that 80 EURO should be paid when the animal is slaughtered. That means that in order to get the amount per living animal and year, the 80 EUROs have to be multiplied by the frequency with which the animal is slaughtered. For male beef cattle it is 1/year whereas it for dairy cows is something like 1/5 years. These numbers come from the CAPRI database. | ||
+ | -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, | ||
+ | |||
+ | 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.)), | ||
+ | |||
+ | 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. | ||
+ | |||
+ | ====Pillar I==== | ||
+ | |||
+ | ===The MTR-reform and the health check=== | ||
+ | |||
+ | On 26 June 2003, EU farm ministers adopted a further fundamental reform of the Common Agricultural Policy (CAP). The central element of the 2003 CAP reform was the introduction of the so-called single payment scheme (SPS). The SPS is based on payments entitlements linked to eligible land, but decoupled from production. However, to avoid abandonment of production, Member States could still choose to maintain a limited link between subsidy and production under well defined conditions and within clear limits. Moreover, these new " | ||
+ | |||
+ | Key elements of the 2003 CAP reform were: | ||
+ | |||
+ | *A single farm payment for EU farmers, independent from production; limited coupled elements may be maintained to avoid abandonment of production; | ||
+ | *land receiving payments should be kept in good agricultural and environmental condition (G.A.E.C). “Good agricultural condition is generally interpreted to mean that the land will not be abandoned and environmental problems such as erosion will be avoided” this requirement could be interpreted as re-establishing the link between the payment and the factors of production employed (land management practices) and ultimately current production; some form of management of the land should be maintained; | ||
+ | *entitlements are tradable within the EU member states (not among them) but certain limitations are imposed (Ciaian, Kancs and Swinnen, 2010). For example, in the Netherlands, | ||
+ | *areas already under permanent pasture should must remain so; in practise, certain reductions at regional level were accepted before Member States would be forced to interact. | ||
+ | *a strengthened rural development policy based on expanded EU budget outlayswith more EU money, new measures to promote the environment, | ||
+ | *a reduction in direct payments (" | ||
+ | *a mechanism for financial discipline to ensure that the farm budget fixed until 2013 is not overshot, | ||
+ | *revisions to the market policy of the CAP: | ||
+ | *asymmetric price cuts in the milk sector: The intervention price for butter will be reduced by 25% over four years, which is an additional price cut of 10% compared to Agenda 2000, for skimmed milk powder a 15% reduction over three years, as agreed in Agenda 2000, is retained, | ||
+ | *reduction of the monthly increments in the cereals sector by half, the current intervention price will be maintained, | ||
+ | *reforms in the rice, durum wheat, nuts, starch potatoes and dried fodder sectors. | ||
+ | |||
+ | In implementing the SPS, member states (MS) could opt for a historical model (payment entitlements based on individual historical reference amounts per farmer), a regional model (flat rate payment entitlements based on amounts received by farmers in a region in the reference period) or a hybrid model (mix of the two approaches, either in a static or in a dynamic manner). An overview of the implementation of direct payments under the CAP in the different MS can be found at [[http:// | ||
+ | |||
+ | Denmark, Germany, Luxembourg, Finland, Sweden, England and Northern Ireland applied a hybrid model. The remaining MS implemented the historical model. From 2007 onwards, dairy payments will be decoupled from production and included in the single payment scheme in all MS. | ||
+ | |||
+ | Although the intention of the CAP reform 2003 is to decouple payments, some payments were not included. In particular the crop specific payment for protein crops, 60% of the payment for starch potatoes, 42% of the payment for rice, the quality premium for wheat and the area payment for nuts. Market organizations for commodities not included in the reform also remained in place. For sugar this changed by the end of 2005 as a reform of the sugar market was decided upon by the EU ministers of Agriculture. The reform included a reduction of the administrative price levels of sugar and sugar beet by with 36%, the introduction of a compensation payment for sugar beet farmers, a premium scheme for the termination of sugar production at factory level (what is referred to as the ' | ||
+ | |||
+ | Until the end of 2007 for several fresh and processed fruit and vegetables coupled payments were given. Since 2008 fruit and vegetables are decoupled and land covered by fruit and vegetables is eligible for payment entitlements under the decoupled aid scheme which applies in other farm sectors (EC, 2007). All existing support for processed fruit and vegetables will be decoupled and the national budgetary ceilings for the SPS will be increased accordingly. | ||
+ | |||
+ | The last step of the EU CAP reform dates from 20 November 2008 when EU agriculture ministers reached a political agreement on the so-called Health Check (HC) of the CAP. Among a range of measures, the agreement abolishes arable set-aside, increases milk quotas gradually leading up to their abolition in 2015, and converts market intervention into a genuine safety net (EC, 2009). Ministers also agreed to increase modulation, whereby direct payments to farmers under the SPS are reduced and the money transferred to the Rural Development Fund. This should allow a better response to the new challenges and opportunities faced by European agriculture, | ||
+ | |||
+ | Under the HC of the CAP it was decided that remaining coupled payments should be decoupled and moved into the Single Payment Scheme (SPS), with the exception of suckler cow, where Member States may maintain current levels of coupled support. Moreover, member states are allowed to review the decision taken on the decoupling of fruit and vegetables in 2007, provided that it results in lower coupled payments. For soft fruits transitional support will continue until 31st December 2011 and be converted into decoupled payment as of 2012 (EC, 2009). Before the HC Member States could retain by sector 10 percent of their national budget ceilings for direct payments for use for environmental measures or improving the quality and marketing of products in that sector (Article 68/69' measures: Assistance to sectors with special problems). Under the HC this possibility will become more flexible. The money will no longer have to be used in the same sector; it may be used to help farmers producing milk, beef, goat and sheep meat and rice in disadvantaged regions or vulnerable types of farming; it may also be used to support risk management measures such as insurance schemes for natural disasters and mutual funds for animal diseases; and countries operating the Single Area Payment Scheme (SAPS) system will become eligible for the scheme (EC, 2009). | ||
+ | |||
+ | Money for Article 68/69’ measures increases as currently unspent money can be used for these measures as well. The Rural Development budget money increases as money shifted away from direct aid based on expanding (modulation) increases to 10% of the direct aid. The additional funding for Rural Development obtained this way may be used by Member States to reinforce programs in the fields of climate change, renewable energy, water management, biodiversity, | ||
+ | |||
+ | In CAPRI, The different implementations of the single farm premium (SFP) introduced with the so-called Mid Term Review of the CAP apply the same logic as for the payment schemes. To give an example, the regional implementation is called DPREG, and might have different payment rates for arable crops (PGARAB) and grass lands (PGGRAS). | ||
+ | |||
+ | The general way these premiums are introduced in CAPRI is shown below. From a reference situation (expost statistical data) and the premiums valid at that time, it is first determined (Decision D1) how much of each existing payments in each scheme are continued to be payed as a coupled scheme, and how much is going into envelops for different types of decoupled payments (part of decision D2). That envelop can be at farm, regional or Member State level and can be implemented in different ways (e.g. historic implementation, | ||
+ | |||
+ | **Figure 16: General way of SFP implementation in CAPRI** | ||
+ | |||
+ | {{:: | ||
+ | |||
+ | 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, | ||
+ | |||
+ | **Single area payment scheme (SAPS)** | ||
+ | |||
+ | The MS who joined the EU since 2004 could choose to apply the single area payment scheme (SAPS), a simplified area payment system, for a transitory period until end 2010 or to apply the same system as in the EU-15 immediately. The most important difference between the SPS and the SAPS is that the entitlements under the SPS can be transferred between farms. | ||
+ | |||
+ | From a technical viewpoint, the single-area premium scheme (SAPS) is the easiest to implement: | ||
+ | |||
+ | {{:: | ||
+ | |||
+ | 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: | ||
+ | |||
+ | {{: | ||
+ | |||
+ | To reach their full level in 2013 (EU 10) or 2016 (Bulgaria and Romania). | ||
+ | |||
+ | 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: | ||
+ | |||
+ | {{: | ||
+ | |||
+ | These top-ups have to be reduced towards the end of the period where the the Pillar I premiums are phased in: | ||
+ | |||
+ | {{: | ||
+ | |||
+ | **Non-SAPS implementation** | ||
+ | |||
+ | 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 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) \\ | ||
+ | {{:: | ||
+ | * And permanent grass land (PGGRAS) is eligble \\ | ||
+ | {{: | ||
+ | * The historic implementation \\ | ||
+ | {{: | ||
+ | |||
+ | 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” | ||
+ | |||
+ | {{: | ||
+ | |||
+ | That information is the basis to define regional premium envelops (= CEILVAL) for the different Member states. That is a rather complex program (‘// | ||
+ | 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. | ||
+ | |||
+ | {{: | ||
+ | |||
+ | There two other factors: | ||
+ | * A possible greening share according to the October 2011 proposal by the Commission, see the section on CAP 2014-2020 for more details | ||
+ | * A national ceiling cut factor which aligns the envelops calculated from the past payments with he total MTR ceiling as defined in the legal texts. | ||
+ | |||
+ | The part which is not longer coupled goes into the decoupled schemes: | ||
+ | {{: | ||
+ | |||
+ | 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: | ||
+ | |||
+ | {{: | ||
+ | |||
+ | After that, a possible share going into the greening payment (from 2014) is deducted: | ||
+ | |||
+ | {{: | ||
+ | |||
+ | 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: | ||
+ | |||
+ | {{: | ||
+ | |||
+ | That sum if then distributed to the relevant MTR implementation scheme according to the distribution keys defined above: | ||
+ | |||
+ | {{: | ||
+ | |||
+ | These calculation require that first the total premiums received in the history period are calculated which is done in ‘// | ||
+ | |||
+ | ===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/ | ||
+ | |||
+ | {{: | ||
+ | |||
+ | 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. | ||
+ | |||
+ | // | ||
+ | |||
+ | {{: | ||
+ | |||
+ | 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”, | ||
+ | |||
+ | {{: | ||
+ | |||
+ | 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, | ||
+ | |||
+ | {{: | ||
+ | |||
+ | The code implementing the logic behind these various settings is generic and found in the file “gams/ | ||
+ | |||
+ | //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/ | ||
+ | |||
+ | The //Greening Measures// can be steered by the modeller. Even though the greening in itself is complex in implementation, | ||
+ | |||
+ | {{: | ||
+ | |||
+ | 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 share of permanent grass land to arable land cannot decline relative to the base year. | ||
+ | * A minimum measure of crop-diversity must be maintained. | ||
+ | * 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 “// | ||
+ | |||
+ | 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 // | ||
+ | |||
+ | **Figure 17: The logic of the CAP 2014-2020 reference policy as implemented in the CAPRI policy module** | ||
+ | |||
+ | {{: | ||
+ | |||
+ | ===Tradable Single Premium Scheme entitlements=== | ||
+ | |||
+ | With the so-called Mid Term Review of the Common Agricultural Policy, the so-called Single Farm Premium (SFP) as a decoupled payment was introduced which is implemented as a subsidy which does not require production, is subject to cross-compliance and paid per ha up to a number of entitlements. The original entitlements, | ||
+ | |||
+ | In CAPRI, the assumption in the baseline is that all hectares used by agriculture are able to claim the SFP and that any unused entitlements had been removed so that the SFP becomes fully capitalized into land. Subsequent changes in the premiums including the SFP, prices or other policy instruments in a counterfactual run could decrease the marginal returns to agricultural land. Based on the land supply curve implemented in CAPRI, agricultural land use would shrink and some entitlements become unused. Vice versa, if changes let the marginal return to land increase, the entitlements become the limiting factor to claim the subsidy. The increase is thus mapped into an economic rent to the entitlement. If changes generate rents on entitlements in some farm types and not in others, one would assume that trade in entitlements will occur. A simple algorithm to trade the entitlement is now included in CAPRI and described below. | ||
+ | |||
+ | //Switching on the entitlement trade// | ||
+ | |||
+ | The trade module is implemented in the file ‘// | ||
+ | |||
+ | {{:: | ||
+ | |||
+ | By default, the entitlement trade is switched OFF in the general settings file of CAPMOD, called gams/ | ||
+ | |||
+ | {{: | ||
+ | |||
+ | 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: | ||
+ | |||
+ | {{: | ||
+ | |||
+ | //How the entitlement trade works// | ||
+ | |||
+ | The following code pieces are taken from ‘// | ||
+ | |||
+ | {{: | ||
+ | |||
+ | From these a maximum of 10% is defined as the demand in each iteration: | ||
+ | |||
+ | {{: | ||
+ | |||
+ | In order to take differences in the marginal returns into account, an indicator based on the squared value is used: | ||
+ | |||
+ | {{: | ||
+ | |||
+ | It serves as the distribution key of unused entitlements, | ||
+ | |||
+ | {{: | ||
+ | |||
+ | Next, the number of unused entitlements is stored: | ||
+ | |||
+ | {{: | ||
+ | |||
+ | 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: | ||
+ | |||
+ | {{: | ||
+ | |||
+ | The supply is then distributed according to the squared value of the individual demanders | ||
+ | |||
+ | {{: | ||
+ | |||
+ | //An example printout// | ||
+ | |||
+ | 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: | ||
+ | |||
+ | {{: | ||
+ | |||
+ | 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. | ||
+ | |||
+ | Finally, we come to the main point which motivated the introduction of that module. As indicated above, we interpret the SFP as a subsidy to agricultural land use which at the margin is capitalized in the land rent. It thus increases the marginal returns to land use in agriculture. In our baseline, we start with a situation with an assumed equilibrium in land markets, i.e. marginal returns in agriculture including any subsidies are equal to marginal returns of alternative uses. | ||
+ | |||
+ | Reducing the SFP will render agricultural land use less competitive so that land owner will rent out less to agriculture and put the land into other uses. That effect can be clearly seen below in the first iteration: in the farm types where the SFP drops due to uniform SFP at NUTS2 in Greece, land use is reduced. Total land use in Greece drops by 1.2%. But if we re-distribute the subsidy between farm types, farms which were competing before with below average subsidies against alternative land use possibilities now would like to expand land use. Without additional entitlements, | ||
+ | |||
+ | ====Pillar II==== | ||
+ | |||
+ | ===Overview=== | ||
+ | |||
+ | Modelling of Pillar II for an EU-wide assessment provides a specific challenge given data availability regarding measures which are programmed and implemented at Member State or even regional level. Official reporting of measures under Pillar II in standardized data bases uses a rather rough categorisation, | ||
+ | |||
+ | The most important measures from a budgetary view point are the Agri-Environmental Schemes and the Less Favourite Area Payments. Therefore some care must be taken to model these measures accurately. The project draws here on the work of a study by LEI and IEEP (LEI and IEEP 2009) for DG-AGRI, which use in the case of the agri-environmental payments analysis based on FADN and for LFA based on FADN and CLUE (Verburg et.al. 2010) results. | ||
+ | |||
+ | **Table 26: Overview of pillar II measures modelled in CAPRI** | ||
+ | |||
+ | |Measure type |Measure codes EU| Modelling approach in CAPRI| | ||
+ | |LFAs |211-212 |Regional direct support. Distribution over sectors and regions based on FADN data and CLUE results.| | ||
+ | |Natura 2000|213, | ||
+ | |Agri-environment|214-215| Regional direct support. Distribution over sectors and regions based on FADN data. 50% of the support directed towards TF8 farm types 1, 2, 3, 4 and 8 is conditional on extensive technology being used, for remaining amounts extensive as well as intensive technology is eligible.| \\ Source: Capri Modelling System | ||
+ | |||
+ | ===Modelling of LFA=== | ||
+ | |||
+ | The LFA measure was implemented as a direct payment to cropping and grassland, with the same amount for all cropping activities except for fallow land. The first challenge encountered when implementing the LFA premiums is that the regions do not coincide with the administrative regions used in CAPRI. – Recall that CAPRI only has one single representative firm in each nuts 2 region (or up to nine farm types). In reality, thus, only a share, generally much less than 100%, of the land in a nuts region is eligible for LFA payments, and it may very well be the case that the agricultural production on that land is different from the regional average. For example, one may expect that a mountainous LFA area contains more grass land than the surrounding flat land agricultural areas in the same nuts 2 region. In order to capture a possible bias of this nature, a GIS tool (CLUE-model) was used to compute the shares \(S_{ij}\) of LFA in different broad land use classes //j// \(\in\) {non-irrigated arable land, irrigated arable land, pasture, permanent crops} in each region //i//. Those shares were used to compute a (potentially) different nominal premium amount for crops belonging to each class //j//. The so computed different amounts were taken to reflect the biased distribution of crops inside and outside of LFA regions. Since CLUE does not distinguish “Mountainous” and “Other” LFA, the nominal amount //A// to which the shares //S// were applied was assumed the same everywhere: 250 euro, the maximum amount in mountainous LFA regions. | ||
+ | |||
+ | \begin{equation} | ||
+ | P_{ij} =AS_{ij} | ||
+ | \end{equation} | ||
+ | |||
+ | where \\ | ||
+ | //P// = Premium per hectare \\ | ||
+ | //i// = Region \\ | ||
+ | //j// = Group of crops \\ | ||
+ | //A// = Maximum amount per hectare, 250 euro \\ | ||
+ | //S// = Share of LFA in all land of class //j// \\ | ||
+ | |||
+ | A value ceiling for the premium was computed by adding the budgets for the component measures. Recall that the premium module of CAPRI will apply a cut factor to the amount P such that the ceiling is not overshot. | ||
+ | |||
+ | In economic terms, the potentially different premium rates for different groups of crops has a production effect, so that the type of production in CAPRI that receives the higher rates may expand on the expense of other activities. The interpretation would be that more farmers in the LFA areas comply with the LFA eligibility rules and modify their production plans to comply with the criteria there. Nevertheless, | ||
+ | |||
+ | === Modelling of N2k === | ||
+ | |||
+ | Each production activity in CAPRI is split into a low and high yield variant with adjusted input coefficients, | ||
+ | |||
+ | The interpretation is the following: If more money is spent on the measure, more farmers within the designated areas may switch to extensive agriculture. Then the average payment per hectare of the nuts 2 region would increase, reflecting that a larger share of the farmers now participate in the measure. It is today indeed the case that not all farms within an N2k area receive support. | ||
+ | |||
+ | ===Modelling agri-environmental payments=== | ||
+ | |||
+ | The agri-environmental payments is a very diverse set of measures, which accounts for the largest share of the second pillar. In the modelling approach opted for here, with one aggregated measure “05 agri-environment”, | ||
+ | |||
+ | The method for “nationalization” of the AE scheme employed here is to use the distribution of the sum of the AE measures, i.e. the measure allocated to class 05, to agricultural sectors using the receipts by farm types according to FADN in 2005 as key. This implies linking the support to production. Whether this corresponds to reality is an empirical question. It is doubtless the case for some measures in some regions, but certainly not so for all AE measures in all regions. Refining the implementation would thus involve conditioning the support on technical constraints. Nevertheless, | ||
+ | |||
+ | **Table 27: Mapping from aggregated farm types in FADN (TF8) to activity groups in CAPRI** | ||
+ | |||
+ | |TF8 type|Group of activities in CAPRI| | ||
+ | |1|Grandes Cultures| | ||
+ | |2|Vegetables| | ||
+ | |3|Wine| | ||
+ | |4|Permanent crops| | ||
+ | |5|Dairy cows including pastures| | ||
+ | |6|Suckler cows, sheep and goats, including pastures| | ||
+ | |7|Pigs and poultry| | ||
+ | |8|All agricultural activities| \\Source: Capri Modelling System | ||
+ | |||
+ | The agri-environmental (AE) payments are implemented as extensification subsidies, and they are distributed to regions based on the distribution of less-favoured areas across regions. However, the distribution is modulated by the national level shares of farms in or out of LFA receiving AE support. We needed the following two probabilities: | ||
+ | |||
+ | p_landPartition(ru, | ||
+ | |||
+ | p_aeLfa(ms, | ||
+ | |||
+ | 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/ | ||
+ | |||
+ | {{:: | ||
+ | |||
+ | 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. | ||
+ | |||
+ | Finally, an extensification effect to the AE payments is introduced using the possibility to make technological variants differently eligible. | ||
+ | |||
+ | {{: | ||
+ | |||
+ | {{: | ||
+ | |||
+ | ====Co-financing rates, assignment of premiums to pillars, WTO boxes and PSE-types==== | ||
+ | |||
+ | **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 // | ||
+ | |||
+ | {{: | ||
+ | |||
+ | **PSEs** | ||
+ | |||
+ | The mapping to the PSE-types is defined in // | ||
+ | |||
+ | {{: | ||
+ | |||
+ | **WTO boxes** | ||
+ | |||
+ | In a similar fashion, the premiums are allocated to the WTO boxes. The following payments are allocated to the green box (‘// | ||
+ | |||
+ | {{: | ||
+ | |||
+ | 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: | ||
+ | |||
+ | {{: | ||
+ | |||
+ | Currently, the following budget categories are supported (see ‘// | ||
+ | |||
+ | {{: | ||
+ | |||
+ | In ‘// | ||
+ | |||
+ | {{: | ||
+ | |||
+ | In order to come to a product based accounting scheme as used by the PSEs and WTO, these payments are assigned to the main outputs of the activities. Payments to obligatory set-aside are allocated to the activities according to set-aside rates: | ||
+ | |||
+ | {{: | ||
+ | |||
+ | For a discussion about the WTO and PSE Boxes and their implementation in CAPRI see: Mittenzwei, K., Britz, W. und Wieck, C. (2012): Studying the effects of domestic support provisions on global agricultural trade: WTO and OECD policy indicators in the CAPRI model, selected paper presented at the 15th Annual Conference on Global Economic Analysis, "New Challenges for Global Trade and Sustainable Development", | ||
+ | |||
+ | =====Market module for agricultural outputs===== | ||
+ | |||
+ | ====Overview on the market model==== | ||
+ | |||
+ | Whereas the outlay of the supply module has not changed fundamentally since the CAPRI project ended in 1999, the market module was completely revised. Even if several independent simulation systems for agricultural world markets are available as OECD’s AgLink, the FAPRI system at the University of Missouri or the WATSIM((In the beginning, the CAPRI market part draw on the data base from the WATSIM modelling system. As the latter is not longer active, the CAPRI market part has become an independent world trade model for agricultural products.)) system at Bonn University, it was still considered necessary to have an independent market module for CAPRI. | ||
+ | |||
+ | The CAPRI market module can be characterised as a comparative-static, | ||
+ | |||
+ | It is deterministic as stochastic effects are not covered and partial as it excludes factor (labour and capital) markets, non-agricultural products and some agricultural products as flowers. It is spatial as it includes bilateral trade flows and the related trade policy instruments between the trade blocks in the model. | ||
+ | |||
+ | The term partial equilibrium model or multi-commodity model stands for a class of models written in physical and valued terms. Demand and supply quantities are endogenous in that model type and driven by behavioural functions depending on endogenous prices. Prices in different regions are linked via a price transmission function, which captures e.g. the effect of import tariffs or export subsidies. Prices in different markets (beef meat and pork meat) in any one region are linked via cross-price terms in the behavioural functions. These models do not require an objective function; instead their solution is a fix point to a square system of equations which comprises the same number of endogenous variables as equations. | ||
+ | |||
+ | The CAPRI market module breaks down the world in about 80 countries, each featuring systems of supply, human consumption, | ||
+ | |||
+ | The processing can be differentiated by processing of (a) oilseeds to cakes and oils; (b) biofuel feedstocks to biofuels; (c) raw milk to dairy products; and (d) any other type of industrial processing. The parameters of all types of behavioural functions are derived from elasticities, | ||
+ | |||
+ | Some of the about 80 countries with behavioural functions (CAPRI set “RMS”) are aggregated for trade policy modelling into in 44 trade blocks or country aggregates (CAPRI set “RM”) with a uniform border protection, and bilateral trade flows are modelled solely between these blocks. Such blocks are EU_WEST, EU_EAST, ‘other Mediterranean’ countries, Uruguay and Paraguay, Bolivia, Chile and Venezuela, and Western Balkan countries. All other countries or country aggregates are identical to one of the 40 trade blocks in the model. | ||
+ | |||
+ | The two EU blocks (EU_WEST, EU_EAST) interact via trade flows with the remaining trade blocks in the model, but each of the EU Member States features an own system of behavioural functions. The prices linkage between the EU Member States and the EU pool is currently simply one of equal relative changes, not at least ease the analysis of results. If regional competitiveness and hence net exports change significantly it may be expected (and has been observed in Hungary since 2004) that prices in ‘surplus’ regions would decrease relative to the EU average, contrary to the assumption of proportional linkage. Alternative specifications have been analysed in the context of the CAPRI-RD project and an option of a flexible definition of EU subaggregates is currently the topic of an ongoing project. | ||
+ | |||
+ | The current break down of the CAPRI market model can be found at [[http:// | ||
+ | |||
+ | The market model in its current layout comprises about 70.000 endogenous variables and the identical number of equations. | ||
+ | |||
+ | //Policy instruments// | ||
+ | |||
+ | ====The approach of the CAPRI market module==== | ||
+ | |||
+ | Multi-commodity models are as already mentioned above a widespread type of agricultural sector models. There are two types of such models, with a somewhat different history. The first type could be labelled ‘template models’, and its first example is Swopsim. Template models use structurally identical equations for each product and region, so that differences between markets are expressed in parameters. Typically, these parameters are either based on literature research, borrowed from other models or simply set by the researcher, and are friendly termed as being ‘synthetic’. Domestic policies in template models are typically expressed by price wedges between market and producer respectively consumer prices, often using the PSE/CSE concept of the OECD. Whereas template models applied in the beginning rather simple functional forms (i.e, constant elasticity double-logs in Swopsim or WATSIM), since some years flexible functional forms are in vogue, often combined with a calibration algorithm which ensures that the parameter sets are in line with microeconomic theory. The flexible functional forms combined with the calibration algorithm allow for a set of parameters with identical point elasticities to any observed theory consistent behaviour which at the same time recovers quantities at one point of observed prices and income. Ensuring that parameters are in line with profit respectively utility maximisation allows for a welfare analysis of results. | ||
+ | |||
+ | Even if using a different methodology (explicit technology, inclusion of factor markets etc.), it should be mentioned that Computable General Equilibrium models are template models as well in the sense that they use an identical equation structure for all products and regions. Equally, they are in line with microeconomic theory. | ||
+ | |||
+ | The second type of model is older and did emerge from econometrically estimated single-market models linked together, the most prominent example being the AGLink-COSIMO modelling system. The obvious advantages of that approach are firstly the flexibility to use any functional relation allowing for a good fit ex-post, secondly that the econometrically estimated parameters are rooted in observed behaviour, and thirdly, that the functional form used in simulations is identically to the one used in parameter estimation. The downside is the fact that parameters are typically not estimated subject to regularity conditions and will likely violate some conditions from micro-theory. Consequently, | ||
+ | |||
+ | The CAPRI market module is a template model using flexible functional forms. The reason is obvious: it is simply impossible to estimate the behavioural equations for about 65 products and 80 countries or country blocks worldwide with the resources available to the CAPRI team. Instead, the template approach ensures that the same reasoning is applied across the board, and the flexible functional forms allow for capturing to a large degree region and product specificities. As such, the results from econometric analysis or even complete parameters sets from other models could be mapped into the CAPRI market model. | ||
+ | |||
+ | ====Behavioural equations for supply, feed demand and land markets==== | ||
+ | |||
+ | The definition of the market model can be found in // | ||
+ | |||
+ | ===Agricultural supply=== | ||
+ | |||
+ | //Supply// for each agricultural output //i// and region //r// (EU Member States or regional aggregate) is modelled by a supply function derived from a normalised quadratic profit function via the envelope theorem. Supply depends on producer prices // | ||
+ | |||
+ | \begin{equation} | ||
+ | v\_prodQuant_{i, | ||
+ | \end{equation} | ||
+ | |||
+ | Supply curves for the EU Member States, Norway, Turkey, Western Balkans are calibrated in each iteration to the last output price vector used in the supply model and the aggregated supply results at Member State level, by shifting the constant terms //as//. The slope terms //bs// which capture own and cross-price effects are set in line with profit maximisation, | ||
+ | |||
+ | For the countries which matching regional models on the supply side, the bs parameters are derived directly from the costs function terms and elements of the constraints matrix (see Chapter 4.3 FIXME above). | ||
+ | |||
+ | ===Land supply and demand=== | ||
+ | |||
+ | The reader should note that land is one of the products in the above system which is an input into agriculture. A land supply curve defines the demand side of the land balance which together with the land demand according to the equation above define the land rent clearing the balance. Equally, the price for feed energy is an input price entering the equations. | ||
+ | |||
+ | \begin{align} | ||
+ | \begin{split} | ||
+ | v\_prodQuant_{r," | ||
+ | &+ p\_cnstLandElas_r \; log(v\_prodPrice_{r," | ||
+ | \end{split} | ||
+ | \end{align} | ||
+ | |||
+ | **Figure 18: Land supply curve examples** | ||
+ | |||
+ | {{:: | ||
+ | |||
+ | 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: | ||
+ | |||
+ | \begin{equation} | ||
+ | \frac {dLand}{dp_i} | ||
+ | \end{equation} | ||
+ | |||
+ | where //Q// denotes quantities and //p// prices. The calibration requires prices for land which is set to 0.3 of the crop revenues. For fodder area demand from animals it was set lower (cp. page 56 in Golub et.al. 2006). The summation term over all products //j// defines the “land demand change” if the price //i// changes. The quantity change of each product //j// is translated into a land demand change based on its yield. The reciprocal of the yield can be interpreted as the land demand per unit produced. | ||
+ | |||
+ | The last term translates first the yield elasticity (an endogenous variable) into a marginal quantity effect and, then again, based on the yield, in a changed land demand. The land demand change is subtracted as the land demand for product //i// per unit decreases if yields increase due to a positive own price yield elasticity. This formulation assumes, as conventionally done in multi-commodity models, that cross-price yield effects are zero. | ||
+ | |||
+ | The CAPRI market model does not handle explicitly non-tradable crop outputs such as grass, silage or fodder maize. However, the land demand for these products is also taken into account in order to allow closing an overall land balance. This is achieved by deriving per unit land demands for animal products. | ||
+ | |||
+ | The link to land supply is straightforward: | ||
+ | |||
+ | If the market balance equation is dropped and the land price fixed, totally elastic land supply to agriculture is assumed. This assumption should be of little empirical value as agriculture is typically the major demander for land suitable to agriculture. The current solution incorporates a land supply curve with exogenous given elasticities (similar to Tabeau et.al. 2006). The parameterization of the land supply curve is currently chosen similar to the land elasticities e.g. reported in GTAP (Ahmed et al. 2008). Generally, land supply is rather inelastic so that price increase of agricultural commodities rather increases land prices and not so much land use. | ||
+ | |||
+ | Although the profit function approach does not allocate areas to individual crops, it captures in a dual formulation how product and land price changes impact on //total// agricultural land use. The estimated yield elasticity may be used however to derive an allocation which is consistent with the assumptions used during parameter calibration. Basically, for each crop product, the yield elasticity is used to derive from the simulated quantity change the implied land change. The resulting land demands are then scaled to match the simulated change in total land. This allocation is currently active at solution time (with explicit equations) in the “trunk” version of CAPRI but not yet in all branches (in particular not in the “star2.4” version underlying the CAPRI Training 2019). | ||
+ | |||
+ | ===Feed demand=== | ||
+ | |||
+ | The system for //feed demand// for countries not covered by the supply part is structured identically to the supply system. However, not producer prices, but raw product prices // | ||
+ | |||
+ | \begin{equation} | ||
+ | v\_feedQuant_{i, | ||
+ | \end{equation} | ||
+ | |||
+ | One of the prices in the equations above is the price for feed energy which is conceptually the output sold by the feed producing industry where products used for feed are its input. A balance between feed energy demanded, derived from the supply quantities and feed energy need for tradeables per unit produced and feed energy delivered from current feed demand quantities drives the price for feed energy: | ||
+ | |||
+ | \begin{equation} | ||
+ | \sum_i v\_feedQuant_{i, | ||
+ | \end{equation} | ||
+ | |||
+ | For countries which matching modules on the supply side, a different system is set-up. In the supply part, individual commodities are aggregated to categories as cereals. The composition of these aggregates is determined by a CES function, whereas total demand for each category depends on the average price aggregated from the ingredients. | ||
+ | |||
+ | As for supply, feed demand for the aggregate EU Member States, Norway, Turkey and Western Balcans, are calibrated in each iteration to the last output price vector used in the supply model and the aggregated feed demand at Member State level. | ||
+ | |||
+ | The disadvantage of the behavioural functions above is the fact that they might generate non-positive values. That situation might be interpreted as a combination of prices where the marginal costs exceed marginal revenues. Accordingly, | ||
+ | |||
+ | ====Behavioural equations for final demand==== | ||
+ | |||
+ | The final demand functions are based on the following family of indirect utility functions depending on consumer prices //cpri// and per capita income //y//((Per capita income and total expenditure are used as synonyms in the following as the demand is cover all goods and thus exhaust available income.)) | ||
+ | |||
+ | \begin{equation} | ||
+ | U(cpri,y) = \frac {-G} {y-F} | ||
+ | \end{equation} | ||
+ | |||
+ | Using Roy’s identity, the following per capita Marshallian demands //PerCap// are derived: | ||
+ | |||
+ | \begin{equation} | ||
+ | PerCap_i = F_i+ \frac {G_i} {G} (y-F) | ||
+ | \end{equation} | ||
+ | |||
+ | where the \(F_i\) and \(G_i\) are the first derivative of //F// and //G// versus own prices. The function //F// is defined as follows: | ||
+ | |||
+ | \begin{equation} | ||
+ | F_r = \sum_i d_i \; cpri_i | ||
+ | \end{equation} | ||
+ | |||
+ | where the \(d_i\) have a similar role as constant terms in the Marshallian demands and can be interpreted as ‘minimum commitment levels’ or consumption quantities independent of prices and income. The term in brackets in the per capita demands in Equation 122 FIXME above hence captures the expenditure remaining after the value //F// of price and income independent commitments //d// (‘committed income’) has been subtracted from available income //y// to give so called ‘non-committed’ income. The function //G// is based on the Generalised Leontief formulation and must be positive to have indirect utility increasing in income: | ||
+ | |||
+ | \begin{equation} | ||
+ | G = \sum_i \sum_j bd_{ij} \sqrt {cpri_i \; cpri_j} | ||
+ | \end{equation} | ||
+ | |||
+ | with the derivative of //G// versus the own price is labelled \(G_i\) and defined as: | ||
+ | |||
+ | \begin{equation} | ||
+ | G_j = \sum_i | ||
+ | \end{equation} | ||
+ | |||
+ | Symmetry is guaranteed by a symmetric //bd// matrix describing the price dependent terms, correct curvature by non-negative the off-diagonal elements of //bd//, adding up is automatically given, as Euler’s Law for a homogenous function of degree one \( \left ( a(x) = \sum_i \frac{\partial a(x)}{\partial x_i}x_i \right ) \) , leads to: | ||
+ | |||
+ | \begin{align} | ||
+ | \begin{split} | ||
+ | \sum_i PerCap_i \; cpri_i &= \frac{\sum_i G_icpri_i}{G}(y-F)+ \sum_i d_icpri_i\\ | ||
+ | &= \frac{ G}{G} (y-F)+ F = \; y | ||
+ | \end{split} | ||
+ | \end{align} | ||
+ | |||
+ | and homogeneity is guaranteed by the functional forms as well. The expenditure function follows from rearranging Equation 121 FIXME : | ||
+ | |||
+ | \begin{equation} | ||
+ | y = e(U, | ||
+ | \end{equation} | ||
+ | |||
+ | The function is flexible to reflect all conceivable own price and expenditure elasticities but the non-negativity imposed on the off-diagonal elements ensuring excludes Hicksian complementarity, | ||
+ | |||
+ | //Human consumption hcom// is simply the sum of population //pop// multiplied with the per capita demands: | ||
+ | |||
+ | \begin{equation} | ||
+ | hcom_{i,r} = pop_r \; PerCap_{i, | ||
+ | \end{equation} | ||
+ | |||
+ | ====Behavioural equations for the processing industry==== | ||
+ | |||
+ | // | ||
+ | |||
+ | \begin{equation} | ||
+ | v\_procMarg_{i, | ||
+ | \end{equation} | ||
+ | |||
+ | The processing margins are replaced by producer prices times -1 for all products besides oilseed. For the latter, the processing margin is defined from the producer prices // | ||
+ | |||
+ | FIXME | ||
+ | |||
+ | \begin{align} | ||
+ | \begin{split} | ||
+ | v\_prodMarg_{seed, | ||
+ | & +v\_prodPrice_{seed \rightarrow cak,r} v\_procYield_{cak, | ||
+ | & +v\_prodPrice_{seed \rightarrow oil,r} v\_procYield_{oild, | ||
+ | \end{split} | ||
+ | \end{align} | ||
+ | |||
+ | Finally, output of oils and cakes //supply// depends on the processed quantities //proc// of the oilseeds and the crushing coefficients: | ||
+ | FIXME | ||
+ | |||
+ | \begin{align} | ||
+ | \begin{split} | ||
+ | supply_{cake, | ||
+ | supply_{oil, | ||
+ | \end{split} | ||
+ | \end{align} | ||
+ | |||
+ | The processing yields in the base year are defined as: | ||
+ | |||
+ | \begin{equation} | ||
+ | v\_procYield_{cak, | ||
+ | \end{equation} | ||
+ | |||
+ | The processing yields are however not fixed during simulation, but depend on a CES function: the share of oil increases very slightly if the oil price increases compared to the cake price, and vice versa. | ||
+ | |||
+ | Special attention is given to the processing stage of //dairy products//. First of all, balancing equations for fat and protein ensure that the processed products use up exactly the amount of fat and protein comprised in the raw milk. The //fat and protein content// of raw milk //cont// and milk products //mlk// is based on statistical and engineering information, | ||
+ | |||
+ | \begin{equation} | ||
+ | v\_prodQuant_{" | ||
+ | \end{equation} | ||
+ | |||
+ | Production of //processed dairy products// is based on a normalised quadratic function driven by the difference between the dairy product’s market price and the value of its fat and protein content. | ||
+ | |||
+ | \begin{align} | ||
+ | \begin{split} | ||
+ | v\_prodQuant_{mlk, | ||
+ | &+ \sum_j bm_{mlk, | ||
+ | \end{split} | ||
+ | \end{align} | ||
+ | |||
+ | And lastly, prices of raw milk are derived from its fat and protein content valued with fat and protein prices and a processing margin. | ||
+ | |||
+ | ====Trade flows and the Armington assumption==== | ||
+ | |||
+ | The //Armington assumption// | ||
+ | |||
+ | The underlying reasoning is that of a two-stage demand system. At the upper level, demand for products such as wheat, pork etc. is determined as a function of prices and income – see above. These prices are a weighted average of products from different regional origins. At the lower level, the composition of demand per product //i// in region //r// stemming from different origins r1 is determined based on a CES utility function: | ||
+ | |||
+ | \begin{equation} | ||
+ | U_{i,r} = \alpha_{i, | ||
+ | \end{equation} | ||
+ | |||
+ | where //U// denotes utility in region //r// and for product //i// due to consumption of the import quantities //M// stemming from the different origins //r1//. If //r// is equal //r1//, //M// denotes domestic sales. \(\delta\) are the share parameters, \(\alpha\) is called the shift-parameter, | ||
+ | |||
+ | \begin{equation} | ||
+ | M_{i,r,r1} = U_{i,r} \delta_{i, | ||
+ | \end{equation} | ||
+ | |||
+ | As seen from the equation, imports from region //r1// will increase if its competitiveness increases – either because of a lower price in //r1// or a higher average import price. The resulting changes in the compositions of imports increase with the size of the related share parameter \(\delta_{i, | ||
+ | |||
+ | The model comprises a two stage Armington system (see below): on the top level, the composition of total demand from imports and domestic sales is determined, as a function of the relation between the domestic price and the average import price. The lower stage determines the import shares from different origins and defines the average import price. This also means that the implementation in the code has to distinguish between a top and lower level level quantity (or price) aggregate. The substitution elasticity on the top level stage is smaller than for the second one, i.e. we assume that consumers will be less responsive regarding substitution between domestic and imported goods compared to changes in between imported goods. | ||
+ | |||
+ | 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 [[scenario simulation# | ||
+ | |||
+ | ^Product (group) ^Substitution elasticity between domestic sales and imports | ||
+ | |Cheese, fresh milk products | | ||
+ | |Other vegetables | | ||
+ | |Other fruits | | ||
+ | |Sugar| 12 | 12 | | ||
+ | |All other products| 8 | | ||
+ | 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. | ||
+ | |||
+ | **Figure 19: Two-stage Armington 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 [[scenario simulation# | ||
+ | |||
+ | 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. | ||
+ | |||
+ | ====Market clearing conditions==== | ||
+ | |||
+ | All quantities in the model are measured in thousand metric tons. The //quantity balances// for the trade blocks first state that production must be equal to domestic sales plus export flows plus changes in intervention stocks: | ||
+ | |||
+ | \begin{align} | ||
+ | \begin{split} | ||
+ | v\_domSales_{i, | ||
+ | & | ||
+ | & | ||
+ | \end{split} | ||
+ | \end{align} | ||
+ | |||
+ | Further on, imports and exports are defined from bilateral trade flows as: | ||
+ | |||
+ | \begin{equation} | ||
+ | v\_impQuant_{i, | ||
+ | \end{equation} | ||
+ | |||
+ | \begin{equation} | ||
+ | v\_expQuant_{i, | ||
+ | \end{equation} | ||
+ | |||
+ | Finally, the //Armington first stage aggregate - arm1//, shown in the diagram above, is equal to the domestic consumption elements feed, human consumption and processing: | ||
+ | |||
+ | \begin{align} | ||
+ | \begin{split} | ||
+ | v\_arm1Quant_{i, | ||
+ | & | ||
+ | & | ||
+ | & | ||
+ | \end{split} | ||
+ | \end{align} | ||
+ | |||
+ | The reader should note that for those trade blocks comprising several countries such as the EU, the right hand side quantities are an aggregate over individual countries. | ||
+ | |||
+ | ====Price linkages==== | ||
+ | |||
+ | All prices in model are expressed as € per metric ton. //Import prices// - \(impp_{i, | ||
+ | |||
+ | \begin{align} | ||
+ | \begin{split} | ||
+ | impp_{i, | ||
+ | \begin{matrix} | ||
+ | v\_marketPrice_{i, | ||
+ | -expsub_{i, | ||
+ | \end{matrix} | ||
+ | \right ] \\ | ||
+ | & | ||
+ | \end{split} | ||
+ | \end{align} | ||
+ | |||
+ | Bilateral tariffs may be endogenous variables if they are determined by a tariff rate quota (TRQ), see below. Equally, export subsidies are endogenous variables. | ||
+ | |||
+ | //Producer prices// are derived from market prices formally using direct and indirect PSEs price wedges – albeit these are all zero at currently -, except for EU_WEST, EU_EAST and Bulgaria and Romania. The reader is reminded that for the EU, the supply model includes a rather detailed description of the different premium schemes of the CAP, so that the EU premiums need not to be modelled as price wedges in the market part. In cases where several countries are comprised in a trade block, the market price refers to the trade block. The “Pmrg” is a factor which is defined such that observed producer prices are recovered. | ||
+ | |||
+ | \begin{equation} | ||
+ | v\_prodPrice_{i, | ||
+ | \end{equation} | ||
+ | |||
+ | {{:: | ||
+ | |||
+ | 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 //average prices of imports// derived from the Armington second stage aggregate are labelled // | ||
+ | |||
+ | \begin{equation} | ||
+ | v\_arm2P_{i, | ||
+ | \end{equation} | ||
+ | |||
+ | Similarly, the //average prices for goods consumed domestically - arm1p// are a weighted average of the domestic market price \(v_marketPrice_{i, | ||
+ | |||
+ | \begin{equation} | ||
+ | v\_arm1P_{i, | ||
+ | \end{equation} | ||
+ | |||
+ | where \(D \in \{M,S\}, P_{i,r,M} = v\_arm2P_{i, | ||
+ | |||
+ | \begin{equation} | ||
+ | v\_consPrice_{i, | ||
+ | \end{equation} | ||
+ | |||
+ | Unit value exports net of border protection are defined as average market prices in the export destination minus tariffs as: | ||
+ | |||
+ | \begin{align} | ||
+ | \begin{split} | ||
+ | v\_unitValueExports_{i, | ||
+ | \end{split} | ||
+ | \end{align} | ||
+ | |||
+ | The unit values exports are used to define the per unit //export subsidies - expsub// as shown in the equation below. The parameter //cexps// is used to line up the market equation with the subsidies observed ex-post. Per unit export subsidies hence increase, if market prices //pmrk// increase or export unit values //uvae// drop, or if the share of subsidised exports //exps// on total exports increase. How the amount of subsidised exports is determined is discussed below. | ||
+ | |||
+ | \begin{equation} | ||
+ | expsub_{i, | ||
+ | \end{equation} | ||
+ | |||
+ | The Armington aggregator functions are already shown in the diagram above. The compositions inside of the Armington composite goods can be derived from first order conditions of utility maximisation under budget constraints and lead to the following conditions: | ||
+ | FIXME | ||
+ | \begin{equation} | ||
+ | \frac{v\_arm2Quant_{i, | ||
+ | \end{equation} | ||
+ | |||
+ | Similarly, relations between import shares are determined by: | ||
+ | |||
+ | |||
+ | \begin{equation} | ||
+ | \frac{v\_tradeFlows_{i, | ||
+ | \end{equation} | ||
+ | |||
+ | ====Modified Armington import demand system ==== | ||
+ | |||
+ | The standard Armington import demand system in CAPRI has been extended in a study on behalf of JRC-IPTS (154208.X1) in order to tackle the zero trade-flow issue. The zero-trade issue concerns the inability to model emerging bilateral trade relations in the current version of the CAPRI model. Emerging trade flows in this context are those that are zero in the corresponding baseline, but that are expected to be significant under specific scenario assumptions (e.g. trade liberalization scenarios removing prohibitive trade barriers). | ||
+ | |||
+ | **Methodology** | ||
+ | |||
+ | The traditional approach in Armington trade models applies the CES functional form in a nested import demand structure. The CES functional form, however, cannot be calibrated against zero observations. The easiest illustration probably is to recall the import demand function and import price aggregator from above. In case of zero flows the share parameter \(\delta_{i, | ||
+ | |||
+ | To overcome the inability of calibrating the import-demand system to zero observations the approach of Witzke et al. (2005) has been implemented in CAPRI. This modifies the standard CES form by shifting them with an additional commitment term. That additional (commitment) term requires not only the observed price/ | ||
+ | |||
+ | |||
+ | **Figure 20: Witzke et al. calibration, | ||
+ | |||
+ | {{:: | ||
+ | |||
+ | 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: | ||
+ | |||
+ | \begin{equation} | ||
+ | M_{i,r,r1} = U_{i,r} \delta_{i, | ||
+ | \end{equation} | ||
+ | |||
+ | The functional form is almost identical to the standard CES formulation, | ||
+ | |||
+ | **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/ | ||
+ | |||
+ | **Figure 21: GUI Option for the non-homothetic Armington system** | ||
+ | |||
+ | {{:: | ||
+ | |||
+ | 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”, | ||
+ | |||
+ | {{: | ||
+ | |||
+ | The calibration model itself is called directly by the arm/ | ||
+ | |||
+ | {{: | ||
+ | |||
+ | The file arm/ | ||
+ | |||
+ | {{: | ||
+ | |||
+ | 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/ | ||
+ | |||
+ | {{: | ||
+ | |||
+ | 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 calibration of the full market model is tested by solving the model at trend values in the CAPRI module arm/ | ||
+ | |||
+ | 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. | ||
+ | |||
+ | ====Biofuel module ==== | ||
+ | |||
+ | An achievement of the CAPRI biofuel module is that biofuel supply and feedstock demand react flexibly to the price ratio of biofuel and feedstock prices as well as biofuel demand and bilateral trade flows react flexibly to biofuel prices and further relevant drivers. | ||
+ | |||
+ | **Figure 22: Construction of the ethanol market implemented in CAPRI** FIXME | ||
+ | |||
+ | {{:: | ||
+ | |||
+ | 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). | ||
+ | |||
+ | A similar technological pathway for biodiesel production has been implemented as shown in Figure 22. The three production pathways for biodiesel are; 1st generation biodiesel (BIOFD) produced from vegetable oils (rape oil, sunflower oil, soya oil, and palm oil), 2nd generation biodiesel (SECG); and non-agricultural biodiesel (NAGR). | ||
+ | |||
+ | **Figure 23: Construction of the biodiesel market implemented in CAPRI** | ||
+ | |||
+ | {{: | ||
+ | |||
+ | 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: | ||
+ | - A product aggregate for agricultural residues (ARES) which covers straw from cereals and oil seed production and sugar beet leaves and | ||
+ | - A product aggregate for new energy crops (NECR) which cover herbaceous and woody crops like poplar, willow and miscanthus. | ||
+ | |||
+ | The use of residues from livestock production, which covers manure and cadavers, is not included in the second generation processing as this source is assumed to have only a marginal importance for biofuel processing, | ||
+ | Furthermore, | ||
+ | |||
+ | **Figure 24: Consideration of 2nd generation biofuel production and related feedstock** | ||
+ | |||
+ | {{:: | ||
+ | |||
+ | ===Biofuel supply and feedstock demand=== | ||
+ | |||
+ | Biofuel feedstock demand is driven by per unit net input costs (µ). These are defined per ton of input used and are calculated for each feedstock in a country by feedstock price minus by product revenues per ton of input. | ||
+ | |||
+ | \begin{equation} | ||
+ | \mu_{r,xf} = p_{r,xf}- \sum_{xbp} p_{r, | ||
+ | \end{equation} | ||
+ | |||
+ | The index r contains all regions in the market module that have biofuel production. All feedstocks that can be used to produce first generation biofuels are stored in the index xf and the by products Glycerine, DDGs and Vinasses in xbp. Prices are denoted by p. One speciality exists in the case of sugar prices in the EU, where a specific ethanol sugar price is assumed in case of the existence of production quotas. This is due to the fact that ethanol beet in the EU purchased at a lower price than beets processed to sugar. These single feedstock costs then form a CES aggregate to give the average cost for the respective biofuel: | ||
+ | |||
+ | The index r contains all regions in the market module that have biofuel production. All feedstocks that can be used to produce first generation biofuels are stored in the index xf and the by products Glycerine, DDGs and Vinasses in xbp. Prices are denoted by p. One speciality exists in the case of sugar prices in the EU, where a specific ethanol sugar price is assumed in case of the existence of production quotas. This is due to the fact that ethanol beet in the EU purchased at a lower price than beets processed to sugar. These single feedstock costs then form a CES aggregate to give the average cost for the respective biofuel: | ||
+ | FIXME | ||
+ | \begin{equation} | ||
+ | \mu_{r,xb} = \mu_{r, | ||
+ | \end{equation} | ||
+ | |||
+ | The superscript c indicates the average input costs in the calibration point which are only introduced to have price variables “around one” in the expression to help the solver. | ||
+ | |||
+ | The decision on the total biofuel production happens simultaneously with the decision on the optimal feedstock mix. The latter is based on the FOC of cost minimisation with a CES cost function for a given biofuel output: | ||
+ | |||
+ | \begin{align} | ||
+ | \begin{split} | ||
+ | fd_{r,xf} &= \phi_{r, | ||
+ | s.t. \quad & | ||
+ | \end{split} | ||
+ | \end{align} | ||
+ | |||
+ | The subsitution elasticity of the CES function is given by σ and their share parameters by \(\phi\). First generation biofuel procuction (\(x^{1st}\)) is then derived by the product sum of feedstock demand fd and their biofuel processing coefficinents: | ||
+ | |||
+ | \begin{equation} | ||
+ | x_{r, | ||
+ | \end{equation} | ||
+ | |||
+ | For biofuel supply from first generation technologies (\(x^{1st}\)) a function of the relation of the respective biofuel price and the corresponding average feedstock per unit costs has been specified. A synthetic supply function was chosen that satisfied some plausibility considerations, | ||
+ | |||
+ | \begin{align} | ||
+ | \begin{split} | ||
+ | x_{r, | ||
+ | \begin{bmatrix} | ||
+ | \partial_{r, | ||
+ | +exp \left ( \beta_{r, | ||
+ | \end{bmatrix} | ||
+ | \end{split} | ||
+ | \end{align} | ||
+ | |||
+ | This function consists of three parts on the RHS: the first part is linear (a small positive value for δ), the second part is semi-log and the third is sigmoid. The linear term guarantees a minimal slope, where the sigmoid function would return a slope of almost 0. The semi-log term is active at processing margins considerably higher than in the baseline point and the sigmoid function guarantees a steeper slope in a range where processing starts and production is close to zero when feedstock costs exceed output values. The coefficients β and δ are behavioural parameters in these functions. All biofuel supply equations are generally of the style presented below with an example of bioethanol in France. | ||
+ | |||
+ | **Figure 25: Biofuel supply function in France** | ||
+ | |||
+ | {{:: | ||
+ | |||
+ | The supply of by products is directly linked to the first generation biofuel output: | ||
+ | |||
+ | \begin{equation} | ||
+ | x_{r,xbp} = fd_{r,xf} \alpha_{r, | ||
+ | \end{equation} | ||
+ | |||
+ | Total biofuel output is then defined as the sum over first generation, second generation (secg), non agricultural (nagr) and some exogenous production (exo) from products not mapped to the feedstocks in CAPRI (only relevant in extra EU countries): | ||
+ | |||
+ | \begin{equation} | ||
+ | x_{r, | ||
+ | \end{equation} | ||
+ | |||
+ | ===Biofuel demand=== | ||
+ | |||
+ | The representation of biofuel demand was simplified compared to the approach chosen first and applied in Becker (2011). There the Aglink demand system was more or less reproduced using a different functional form but keeping the three types of biofuel demand, the use as additive, as low blends and in flexible fuel vehicles. The actual biofuel demand equations consist of only one sigmoid function instead of stacking three of them. The share of biofuel in total fuel demand (bsh) is hereby defined as: | ||
+ | |||
+ | \begin{equation} | ||
+ | bsh_{r,xb} = bsh_{r, | ||
+ | \end{equation} | ||
+ | |||
+ | Again the coefficients X are used to specify the exact slope of these functions. The first term (bshq) defines the part of the biofuel demand which is enforced by any kind of obligation quota or mandate, while the second part defines an “endogenous” part of the demand. This term has the upper linmit \(bsh_{max}\) which represents the maximum biofuel share on top of the quota obligation that is deemed reachable in a certain country. The endogenous demand component is driven by the price relation of a biofuel ( \(p_{r, | ||
+ | |||
+ | **Figure 25: Biofuel demand share function in France** | ||
+ | |||
+ | {{:: | ||
+ | |||
+ | Total biofuel demand (\(d_{r, | ||
+ | |||
+ | \begin{equation} | ||
+ | d_{r,xb} = bsh_{r,xb} +d_{r,f} | ||
+ | \end{equation} | ||
+ | |||
+ | ===Total fuel demand=== | ||
+ | |||
+ | |||
+ | //Total fuel demand// is exogenous to the CAPRI model. However, an econometric estimation was undertaken to receive a demand reaction on exogenous drivers like the oil price and GDP. This function can then be used in Scenarios to adjust total fuel demand, if these drivers are altered. A response surface estimation on the basis of available PRIMES scenarios from 2008 was undertaken. The PRIMES output files at hand allow for estimating the relation between total fuel demand, GDP and fossil fuel prices. For the estimation an ordinary least square estimator is used. A double log demand function is chosen where the estimation coefficients can directly be interpreted as elasticities. The regression function and thereby the total fuel demand function is defined by: | ||
+ | |||
+ | \begin{align} | ||
+ | \begin{split} | ||
+ | log(y_{i, | ||
+ | & | ||
+ | \end{split} | ||
+ | \end{align} | ||
+ | |||
+ | where, \\ | ||
+ | //i// = Fuel type \\ | ||
+ | //r// = Region \\ | ||
+ | //s// = Scenario \\ | ||
+ | //t// = Year \\ | ||
+ | //y// = Fuel demand \\ | ||
+ | //p// = Fuelprice including tax \\ | ||
+ | //gdp// = Gross Domestic Product \\ | ||
+ | //trend// = Trend variable \\ | ||
+ | \(\epsilon\) = Error term for regression \\ | ||
+ | \(\delta\) = Intercept \\ | ||
+ | \(\alpha\) = price elasticity of demand \\ | ||
+ | \(\beta\) = GDP elasicity of demand \\ | ||
+ | \(\gamma\) = Trend elasicity of demand \\ | ||
+ | |||
+ | The results of the regression analysis (differentiated into biodiesel and ethanol for every EU MS) cover estimates for α, β, γ and the intercept (δ). The significant estimates are used directly in the respective fuel demand function. If no significance was observed for a coefficient in a respective country, the estimated value is replaced by an average value which is derived from the weighted average of significant coefficients over all EU MS. The resulting matrix of regression coefficients (elasticities) in the fossil fuel demand function are displayed in table below. As the PRIMES data only covers values for European countries but also estimates for the non-European CAPRI regions are required it was assumed that the coefficient estimates for the aggregated EU27 are also applicable for those regions. | ||
+ | |||
+ | Assumed elasticities for total fuel demand after filling with average values are demonstrated in the table below. | ||
+ | |||
+ | **Table 29: Overview of pillar II measures modelled in CAPRI** FIXME | ||
+ | |||
+ | {{:: | ||
+ | |||
+ | **Biofuel Trade** | ||
+ | |||
+ | Behavioural functions for global bilateral trade of biodiesel and ethanol are intrinsically tied to the final biofuel demand functions. The general methodology is that of a two stage demand system relying on the Armington assumption as already applied for other agricultural commodities in the standard CAPRI version. Biofuel demand for fuel use is considered a derived demand of refineries and responsive to the price ratio of biofuels to fossil fuels. The non fuel demand for biofuels (e.g. ethanol demand of the chemical industry) is consequently set on INDM or PROC (industrial use). | ||
+ | |||
+ | ===Calibration of the biofuel system=== | ||
+ | |||
+ | So far, only the general form of the biofuel supply and demand functions where derived, but without any adjustments, | ||
+ | |||
+ | 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, | ||
+ | |||
+ | * It recovers the baseline combination of price and quantity relations | ||
+ | * It reaches 90% of the max share (\(bsh_{max}\)) at a certain price relation (currently 0.5 for ethanol and 0.3 for biodiesel)((These values were chosen by trial and error to achieve a reasonable demand response in certain scenarios. However a more empirically based representation of the demand response would greatly improve the system. )). | ||
+ | |||
+ | |||
+ | The maximum biofuel demand share of a region is chosen 2% above the observed baseline share. | ||
+ | |||
+ | The parameters \(\beta^2\), | ||
+ | |||
+ | ====Endogenous policy instruments in the market model==== | ||
+ | |||
+ | ===Subsidised exports=== | ||
+ | |||
+ | On the market side, the amount of subsidised exports (exps) are modelled by a sigmoid function, driven by the difference between EU market (//pmrk//) and administrative price (//padm//), see equation below. The sigmoid function used looks like: | ||
+ | |||
+ | \begin{equation} | ||
+ | Sigmoid(x)= exp \frac {min(x, | ||
+ | \end{equation} | ||
+ | |||
+ | where //x// is replaced by the expression shown below in the equations. | ||
+ | |||
+ | The response was chosen as steep as technically possible by setting a high value for \(\alpha\), i.e. intervention prices are undercut solely if WTO commitment (QUTE) and the maximum quantity of stock changes are reached. | ||
+ | |||
+ | \begin{equation} | ||
+ | expsVal_{i, | ||
+ | \end{equation} | ||
+ | |||
+ | The parameters \(\alpha\), \(\beta\) are determined based on observed price and quantities of subsidised exports. The per unit subsidy is defined from non-preferential exports and the value of the subsidies: | ||
+ | |||
+ | \begin{equation} | ||
+ | expSub_{i, | ||
+ | \end{equation} | ||
+ | |||
+ | The relation is shown in the figure below. | ||
+ | |||
+ | **Figure 27: Modelling of subsidised export costs by a logistic function** | ||
+ | |||
+ | {{:: | ||
+ | |||
+ | ===Endogenous administrative stocks=== | ||
+ | |||
+ | For years, the CAP defended administrative prices in key markets such as cereals, beef, butter and skim milk poweder by direct interventions into markets which where out into public stocks. The basic functioning of that mechanism in CAPRI in shown in the figure below. | ||
+ | |||
+ | **Figure 28: Endogenous administrative stocks in CAPRI** | ||
+ | |||
+ | {{:: | ||
+ | |||
+ | **Purchases to intervention stocks** // | ||
+ | |||
+ | \begin{equation} | ||
+ | v\_buyingToIntervStocks_{i, | ||
+ | \end{equation} | ||
+ | |||
+ | A decrease of the administrative price or an increase of the market price will hence decrease purchases to intervention stocks. | ||
+ | |||
+ | **Releases from intervention stocks** // | ||
+ | |||
+ | \begin{equation} | ||
+ | intd_{i,r} = (intk_{i, | ||
+ | \end{equation} | ||
+ | |||
+ | Releases will hence increase if world market price increases or the EU market price drops, and if the size of the intervention stock increases. The parameters \(\gamma\) are determined from ex-post data on prices and intervention stock levels. The change in intervention stocks //ints// entering the market balance is hence the difference between intervention purchases //intp// and intervention stock releases //intd//: | ||
+ | |||
+ | \begin{equation} | ||
+ | ints_{i,r} = intp_{i,r} - intd_{i,r} | ||
+ | \end{equation} | ||
+ | |||
+ | ====Endogenous tariffs under Tariff Rate Quotas, flexible levies and the minimum import price regime for fruits and vegetables of the EU==== | ||
+ | |||
+ | ===Tariff Rate Quotas=== | ||
+ | |||
+ | Tariff Rate Quotas (TRQs) establish a two-tier tariff regime: as long as import quantities do not exceed the import quota, the low in-quota tariff is applied. Quantities above the quota are charged with the higher Most-Favoured-Nation (MFN) tariff. CAPRI distinguishes two types of TRQs: such open to all trading partners, and bi-laterally allocated TRQs. As a rule, bi-lateral allocated quotas are filled first. Equally, as for all tariffs, TRQs may define ad valorem and/or specific tariffs. | ||
+ | |||
+ | A market under a TRQ mechanism may be in one of the following regimes: | ||
+ | |||
+ | **Quota underfill**: | ||
+ | |||
+ | **Figure 29: Quota underfill regime** | ||
+ | |||
+ | {{: | ||
+ | |||
+ | **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. | ||
+ | |||
+ | **Figure 30: Quota binding regime** | ||
+ | |||
+ | {{: | ||
+ | |||
+ | **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. | ||
+ | |||
+ | **Figure 31: Quota overfill regime** | ||
+ | |||
+ | {{: | ||
+ | |||
+ | 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), | ||
+ | |||
+ | {{:: | ||
+ | |||
+ | There are a couple of further complications, | ||
+ | |||
+ | Besides the problem of defining the regime ex-post, the relation between the import quantity and the tariff is not differentiable but kinked. Therefore, again a sigmoid function is applied in the CAPRI market part: | ||
+ | |||
+ | In many cases, the EU features for the very same market so-called bi-lateral quotas and market access quotas from the URA round which must be open to all imports (“erga omnes”). As the allocation shares for the latter are currently not know to the CAPRI team, any importer is allowed to import under these global TRQs. Importers have bi-lateral quotas might import under global TRQs once the bi-lateral TRQs are overshot. | ||
+ | |||
+ | ===Flexible tariffs=== | ||
+ | |||
+ | Geneally, the WTO rules only set upper bounds on the tariffs (so-called Most Favorite Nature or MFN for short rates), but allows its members to reduce the tariffs as long as the same tariff is applied for all WTO members. Exemption from MFN rates which are implemented in CAPRI are preferential rates for Developing countries (Everything But Arms agreement of the EU), Free Trade Agreements and bi-lateral concessions e.g. results from minium market access obligation from the Uruguay rounds under TRQ. The EU generally uses MFN rates, but operates in the cereal markets a specific form of a variable tariff called the “levy” system. The last WTO EU trade policy review described the operation of the CAP import regime for cereals as follows: “In response to fluctuations in world prices, the EU has, within the limits of its bound tariffs, changed its MFN applied tariffs. It reduced tariffs on cereals to zero in January 2008 in response to high world prices, and reintroduced them at the end of October 2008. For wheat, the tariff is based on the difference between world prices and 155% of the intervention price, up to the bound rate of €95 per tonne for high quality wheat and €148 per tonne for high quality durum wheat with similar systems for other cereals.” | ||
+ | |||
+ | **Figure 32: | ||
+ | |||
+ | {{: | ||
+ | |||
+ | In CAPRI, the system is implemented as follows: | ||
+ | |||
+ | \begin{equation} | ||
+ | v\_flexLevy_{i, | ||
+ | \end{equation} | ||
+ | |||
+ | The actual implementation in the code differs somewhat, as the min and max operators are replaced by “fudging function”, | ||
+ | |||
+ | {{:: | ||
+ | |||
+ | The second equation defines the actual tariff applied: | ||
+ | |||
+ | {{:: | ||
+ | |||
+ | ===Entry price system for fruits and vegetables=== | ||
+ | |||
+ | A somewhat similar instrument is the entry price system used in the fruit and vegetable sectors of the EU. The entry price relates the applied tariff to a specified trigger price in a way that encourages imports at a price (CIF plus tariffs) that is between 92% and 98% of the trigger price. | ||
+ | |||
+ | **Figure 33: EU entry price system for fruits and vegetables** | ||
+ | |||
+ | {{: | ||
+ | |||
+ | 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. | ||
+ | |||
+ | {{:: | ||
+ | |||
+ | That factor is the fed into a modified sigmoid function which as a result approximates the relations in the graphic shown above: | ||
+ | |||
+ | {{:: | ||
+ | |||
+ | ===Tariff computation in the model=== | ||
+ | |||
+ | The figure below depicts the interaction of the various elements of the tariff calculation discussed above. The blue boxes are policy instruments depicted in the model; the purple ones describe endogenous switches and the green ones intermediate model variables which can be interpreted as intermediate results for the applied tariffs. The red boxes show the rate applied to derive the import price. Arrows upwards from a decision box mean yes, to the left no. | ||
+ | |||
+ | The simplest decision is in the left lower corner: a check if the importer benefits from duty and quota free accesss. Examples are intro-EU trade or import from LDCs into the EU under the “Everything But Arms”-Agreement. If that is the case, the applied tariff is zero. | ||
+ | |||
+ | Next we check for a bi-lateral TRQ. If we find one, we check if it is underfilled in which case we apply the in-quota rate. Next we check if the quota is just binding, in which case the applied rate represents the sum of the in-quota rate and an endogenous per unit quota rent. The remaining case is that of a quota overfill where we are left with the MFN rate. | ||
+ | |||
+ | Next we check for a multi-lateral TRQ, also in case we have an overfilled bi-lateral TRQ. If we find one, we check if it is underfilled in which case we apply the in-quota rate. Next we check if the quota is just binding, in which case the applied rate represents the sum of the in-quota rate and an endogenous per unit quota rent. The remaining case is that of a quota overfill in which case the MFN rate is applied. | ||
+ | |||
+ | In all cases for specific tariffs, the results applied rates are checked against the existence of a minimum border price system. In that case, the import price resulting from applying the tariff to the cif price is compared to the minimum price. If it is higher than the minimum price, the tariff is cut such that the import price becomes equal to the minimum border price as long as the resulting tariff does not become negative. | ||
+ | |||
+ | **Figure 34: Tariff computation in the model** | ||
+ | |||
+ | {{:: | ||
+ | |||
+ | ====Welfare-consistent tariff aggregation module ==== | ||
+ | |||
+ | The heterogeneity of trade policies across different traded goods generates a serious index number problem for large-scale applied equilibrium modelling. Trade policies must be described with aggregate indices in order to incorporate them in the aggregate commodity structure of applied equilibrium models. | ||
+ | |||
+ | **Review of current tariff aggregation approach in CAPRI** | ||
+ | |||
+ | The tariff aggregation in CAPRI is based on the weighted average method, but applies a combination of different weights in order to (1) overcome the endogeneity bias and to (2) correct for outliers that are frequently created by statistical errors in the trade data. Technically, | ||
+ | |||
+ | Although Tariff Rate Quotas (TRQ) are typically defined in the legal texts over tariff lines, the CAPRI database does not contain data on TRQs at that level of product aggregation. In fact, TRQs are defined in CAPRI at a much more aggregated commodity level. As a consequence, | ||
+ | |||
+ | **Advanced tariff aggregation techniques considered** | ||
+ | |||
+ | The two fundamental obstacles to aggregate tariffs and other border protection measures are | ||
+ | |||
+ | * The conversion problem, i.e. different policy instruments need to be expressed in a common metric before they can be aggregated | ||
+ | * The index number problem, i.e. individual trade restrictions must be appropriately aggregated (weighted) | ||
+ | |||
+ | A large number of tariff aggregation techniques are available in the literature, each having its specific objective, drawbacks and merits. Cipollina and Salvatici 2008 provide a typology for the aggregate measures of border protection: | ||
+ | |||
+ | - Incidence measures are based on the intensities of the policy measures, and are derived only from direct observations on policies. They do not consider the distortive effects of the trade policies on the economy. Typical incidence measures are tariff dispersion or the frequency of various types of Non-Tariff Measures. | ||
+ | - Outcome measures incorporate other variables than policy variables in order to take into account the distortive impacts of policies on the economy. Typical outcome measures include trade weighted average tariffs. Outcome measures remain ' | ||
+ | - Equivalence measures provide aggregates that are equivalent to the original data in terms of selected economic variables. Welfare-consistent measures, for example, provide aggregates that are equivalent in their impact on selected indicators of the the economy' | ||
+ | |||
+ | The advanced tariff aggregation module provides three welfare-consistent aggregators: | ||
+ | |||
+ | A traditional outcome measure, called the MacMap-type aggregator, is also available in the tariff aggregation module. The aggregator is named after the conversion rule for TRQs, which is the same as the one underlying the MacMap database: TRQs are converted to an ad-valorem equivalent based on the fill rate of the TRQ. This approach takes into account the quota rent generated by the TRQ, but defines its level arbitrarily (the unit quota rent is set to half of the difference between out-of-quota and in-quota rates). | ||
+ | |||
+ | **Additional data requirement and its integration in CAPRI** | ||
+ | |||
+ | An extraction from the UN-COMTRADE database has been integrated in the global module of CAPRI. The dataset comprises of import values and calculated unit prices for 326 tariff lines (mainly agricultural commodities), | ||
+ | |||
+ | A major difficulty arises when we use raw UN-COMTRADE data for modelling purposes, due to their lack of symmetry. Country A’s import of a given product from country B is not the same as country B’s export of that product to country A. The literature identifies three main causes for this discrepancy (McCleery and DePaolis, 2014): | ||
+ | |||
+ | * An obvious wedge between import and export values is created by the valuation of exports at point of origin (usually f.o.b. prices) and the valuation of imports at destination (mostly c.i.f. prices). | ||
+ | * Border disputes, export bans or prohibitive trade restrictions may lead to only one half of the trade transactions being recorded. | ||
+ | * Border frictions may also lead to distorted trade statistics, e.g. large discrepancies in the US-China trade statistics can be observed due to recording trade with Hong-Kong differently | ||
+ | |||
+ | |||
+ | This problem is currently solved by using UN-COMTRADE data only on imports, applying the assumption that countries tax and regulate imports more thoroughly than exports. | ||
+ | |||
+ | 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 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, | ||
+ | |||
+ | **Figure 35: Tariff computation in the model** | ||
+ | |||
+ | {{: | ||
+ | |||
+ | The different tasks implemented in the aggreg_tariffs.gms tariff aggregation module includes: | ||
+ | |||
+ | * Defining nomenclatures and sets for the UN-COMTRADE dataset (‘global/ | ||
+ | * 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. | ||
+ | |||
+ | |||
+ | Unit values in the UN-COMTRADE dataset have been found to be subject to significant statistical errors. An outlier-detection algorithm has been therefore implemented in order to tackle this problem. Using a simple and robust approach, observations outside a given range around the mean are identified as outliers and replaced with the mean. The outlier detection is implemented in R((As a consequence, | ||
+ | |||
+ | **Defining Tariff cut scenarios at the tariff line level** | ||
+ | |||
+ | The tariff aggregation module is loosely linked to the CAPRI modelling system. The feature can be activated by a GUI option (see below), assuming that the intermediate database has been already created by the global module. | ||
+ | |||
+ | **Figure 36: Activation of the tariff aggregation module on the GUI** | ||
+ | |||
+ | {{: | ||
+ | |||
+ | 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. | ||
+ | |||
+ | **CES demand structure** | ||
+ | |||
+ | With specific assumptions on the demand side, it is possible to take into account the changes in the consumption bundle, as a response to relative price changes induced by the tariff cut scenario. Loosely speaking, the tariff aggregation module takes into account the substitution between goods within an aggregated CAPRI commodity, under specific assumptions on the demand structure. We assume a nested CES import demand structure on the lines of the usual Armington approach to model bilateral imports with cross-hauling. The current implementation is a “small country” approach: tariffs are aggregated for one importer region after the other, assuming fix border (c.i.f.) prices. | ||
+ | |||
+ | Dropping the small country assumption would require a full partial equilibrium model at the tariff line level for the commodity considered, as done in e.g. Grant et al. (2007). This, however, requires a substantial extension of the CAPRI database by including tariff line-specific trade and trade policy information at the global scale. The complexity of the market model would increase rapidly by adding trade flows at the tariff line level. A simultaneous solve for all commodity markets would be technically impossible. No surprise that similar examples in the literature only focus on selected markets and do not implement a full-fledged market model with many interacting markets at the tariff line level. Grant et al. (2007) focus on the dairy market only, and implements a sequential model linkage in order to reduce the computational requirements of solving the complete system whereas Narayanan et al. (2010) extend the standard GTAP model with a partial equilibrium component that only covers the automobile industry. | ||
+ | |||
+ | **Technical details of implementing tariff aggregation scenarios** | ||
+ | |||
+ | 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. | ||
+ | |||
+ | {{:: | ||
+ | |||
+ | {{:: | ||
+ | |||
+ | **Reporting (GUI tables)** | ||
+ | |||
+ | The GUI has been extended with tables under ' | ||
+ | |||
+ | {{: | ||
+ | |||
+ | The MacMap-type aggregators are calculated both with respect to bilateral trade relations and with respect to a total ('from World' | ||
+ | |||
+ | {{: | ||
+ | |||
+ | 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): | ||
+ | |||
+ | {{: | ||
+ | |||
+ | 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 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: | ||
+ | |||
+ | {{: | ||
+ | |||
+ | ====Overview on a regional module inside the market model==== | ||
+ | |||
+ | The resulting layout of a market for a country (aggregate) in the market module is shown in the following diagram. Due to the Armington assumption, product markets for different regions are linked by import flows and import prices if observed in the base year. Accordingly, | ||
+ | |||
+ | **Figure 37: Graphical presentation for one region of a spatial market system ** | ||
+ | |||
+ | {{: | ||
+ | |||
+ | ====Basic interaction inside the market module during simulations==== | ||
+ | |||
+ | As with the supply module, the main difficulty in understanding model reactions is based on the simultaneity of changes occurring after a shock to the model. Cross-price effects and trade relations interlink basically all product markets for all regions. Whereas in the supply model, interactions between products are mostly based on explicit representation of technology (land balances, feed restrictions), | ||
+ | |||
+ | Even if the following narrative is simplifying and describing reactions as if they would appear in a kind of natural sequence where they are appear simultaneously in the model, we will nevertheless ‘analyse’ the effect of an increased supply at given prices for one product and one region. Such a shift could e.g. result from the introduction of a subsidy for production of that product. The increased supply will lead to imbalances in the market clearing equation for that product and that region. These imbalances can only be equilibrated again if supply and demand adjust, which requires price changes. In our example, the price in that region will have to drop to reduce supply. That drop will stimulate feed demand, and to a lesser extent, human consumption. The smaller effect on human consumption has two reasons: firstly, price elasticities for feed demand are typically higher, and secondly, consumer prices are linked with rather high margins to farm gate prices. | ||
+ | |||
+ | The resulting lower price at farm gate increases international competitiveness. Due to the Armington mechanism, consumers around the world will now increase the share of that region in their consumption of that product, and lower their demand from other origins. That will put price pressure in all other regional markets. The pressure will be the higher, the higher the import share of the region with the exogenous increase of supply on the demand of that product. The resulting price pressure will in turn reduce supply and stimulate demand and feed everywhere, and, with reduced prices, offset partially the increased competitiveness of the region where the shock was introduced. | ||
+ | |||
+ | Simultaneously, | ||
+ | |||
+ | =====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 // | ||
+ | |||
+ | 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, | ||
+ | |||
+ | 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, | ||
+ | |||
+ | 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, | ||
+ | |||
+ | =====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, | ||
+ | |||
+ | 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, | ||
+ | |||
+ | ===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, | ||
+ | |||
+ | 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< | ||
+ | |||
+ | 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, | ||
+ | |||
+ | 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