CAPRI Online Manual (update)

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 WATSIM¹⁾ 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, deterministic, partial, spatial, global equilibrium model for most agricultural primary and some secondary products, in total about 65 commodities, including the young animals that only matter for market clearing in European regions. The list of commodities is chosen to cover as far as possible all products used for food and feed.

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, feed and processing functions. The regional breakdown is a compromise between full coverage of all individual countries (there are close to 200 UN member countries) and computational data quality considerations. Most countries which a high population number are covered independently, sometimes aggregated with smaller countries. Given the EU focus of CAPRI, agricultural trading partners of the EU are captured in some detail and the regional break down is occasionally updated in view of new trade agreements.

The processing can be differentiated by processing of (a) oilseeds to cakes and oils; (b) biofuel feedstocks to biofuels; © 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, borrowed from other studies and modelling systems, and calibrated to projected quantities and prices in the simulation year. The choice of flexible functional forms (normalised quadratic for feed and processing demand as well as for supply, Generalised Leontief Expenditure function for human consumption) and imposition of restrictions (homogeneity of degree zero in prices, symmetry, correct curvature, additivity) on the parameters used ensure regularity as discussed below. Accordingly, the system allows for the calculation of welfare changes for the different agents represented in the market model.

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://www.capri-model.org/dokuwiki/doku.php?id=capri:concept:regMarket.

The market model in its current layout comprises about 70.000 endogenous variables and the identical number of equations.

Policy instruments in the market module include (bi)lateral ad-valorem and specific tariffs and, possibly, Producer/Consumer Subsidy Equivalent price wedges (PSE/CSE) where no current data is entered. However, negative entries on the “PSEi” position (for indirect support) have been used in several appications to reflect a global carbon price. Tariff Rate Quotas (TRQs), billaterally allocation or globally open are integrated in the modelling system, as are intervention stock changes and subsidised exports under WTO commitment restrictions for the EU. Subsidies to agricultural producers in the EU are not covered in the market model, but integrated in a very detailed manner in the supply model. For the EU, flexible tariffs for cereals and the minimum import price regime for fruits & vegetables are introduced. Flexible tariffs related to minimum import prices are also present for Switzerland.

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, these models are typically not used for welfare analysis. Examples of such models are AGLink-COSIMO at the OECD_FAO, the FAPRI set of market models, or the set of models emerging from AgMemod. However, AGLink-COSIMO is currently in the process to move closer to a template model.

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.

The definition of the market model can be found in ‘arm\market_model.gms’

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 v_prodPrice normalised with a price index. The price index relates to all those goods – either inputs or outputs – which are not explicitly modelled in the system:

\begin{equation} v\_prodQuant_{i,r} = as_{i,r}+ \sum_j bs_{i,j,r} \frac{v\_prodPrice_{j,r}}{p_{index,r}} \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, as discussed below. The calibration of the price dependent parameters bs is discussed below.

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 above).

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,"Land"} = \; & p\_cnstLandSpply_r \\ &+ p\_cnstLandElas_r \; log(v\_prodPrice_{r,"Land"}) \end{split} \end{align}

Figure 18: Land supply curve examples

Source: own calculations

In order to parameterize the land demand function, information about yield and supply elasticities is used. The marginal reaction of land to a marginal change in one of the prices is defined as the total supply effect minus the yield effect:

\begin{equation} \frac {dLand}{dp_i} = \sum_j \frac {dQ_j}{dp_i} 1/yield_j -ela_i \frac {Q_i}{p_i} 1/yield_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 land supply curve is known, a market balance equilibrates the simulated land demand based on the behavioral equation derived from the NQ profit function with that land supply curve. The land price is the equation multiplier attached to the land market clearing equation. If the land supply curve collapses to a constant, any output price induced change in land demand is leveled out by a change in the land price. That solution is equivalent to the behavior of programming model with a fix land endowment.

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).

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 v_arm1Price determined by the Armington top level aggregator drive feed demand v_feedQuant, combined with changes in the supply of animal products weighed with feed use factors w:

\begin{equation} v\_feedQuant_{i,r} = \left( af_{i,r} + \sum_j bf_{i,j,r} \frac {v\_arm1Prices_{j,r}} {p_{index,r}} \right) \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,r} \; p\_calContent_r = \sum_iv\_prodQuant_{i,r} \; pv\_feedConv_{i,r} \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, a fudging function is applied for supply, feed and (see below) processing demand which ensures strictly positive quantities. That fudging function is highly non-linear, and therefore only switched on on demand.

The final demand functions are based on the following family of indirect utility functions depending on consumer prices cpri and per capita income y²⁾ where G and F are functions of degree zero in prices (RYAN & WALES 1996) which will be defined below³⁾:

\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 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 bd_{ij} \sqrt {cpri_i / cpri_j} \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 :

\begin{equation} y = e(U,cpri)=F- \frac{G}{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, a restriction not deemed important in the light of the product list covered. Note that concavity of e is given if G is concave, as U < 0 and F is linear. Concavity of G in turn follows from nonnegative off-diagonal \(bd_{ij}\) without further restrictions, because G is then a sum of concave elementary functions \(bd_{i,j} (cpri_i cpri_j)^0.5\) with the linear terms on the diagonal being both concave and convex regardless of signs of \(bd_{ii}\).

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,r} \end{equation}