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--- module_for_agricultural_supply_at_regional_level [2020/03/11 13:27] – matsz
+++ module_for_agricultural_supply_at_regional_level [2020/03/13 11:31] – [Calibration of the regional programming models] matsz
@@ Line 335: / Line 335: @@
 ====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: for the land balance and for milk quotas. The remaining shadow prices mostly relate to the feed block, and are less critical as they have a clear connection to prices of marketable feed as cereals which are not subject to the problems discussed above.
+====Estimating the supply response of the regional programming models====
+The development, test and validation of econometric approaches to estimate supply responses at the regional level in the context of regional programming models form an important task for the CAPRI team. Up to now, there is still no fully satisfactory solution of the problem, but some of the approaches are discussed in here.
+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 ‘//endog_yields.gms//’ change the yields iteratively in between iterations t, using relative changes:
+\begin{equation}
+Y_{j,t}=Y_{j,t-1}^{[\epsilon_jlog \frac{p_o,t-1}{p_t}]}
+\end{equation}