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calibrating_the_supply_models_to_the_captrd_projection

Calibrating the supply models to the CAPTRD projection

Introduction

The supply side models of the CAPRI simulation tool are programming models with an objective function. If we want the optimal solution to coincide with the forecast procuced by the projection tools of CAPTRD, we need to ensure that first and second order optimality conditions (marginal revenues equal to marginal costs, all constraints feasible, and the solution is a maximum point) hold in the calibration point for each of the NUTS 2 or farm type models. The consequences regarding the calibration are threefold:

  1. Elements not projected so far but entering the constraints of the supply models (e.g. feed, fertilization) must be defined in such way that constraints are feasible,
  2. The cost function of the models must be shifted so that marginal costs and marginal revenues are equal in the calibration point.
  3. The curvature of the functions must be such that the solution obtained is a maximum, not a minimum or a saddle point.

Calibrating feed and fertilizer restrictions

The calibration of feed and fertilization restrictions happens in the file gams\capmod\def_fert_and_requirement.gms. As explained above, the requirement functions used in the projection tools are linear approximations for the ones used in the simulation tool; additional constraints restrict the feed mix in the supply modules.

It is hence necessary to find a feed mix in the projected point which exhausts the projected production of non-tradable feed and the projected feed mix of marketable bulk feeds (cereals, protein feed, …), fits in the requirement constraints and leads to plausible feed cost. In order to do so, the feed allocation framework used to construct the base year allocation of feedstuff to animals is re-used. The resulting factors are stored in external files and reloaded by counterfactual runs.

Similar to animal feed balance, the crop nutrient needs must be consistent with available projected nutrients from various sources. To find such a feasible point, the distribution of various fertilizer sources (manure, mineral fertilizers and crop residues) to crops estimated in the database (CAPREG), is shifted with changes in crop areas to make a first best guess (prior) of the allocation to crops in the baseline. This prior is used as the modal value of a probability density function of a Bayesian estimation, similar to the CAPREG procedure described in a previous section of the documentation. Thus, a crop nutrient allocation is sought that is in some sense “as similar” to the base year estimate as possible. The result of the fertilizer calibration for the baseline is stored in a GDX file for each country, found in the directory “results\fert”, from where it is loaded in simulations (by the file gams\capmod\load_fert_baseline.gms).

Calibrating the marginal cost functions

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.

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 are 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, see also Kempen, M., Witzke. P., Pérez-Dominguez. I., Jansson, T. and Sckokai, P. (2011): Economic and environmental impacts of milk quota reform in Europe, Journal of Policy Modeling, 33(1), pp 29-52.

Calibration tests with supply models

After calibrating the various functions of the supply models, a test for successful calibration is carried out. The purpose of the test is to ensure that the models are really properly calibrated, and to avoid that a disequilibrium in the baseline is misinterpreted as the effect of some policy change in a scenario.

To test for successful calibration, all supply models are solved directly after the calibration, and the solutions are compared to the target values to which the models should have been calibrated. If the solutions deviate more than some tiny amount, an error message is produced and the execution terminated. The calibration test checks for deviations of activity levels and allocation of fertilizers to crops.

Sensitivity experiments with the supply models

The market model of CAPRI is solved with a simplified representation of the supply model behaviour (see model overview). Even in countries where we do have a detailed supply model representation of agriculture, the market model contains, for technical / numerical reasons, a simpler linearized supply model that is iteratively re-calibrated to reflect the results of the underlying supply models in the current iteration between supply and demand.

If the linearized supply models would replicate the behaviour of the supply models exactly, then no iterations would be needed. In fact, no programming models of supply would be needed either. However, the approximation is not perfect, and hence the model needs to iterate between supply and demand. Since these iterations with re-calibrations are time consuming, it is desirable to have as good an approximation as possible.

The functional form of the approximation is derived from a ”normalized quadratic profit function”, meaning that the supply of any commodity is a linear function of all prices divided by a price index. Hence, the slope of those supply functions is a square matrix equivalent to the Hessian matrix of the normalized quadratic profit function itself. In order to find out how the supply models, including all policies and constraints, respond to changes in market prices, the calibration procedures of the CAPRI system contains a suite of structured and automated simulation experiments. The GAMS scenario solver is used to vary prices one by one and evaluate changes in supply. The results are summarized in the matrix of second-order derivatives used in the supply approximation in the market model.

calibrating_the_supply_models_to_the_captrd_projection.txt · Last modified: 2020/03/01 10:50 by matsz