Positive Mathematical Programming for Agricultural and Environmental Policy Analysis: Review and Practice
The unequal treatment of marginal and preferable activities
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- 3.3 The first phase estimation bias
- 4.The SEPALE model and applications
3.2The unequal treatment of marginal and preferable activitiesAnother PMP shortcoming discussed at several occasions in the literature is the unequal treatment of the marginal and preferable activities. Because the differential marginal costs of the marginal activities captured by the dual vector are zero, the actual marginal costs of supplying these activities are independent of their levels while those of supplying the preferable activities are not under the average cost approach of calibration. For these marginal activities, calibrated marginal costs are equal to average costs and marginal profits are equal to average profits. Gohin and Chantreuil (1999) show that an exogenous choc on one preferable activity would uniquely modify the levels of this activity and the levels of the marginal activities, not those of the other preferable activities. One ad hoc solution to obtain an increasing marginal cost function for these marginal activities consists in retrieving some share of one limiting resource dual value and adding it to the calibration dual vector to obtain a modified calibration dual vector M (Rohm and Dabbert, 2003). A more severe solution consists in skipping the first step of PMP altogether. Judez et al. (2001) use this approach to represent the economic behaviours of different farm types based on farm accounting data from the Spanish part of the FADN. 3.3 The first phase estimation biasMore fundamentally, Heckelei and Wolff (2003) recently explain that PMP is, however, not well suited to the estimation of programming models that use multiple cross-sectional or chronological observations. They show that the derived marginal cost conditions (8) prevent a consistent estimation of the parameters when the ultimate model (7) is seen as representing adequately the true data generating process. Their argument goes as follows. On the one hand, the shadow price value vector implied by the ultimate model (7) is determined by the vectors p, d and b and the matrices A and Q through the first-order condition derived expression (8). On the other hand, the various dual value vectors from the sample initial models (1) are solely determined by the vectors p and c and matrix A of only those marginal activities bounded by the resource constraints through the first-order derived expression (4). As a result, the various vectors of resource duals of the initial models are most generally different from the vector of resource duals of the ultimate model. Since the first step simultaneously sets both the initial dual vectors and and the second step uses the initial dual vector to estimate the vector MCv, this latter vector must generally be inconsistent with the ultimate model (7). The derived marginal conditions (6) are, therefore, most likely to be biased estimating equations yielding inconsistent parameter estimates.2 To avoid inconsistency between steps 1 and 3 as further exposed in Heckelei and Britz (2005), Heckelei and Wolff (2003) suggest to skip the first step altogether and employ directly the optimality conditions of the desired programming model to estimate, not calibrate, simultaneously shadow prices and parameters. They illustrate this general alternative to the original PMP through three examples relying on the Generalised Maximum Entropy (GME) procedure for estimating the model parameters. Their examples deal with the estimation of the parameters of various optimisation models that (1) incorporate a quadratic cost function and only one constraint on land availability, (2) allocate variable and fixed inputs to production activities represented by activity-specific production functions or (3) allocate fixed inputs to production activities represented by activity-specific profit functions. As stated by their authors, this alternative approach to PMP has some theoretical advantage over the original PMP for the estimation of programming models. It also has some empirical advantage over standard econometric procedures of duality-based behavioural functions for the estimation of more complex models characterized by more flexible functional forms and more constraints as well as the incorporation of additional constraints relevant for simulation purpose. The application in the next section also skips the first step of PMP to use directly the optimality conditions of the desired programming model.
Exploiting the richness of the FADN data, this model is part of an effort initially funded by the Belgian Federal Ministry of Agriculture to develop a decision support system for agricultural and environmental policy analysis. The model is known under the name of SEPALE and is developed by a group of agricultural economists based at the Université Catholique de Louvain, the University of Ghent and the Centre for Agricultural Economics of the Ministry of the Flemish Community. Since this model only predominantly uses FADN data, it is conceivably applicable to all the EU-15 58,000 representative commercial farms recorded in this database accessible by any national or regional administrative agencies. Before presenting an application drawn from the recently agreed mid-term review of Agenda 2000, the following subsection first presents how key parameters of the model are calibrated in the farm generic model and how animal feeding and quota constraints are added to the generic farm model.
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