The use of Howitt's Positive Mathematical Programming (PMP) method for calibrating total supply forms the basis of the TASM (Kasnakoğlu and Bauer, 1988), TASM-EU (Çakmak and Kasnakoğlu, 2002) and TAGRIS (Eruygur, 2006; Eruygur and Çakmak, 2008) models.  Howitt's Positive Mathematical Programming (PMP) method provides the positive approach necessary for conducting policy analysis within their model structures.

 

 

 

 

The PMP method calibrates the model to the observed values of the base period by incorporating the behaviors that determine the farmer's production decisions into a mathematical formulation. The method allows the modeler to reconstruct the cost function of the agricultural sector for a given product by estimating the hidden (opportunity) cost information of the production process, which cannot be directly observed due to data limitations, from the observed production levels of the base period. This approach is consistent with the primary objective of sector models, which is to simulate producers' responses to changes in market conditions, resource allocation, and production techniques. In other words, by modeling producer behaviors, sector models (while being mathematical optimization models) become policy simulation models.

 

In 1998, Paris and Howitt (1998) integrated the Generalized Maximum Entropy (GME) estimator of Golan et al. (1996) into the PMP method, thereby advancing the method. This contribution enabled the estimation of all terms in the cost functions, including cross terms.

 

Subsequently, the Maximum Entropy-based PMP approach was developed by Heckelei and Britz (1999 and 2000) and used in the EU's Agricultural Sector Model CAPRI (Common Agricultural Policy Regional Impact Model). The approaches of Heckelei and Britz (1999 and 2000) allow for the use of multiple cross-sectional data in estimating PMP cost functions, considering regional profitability and differences in production scale. In light of these developments in the literature, the approaches of Heckelei and Britz (1999 and 2000) have been used in the supply calibration of TAGRIS.

 

The model is a nonlinear programming-based, static, partial equilibrium agricultural sector model. It maximizes the Marshallian surplus; therefore, output prices are endogenous (Samuelson, 1952; Takayama and Judge, 1964 and 1971). Demand calibration is based on elasticities. As mentioned above, for supply calibration, the Positive Mathematical Programming approach with cross-sectional observations based on Maximum Entropy by Heckelei and Britz (1999 and 2000) has been used. Foreign trade is modeled in raw equivalent form for raw and processed products and divided into three blocks: the EU, the USA, and other world countries. The base period of the last version of the model is the average of 2014, 2015, and 2016. To account for interregional comparative advantages in policy impact analysis, the production part of the model is divided into four separate regions: Coastal Region, Central Anatolia, Eastern Anatolia, and GAP (Southeastern Anatolia Project) regions. To minimize aggregation error, regional data is obtained from data at the provincial level. Production activities are distributed among the regions based on the production levels of the base period. The crop and livestock sub-sectors are internally linked to each other; in other words, the livestock sub-sector uses the outputs of the crop production sub-sector.

 

The assumptions used in the setup of the model are as follows: (1) The production of the agricultural sector can be distributed across regions. (2) There is a fixed relationship between inputs and outputs in all production activities. (3) Four classes of goods can be defined: (i) resources used in production, (ii) internal intermediate inputs produced in farm-level activities and used as inputs in another production activity, (iii) intermediate outputs produced in farm-level activities and used as inputs in processing activities, and (iv) products consumed as they are produced at the farm level. (4) Consumption occurs at the national level. (5) The resource availability of the regions is known and fixed. (6) The supply elasticity of inputs such as chemical fertilizers is infinite. (7) The income level of other sectors of the economy is taken as given. (8) Export supply has increasing marginal costs. (9) The demand for products is determined by linear and price-dependent functions. (10) All agents participating in the system exhibit competitive behavior, and the trade of goods is conducted in competitive markets.

 

 

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