TURKISH AGRICULTURAL SECTOR MODEL & H. Erol Çakmak and H. Ozan Eruygur FUTURE DEVELOPMENTS H. Erol Çakmak and H. Ozan Eruygur Turkish Agricultural Sector Modelling System E. Çakmak and O. Eruygur

TURKISH AGRICULTURAL SECTOR MODEL for EU (TASM-EU) PART 1 TURKISH AGRICULTURAL SECTOR MODEL for EU (TASM-EU) Turkish Agricultural Sector Modelling System E. Çakmak and O. Eruygur

REGIONAL AGRICULTURAL SECTOR MODEL FOR TURKEY (TASM-EU) The purpose is to provide a consistent and integrated framework to ponder about the potential developments in the Turkish agricultural sector, in the case of EU membership. Model permits a thorough analysis of the crop and livestock production. A single period model. A non-linear programming model. It maximizes the consumers' and producers' surplus. Turkish Agricultural Sector Modelling System E. Çakmak and O. Eruygur

TASM-EU The model incorporates a technique known as Positive Mathematical Programming (PMP) to overcome the overspecialization problem in production by using the information provided by the actual actions taken by the farmers. It provides an internally consistent quantitative framework of analysis to study the impact of changes in resource prices, resource availabilities, policies, techniques of production, and economic growth on the location, production, consumption and price of agricultural commodities. Turkish Agricultural Sector Modelling System E. Çakmak and O. Eruygur

Most important features The production side of the model is disaggregated to four regions (Coastal, Central, Eastern, and GAP Region) for the exploration of interregional comparative advantage in policy impact analysis. The crop and livestock sub-sectors are integrated endogenously, i.e. the livestock sub-sector gets inputs from crop production. Foreign trade is allowed in raw and in raw equivalent form for processed products and trade is differentiated for EU and the rest of the world. Turkish Agricultural Sector Modelling System E. Çakmak and O. Eruygur

Turkish Agricultural Sector Modelling System E. Çakmak and O. Eruygur

On the demand side, consumer behavior is regarded as price dependent, and thus market clearing commodity prices are endogenous to the model. Demand, supply and policy interactions at the national level are sketched in Figure 2. Turkish Agricultural Sector Modelling System E. Çakmak and O. Eruygur

Turkish Agricultural Sector Modelling System E. Çakmak and O. Eruygur

Structure of Crop and Livestock Production The model contains more than 200 activities to describe the production of about 50 commodities with approximately 250 equations and 350 variables. Each production activity defines a yield per hectare for crop production, yield per head for livestock and poultry production. Crop production activities use fixed proportion of labor, tractor power, fertilizers, seeds or seedlings. The livestock and poultry activities are defined in terms of dry energy requirements. Turkish Agricultural Sector Modelling System E. Çakmak and O. Eruygur

Crop Production Activities crop production activities is divided into three categories: crop yield for human consumption, crop yield for animal consumption and crop by-product yield (forage, straw, milling by-products and oil seed by-products) for feed. Five groups of inputs i.e. land, labor, tractor power, fertilizer and seed, for the crop production are incorporated. Land is classified in four classes: Dry and irrigated land for short cycle activities Tree land for long cycle activities Pasture land which includes range-land and meadow. Turkish Agricultural Sector Modelling System E. Çakmak and O. Eruygur

Turkish Agricultural Sector Modelling System E. Çakmak and O. Eruygur

Livestock Production Activities Feed supply is provided from the crop production sector, and it is disaggregated into six categories Direct or raw equivalent commercial feed consumption of cereals i.e. wheat, barley, corn, rye, oats, millet and spelt. Two categories of processing by-products: milling by-products, i.e. wheat, rice, sugar beet, and oil seed by-products, i.e. cotton, sunflower, groundnut, and soybean. Straw or stalk by-products from the crop production: wheat, barley, corn, rye, oats, millet, spelt, rice, chickpea, dry bean, lentil. Fodder crops: alfalfa, cow vetch, wild vetch, and sainfoin. Range land and meadow Turkish Agricultural Sector Modelling System E. Çakmak and O. Eruygur

Calibration Method Model uses the PMP approach to calibrate the model rather than flexibility constraints First, the model was run with regional production constraints with a small perturbation to prevent degeneracy. The shadow prices of the regional production constraints obtained from the first-step run reflect the unaccounted portion of the cost function. Then, the shadow prices of the regional constraints are normalized with the actual production figures and are integrated into the objective function as a quadratic penalty term. The calibration constraints are then removed and the model has been adjusted for the validation exercise in the second-step run. Turkish Agricultural Sector Modelling System E. Çakmak and O. Eruygur

Steps of Standard PMP The first step of the model can be written in simple matrix notation as follows: where Z is the objective function. Domestic and foreign demand, import costs of the products, and the variable costs of all production activities are included in the objective function. The vector x and the matrix A denote the activities and input-output coefficients. Vector b shows the RHS of the equations. Turkish Agricultural Sector Modelling System E. Çakmak and O. Eruygur

Standard PMP The slope terms are dependent on the gross revenue and the level of activities. where  is the slope term, SE and P represent supply elasticity and price, respectively; Y is the yield, and BPA denotes base period activity level. The indices are defined as follows: r, region; a, production activity; t, technology; and o, output. Turkish Agricultural Sector Modelling System E. Çakmak and O. Eruygur

Standard PMP The intercept terms are found by using the dual values of the calibration constraints and the slope terms: where  is the intercept term of the cost function, and DVC denotes the dual value of the calibration constraint in (3). Turkish Agricultural Sector Modelling System E. Çakmak and O. Eruygur

Hence, the cost functions are obtained from the production decisions of the farmers in the base period. In the second step the cost functions are incorporated in the model shown in equations from (1) to (4), and calibration constraints (3) are removed. The model used for policy experiments is shown below: The model now replicates the base year production and prices without the calibration constraints. Turkish Agricultural Sector Modelling System E. Çakmak and O. Eruygur

Turkish Agricultural Sector Modelling System PART 2 FUTURE DEVELOPMENT: Turkish Agricultural Sector Modelling System (TAGRIS) Turkish Agricultural Sector Modelling System E. Çakmak and O. Eruygur

Turkish Agricultural Sector Modelling System (TAGRIS) TAGRIS-SM (Sector Model) TAGRIS-CGE (Computable General Equilibrium Model) Turkish Agricultural Sector Modelling System E. Çakmak and O. Eruygur

A. NEAR FUTURE: TAGRIS-SM Turkish Agricultural Sector Modelling System E. Çakmak and O. Eruygur

Development Paths Three basic approaches are available for development of Turkish Agricultural Sector Modelling System –Sector Model (TAGRIS-SM). Paris, Q., and Howitt R.E. , 1998, An Analysis of Ill-Posed Production Problems Using Maximum Entropy, AJAE, 80(1), pp. 124-138. Heckelei, T., and Britz, W., 2000, Positive mathematical programming with multiple data points: a cross-sectional estimation procedure, Cahiers d'Economie et Sociologie Rurales, 57, pp. 28-50. Heckelei, T., and Wolff, H., 2003, Estimation of constrained optimisation models for agricultural supply analysis based on generalised Maximum Entropy, European Review of Agricultural Economics, 30(1), pp. 27-50. Turkish Agricultural Sector Modelling System E. Çakmak and O. Eruygur

Review of Standard PMP Turkish Agricultural Sector Modelling System E. Çakmak and O. Eruygur

first-order conditions... Assuming that all activity levels are strictly positive and all allocable resource constraints are binding at the optimal solution, the first-order conditions of model (1) provide the following dual values Turkish Agricultural Sector Modelling System E. Çakmak and O. Eruygur

Second step.. The second step of PMP consists in using the duals to calibrate the parameters of the non-linear objective function. A usual case considers calibrating the parameters of a variable cost function Cv that has the typical multi-output quadratic functional form, however, holding constant variable input prices at the observed market level as follows: Turkish Agricultural Sector Modelling System E. Çakmak and O. Eruygur

variable marginal cost vector... The variable marginal cost vector MCv of this typical cost function is set equal to the sum of the accounting cost vector c and the differential marginal cost vector  as follows To solve this system of n equations for [n + n(n + 1)/2] parameters and, thus, overcome the under-determination of the system, PMP modellers rely on various solutions. Turkish Agricultural Sector Modelling System E. Çakmak and O. Eruygur

The following PMP model is ready for simulation The third step of PMP uses the calibrated non-linear objective function in a non-linear programming problem similar to the original one except for the calibration constraints. This calibrated non-linear model exactly reproduces observed activity levels and original duals of the limiting resource constraints. The following PMP model is ready for simulation Turkish Agricultural Sector Modelling System E. Çakmak and O. Eruygur

The under-determination problem To overcome the shortcoming of under-determination of the equations system (6), an earlier ad hoc solution consists in assuming that the symmetric matrix Q is diagonal, implying that the change in the actual marginal cost of activity i with respect to the level of activity i' (ii') is null and, then, in relying on additional assumptions. Turkish Agricultural Sector Modelling System E. Çakmak and O. Eruygur

qii = (ci + i)/ xio and di = 0 for all i = 1, …n, Common additional assumptions consist in posing the vector d of the quadratic cost function to be either equal to zero, which leads to: qii = (ci + i)/ xio and di = 0 for all i = 1, …n, or equal to the accounting cost vector c, which leads to: qii = i / xio and di = ci for all i = 1, …n. Another calibration rule called the average cost approach equates the accounting cost vector c to the average cost vector of the quadratic cost function, which leads to: qii = 2 i / xio and di = ci - i for all i = 1, …n. Exogenous supply elasticities ii are also used to derive the parameters of the quadratic cost function: qii = pio / ii xio and di = ci + i - qii xio for all i = 1, …n. Turkish Agricultural Sector Modelling System E. Çakmak and O. Eruygur

1. Paris and Howitt (1998) “An Analysis of Ill-Posed Production Problems Using Maximum Entropy” A subsequent development from Paris and Howitt (1998) to calibrate the marginal cost function is to exploit the maximum entropy estimator to determine all the [n + n(n + 1)/2] elements of the vector d and matrix Q using the Cholesky factorisation of this matrix Q to guarantee that the calibrated matrix Q is actually symmetric positive semi-definite. This estimator in combination with PMP enables to calibrate a quadratic variable cost function accommodating complementarity and competitiveness among activities still based on a single observation but using a priori information on support bounds. Nevertheless, as argued in Heckelei and Britz (2000), the simulation behaviours of the resulting calibrated model would be still arbitrary because heavily dominated by the support points. Turkish Agricultural Sector Modelling System E. Çakmak and O. Eruygur

2. Heckelei and Britz (2000) ”Positive mathematical programming with multiple data points: a cross-sectional estimation procedure” Heckelei and Britz (2000) exploit the suggestion from Paris and Howitt (1998) to use the maximum entropy estimator to determine these parameters on the basis of additional observations of the same farm or region in a view to collect information on second order derivatives. They estimate the parameters of the vector d and matrix Q on the basis of cross sectional vectors of marginal costs and the use of the Cholesky decomposition of the matrix of the second order derivatives as additional constraints. Turkish Agricultural Sector Modelling System E. Çakmak and O. Eruygur

2. Heckelei and Britz (2000) ”Positive mathematical programming with multiple data points: a cross-sectional estimation procedure” They obtain a greater successful ex-post validation than using the standard "single observation" maximum entropy approach. This cross sectional procedure is an interesting response to the lack of empirical validation for models that are calibrated on a single reference period. It is used to calibrate the cost functions of the regional activity supplies of the Common Agricultural Policy Regional Impact (CAPRI) modelling system (Heckelei and Britz, 2001). Turkish Agricultural Sector Modelling System E. Çakmak and O. Eruygur

3. Heckelei and Wolff (2003) ”Estimation of constrained optimisation models for agricultural supply analysis based on Generalised Maximum Entropy” 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. Turkish Agricultural Sector Modelling System E. Çakmak and O. Eruygur

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). Turkish Agricultural Sector Modelling System E. Çakmak and O. Eruygur

Their argument goes... 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. Turkish Agricultural Sector Modelling System E. Çakmak and O. Eruygur

skip the first step altogether... 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 propose A General Alternative to PMP Turkish Agricultural Sector Modelling System E. Çakmak and O. Eruygur

A General Alternative to PMP The 'general' alternative to PMP with respect to calibrating or estimating a programming model is nothing but a simple methodological principle: Always to directly use the first order conditions of the very optimisation model that is assumed to represent or approximate producer behaviour and is suitable for the simulation needs of the analysts. Turkish Agricultural Sector Modelling System E. Çakmak and O. Eruygur

To avoid Inconsistency... No first phase calculating dual values of calibration constraints based on a different model is necessary. We can avoid the implied methodological inconsistency altogether and generally estimate shadow prices of resource constraints simultaneously with the other parameters of the model. Turkish Agricultural Sector Modelling System E. Çakmak and O. Eruygur

The basic principle can be illustrated by writing a general programming model with an objective function h(y| ) to be optimised subject to a constraint vector g(y|) = 0 in Lagrangian form: Turkish Agricultural Sector Modelling System E. Çakmak and O. Eruygur

Estimation of programming models using first order conditions HECKELEI and WOLFF (2003) provide an illustration of the estimation approach using first order conditions with just one resource constraint (land) based on multiple observations. With a sufficient number of observations, the specification problem becomes overdetermined and an exact calibration to observed activity levels is not possible anymore. Consequently, the authors introduce error terms allowing for a deviation of estimated from observed variable values. In principle, the parameter estimation can now proceed with classical estimation techniques such as Least Squares or Generalized Methods of Moments. However, HECKELEI and WOLFF employ the maximum entropy criterion as they also investigate the impact of additional prior information on the estimation results. Turkish Agricultural Sector Modelling System E. Çakmak and O. Eruygur

Development: Which Way Now? Which way for the generation of Turkish Agricultural Sector Modelling System-Sector Model (TAGRIS-SM)? A pure ME version of PMP; Howitt and Paris (1998)? A CAPRI model base; Heckelei and Britz (2000)? Adoption of a General Alternative to PMP; Heckelei and Woff (2003), Heckelei and Britz (2005)? Turkish Agricultural Sector Modelling System E. Çakmak and O. Eruygur

B. FUTURE TAGRIS-CGE Turkish Agricultural Sector Modelling System E. Çakmak and O. Eruygur

TAGRIS-CGE Developement of a CGE extension. Integration of TAGRIS-SM and TAGRIS-CGE leading to fully complete agricultural system analysis tool: TAGRIS. TAGRIS will be a Macro-Integrated Agricultural Sector Model for Turkey. Cakmak,-Erol; Yeldan,-Erinc; Zaim,-Osman, "The Rural Economy Under Structural Adjustment and Financial Liberalization: Results of a Macro-Integrated Agricultural Sector Model for Turkey", Canadian Journal of Development Studies, 17(3), 1996, pp 427-447. Turkish Agricultural Sector Modelling System E. Çakmak and O. Eruygur

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