In the following two chapters, we illustrate the proposed methodology and theory on efficiency and elasticity using the Turkish FADN data set identified above. The chapters are designed to reflect different implications of our methodology. We aim to provide an insight on the use of production trade-offs in agricultural efficiency evaluation with DEA and on the elasticity measures under different considerations of returns-to-scale, elasticity scenarios17
and ranges of trade-offs. Our objective is to illustrate and observe whether the method we propose, the statements we provide and theory we develop throughout the research can be verified in a real world case. The design of empirical applications are summarised in Figure 6.2.
Throughout the empirical applications, all the calculations are performed using General Algebraic Modeling System (GAMS)18. Linear programming (LP) models of DEA and
elasticity measures with or without trade-offs under both VRS and CRS are coded and
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solved. Relying on the preliminary experiments done, as an LP solver, MOSEK solver19 embedded in GAMS is used. With the default LP solver of GAMS, some problems arise in solving the elasticity models related to handling of the infeasible and unbounded solutions, therefore after several experimenting, MOSEK solver is found more reliable and used in calculations.
Figure 6.2. Summary of Empirical Applications in Turkish FADN
Chapter 7 includes illustrative examples of elasticity measures. It aims to demonstrate the applicability of elasticity measures under different scenarios of changing and responding sets of inputs and outputs considering both VRS and CRS assumptions with or without trade-offs are incorporated. We use the West Anatolia sample of the data set and the broad range of trade-offs identified for our illustrative purposes. We calculate elasticities for either
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19 http://www.gams.com/solvers/solvers.htm#MOSEK
Emprical Applications
Illustrative Examples (Chapter 7) West Anatolia Region Different Scenarios of Elasticity
Broad Trade-offs
Efficiency Analysis (Section 7.1)
Elasticity Measurement (Section 7.2)
Application in All Regions (Chapter 8)
8 Regions
Two scenarios of Elasticity 3 ranges of trade-offs
Efficiency Analysis (Section 8.1)
Elasticity Measurement (Section 8.2)
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output or input sets under different scenarios of changing and responding sets. The chapter serves as a preliminary exercise for measuring elasticity on DEA frontiers.
In Chapter 8, we extend our application scope to all over the 8 regions’ data. In this chapter, we also introduce different ranges of trade-offs into models in order to observe the effect of changing trade-offs on efficiency and elasticity measures. We pursue two scenarios of elasticity measures for output sets throughout the chapter and interpret the results relying on the methodological aspects. In both scenarios, changing set consists of “Crop Production Costs” and “Labour” inputs. Responding set contains “Cereals” in one scenario and “Field Crops” in the other. All calculations are also performed under both VRS and CRS considerations.
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Chapter 7
Illustrative Examples of Efficiency and Elasticity Measures in Turkish Agriculture
In this chapter, we cover a series of illustrative examples on the proposed methodology. The aim is to demonstrate how efficiency scores with and without trade-offs differ in a sample of farms and more importantly, how elasticity measures (both existing in the literature or developed in this research) can be applied to a real world sample considering different scenarios of changing and responding sets. We design a bundle of examples addressing different scenarios. We calculate efficiency and elasticity measures using DEA methodology. Both variable returns-to-scale (VRS) and constant returns-to-scale (CRS) technologies with and without trade-offs included in the models are considered. We also verify the discussions on special cases of CRS models provided in Section 4.4 of Chapter 4.
For the illustrative examples in this chapter, we use the West Anatolia region sample in our data set consisting of 35 farms producing 17 types of crops. The crop types produced in this region are given with their classifications and the number of farms producing them in Table 7.1 below. DEA models include 17 outputs representing the production amount of each crop in tons. The inputs selected are land (in daa), labour (as labour costs in TL), crop production costs (TL) and capital expenditures (TL). The selection of inputs is discussed thoroughly in the Chapter 6.
Throughout the examples, as production trade-off relations, the broadest ranges provided to us by the experts are used in order to show how the models work even with a broadest range of trade-offs. A detailed discussion of how the changes in trade-off ranges affect the efficiency scores and the elasticity measures is covered in extensive applications given in Chapter 8. The broadest trade-off relations for the crops produced by the farms in West Anatolia region are also provided in Table 7.1. We have the up and low limits of production amounts for each crop in relation to the wheat production. Only, the trade-off relation of
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grass is missing (which is not provided by the experts); therefore, we do not include any trade-off constraints for grass production. The trade-offs are translated into judgements and then to weight restrictions as explained in previous discussions (see Section 6.6 in Chapter 6 and Section 2.7.2 in Chapter 2).
Table 7.1. Crops in West Anatolia Region
Crops Class Farms # of TO related to 1 ton of Wheat
Low Up
1 Wheat Cereals 35 - -
2 Barley Cereals 22 0.75 1
3 Sugar beet Field crops 21 13 20
4 Lucerne Fodder crops 9 1.2 6
5 Sunflower Field crops 7 0.4 0.9
6 Vetch Field crops 7 0.3 0.6
7 Fodder maize Fodder crops 7 10 20
8 Beans Field crops 7 0.25 0.4
9 Peas Field crops 5 0.2 0.4
10 Potatoes Field crops 3 4 7
11 Oats Cereals 3 0.25 0.4
12 Grain Maze Cereals 3 2 3
13 Apple Permanent crops 2 1 2.5
14 Cherry Permanent crops 2 0.5 1
15 Grass Fodder crops 1 - -
16 Rye Cereals 1 0.5 0.8
17 Lentil Field crops 1 0.15 0.3
Two types of examples regarding the orientation of the models are considered: output- oriented and input-oriented. First of all, the efficiency scores with and without trade-offs are calculated for both orientations in order to discuss how the discrimination of efficiency scores is affected in the presence of production trade-offs. After the efficiency analysis, elasticities of responses are evaluated under different scenarios of changing and responding sets. In the elasticity analysis of output sets, the responding set consists of only outputs (i.e. a set of outputs are responding to the changes in input and/or output sets), whereas in the analysis of input sets, changing set consists of only inputs (i.e. a set of inputs are responding to the changes in inputs and/or output sets). All the calculations are performed for both
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7.1. Efficiency Analysis
Output-oriented (OO) and input-oriented (IO) VRS and CRS DEA efficiency scores for the farms in West Anatolia region, with (WTO) and without trade-off relations included in the models, are provided in Table 7.2. In calculations, multiplier forms are considered. Standard DEA models in multiplier forms are given in Table 2.7 for VRS and Table 2.6 for CRS in Chapter 2. The multiplier models with trade-offs are given in Table 2.9 for VRS and Table 2.10 for CRS in Chapter 2. 35 farms are included in the analysis and the farm codes given in the second column of Table 7.2 indicate the label of the farm in the original FADN data set.
It can be observed in Table 7.2 that in both VRS and CRS cases and in both orientations, the discrimination of efficiency scores gets better when the trade-off relations are integrated to the models. In VRS models, nearly all the farms are obtained as efficient due to the large number of outputs in the model. When the trade-off relations are considered, the number of efficient units dropped to 19 and the average efficiency is reduced to 86% in output orientation and 87% in input orientation. In the CRS cases, (efficiency scores are the same for both orientations as discussed in Section 2.4.2), the discrimination gets even better where in the presence of trade-offs only 7 farms are efficient and the average efficiency score drops from 94% to 72% with the inclusion of production trade-offs to DEA models. Above results reveal that even with a small sample of units, the integration of production trade-offs (even when broadest trade-offs are considered) leads to a considerable improvement in the efficiency score discrimination.
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Table 7.2. Efficiency Scores of Farms in West Anatolia
Farm Code OO VRS OO VRS (WTO) OO CRS OO CRS (WTO) IO VRS IO VRS (WTO) IO CRS IO CRS (WTO) 1 288 1 1 1 0.95 1 1 1 0.95 2 289 1 1 0.87 0.61 1 1 0.87 0.61 3 290 1 1 0.58 0.36 1 1 0.58 0.36 4 291 0.99 0.81 0.87 0.62 0.97 0.70 0.87 0.62 5 293 1 0.89 1 0.64 1 0.74 1 0.64 6 295 1 0.54 0.99 0.53 1 0.61 0.99 0.53 7 296 1 1 1 1 1 1 1 1 8 297 1 0.94 1 0.65 1 0.92 1 0.65 9 298 1 0.82 1 0.78 1 0.78 1 0.78 10 300 0.22 0.14 0.19 0.13 0.47 0.47 0.19 0.13 11 301 1 0.93 1 0.88 1 0.92 1 0.88 12 302 1 0.66 1 0.59 1 0.62 1 0.59 13 303 1 0.28 1 0.26 1 0.91 1 0.26 14 304 1 1 1 0.86 1 1 1 0.86 15 306 1 0.69 1 0.67 1 0.69 1 0.67 16 307 1 1 1 1 1 1 1 1 17 309 1 0.45 1 0.37 1 0.38 1 0.37 18 310 1 1 1 0.69 1 1 1 0.69 19 311 1 1 0.97 0.84 1 1 0.97 0.84 20 312 1 0.65 0.80 0.42 1 0.52 0.80 0.42 21 313 1 0.72 0.90 0.55 1 0.57 0.90 0.55 22 314 1 1 1 0.81 1 1 1 0.81 23 315 1 1 1 0.94 1 1 1 0.94 24 316 1 0.67 0.93 0.67 1 0.88 0.93 0.67 25 317 1 1 1 0.94 1 1 1 0.94 26 318 1 1 1 1 1 1 1 1 27 319 1 1 1 1 1 1 1 1 28 320 1 1 1 1 1 1 1 1 29 321 1 0.99 1 0.62 1 0.99 1 0.62 30 322 1 0.85 1 0.62 1 0.79 1 0.62 31 323 1 1 1 0.94 1 1 1 0.94 32 325 1 1 1 0.79 1 1 1 0.79 33 326 1 1 1 1 1 1 1 1 34 327 1 1 1 1 1 1 1 1 35 328 1 1 0.91 0.38 1 1 0.91 0.38 Average 0.98 0.86 0.94 0.72 0.98 0.87 0.94 0.72 # of Efficient 33 19 25 7 33 19 25 7 # of Inefficient 2 16 10 28 2 16 10 28