Pruebas de Hipótesis

In agricultural efficiency studies, parametric and non-parametric approaches and their theoretical and methodological variations are widely applied. A large number of studies are implementing more than one method, either as complementary to each other or as alternative approaches to compare. In terms of DEA, different variations and related models are applied such as additive DEA models (Haag et al., 1992), models with allocative input (Färe et al., 1997), sub-vector approach (Piot-Lepetit et al., 1997; Lansink et al., 2002; Asmild and Hougaard, 2006; Lilienfeld and Asmild, 2007), bootstrap DEA approaches (Balcombe et al., 2006; Davidova and Latruffe, 2007; Latruffe et al., 2008a; Balcombe et al., 2008a; 2008b; Odeck, 2009; Monchuk et al., 2010), weight restrictions (Garcia and Shively, 2011) and Malmquist Productivity Indices (Millian and Aldaz, 1998; Balcombe et al., 2008a; Odeck 2009; Thirtle et al., 2003).

Parametric methods such as production function approaches or Stochastic Frontier Analysis (SFA) appear as common techniques applied together with DEA and its related approaches. In addition, regression models have been used in many studies to identify the several factors underlying the inefficiencies. Below, common related approaches of DEA and the methods used together with DEA in the agricultural efficiency evaluation research are reviewed.

• Sub-vector Approach: Sub-vector approach is one of the variations of DEA models, which is applied in several agricultural efficiency studies. In real world applications of DEA, a distinction of variables can arise being controllable and non-controllable. Sub-vector variation of DEA enables to estimate only the relative input reduction or output expansion potentials in a subset of the inputs or outputs, rather than the reduction or expansion potential in all inputs or outputs simultaneously (Lilienfeld and Asmild, 2007). Sub-vector technical efficiency has been developed by Kopp (1981) and Färe et al. (1983). It is first applied by Banker and Morey (1986).

The work by Piot-Lepetit et al. (1997) in France is one example of studies, in which sub-vector variation of DEA is employed in agriculture. In this study, sub-vector approach is used to consider land and labour as fixed inputs, whereas other inputs such as equipment, fertilizer, pesticides and seeds are considered to be variable. Lansink et al. (2002) also apply sub-vector approach together with the standard technical and scale efficiency calculations in conventional and organic farming of Finland. Each output is considered separately in different models and capital, land, labour and energy specific models are developed in addition to analysis for standard calculations of technical and scale efficiencies. Furthermore, Asmild and Hougaard (2006) evaluate the efficiency in Danish pig farms using different types of models, two of which are based on sub-vector approach. In one model, the efficiency

fixed and letting only the revenue variable to vary. Another study of sub-vector approach in agriculture is by Lilienfeld and Asmild (2007), evaluating the irrigators in Kansas, USA. In this study, since the irrigation is the main interest, the models are built in water use-specific way and the reduction potential for just this input is investigated.

• Malmquist Productivity Index: As mentioned in Section 3.1.3, the foregoing use of DEA is based on relative measurement of efficiency at the same point in time. To evaluate the changes in the efficiency overtime, Malmquist Productivity Index (MPI) is introduced by Malmquist (1953) and Caves et al. (1982) and improved further by Färe et al. (1992). Tone (2004) defines Malmquist Productivity Index as ‘an index representing Total Factor Productivity (TFP) growth of a Decision Making Unit (DMU), in that it reflects progress or regress in efficiency along with progress or regress of the frontier technology over time under the multiple inputs and multiple outputs framework’. In other words, Malmquist Productivity Index is a measure of productivity change, which also contains information about the source of this change (Asmild and Tam, 2007). Several studies in agricultural efficiency evaluation apply Malmquist Productivity Index (MPI) approach. Examples can be given as Millian and Aldaz (1998), Balcombe et al. (2008a), Odeck (2009) and Thirtle et al. (2003) as discussed also productivity change studies part in Section 3.1.3.

• DEA and Stochastic Approaches: Stochastic Frontier Analysis (SFA) is one parametric technique, which is remarkably applied together with DEA in agricultural efficiency studies. It is based on a stochastic frontier production function approach, which is developed by Aigner et al. (1977) and Meeusen and Van den Broeck (1977). The SFA approach requires that a functional form be specified for the frontier production function. An advantage of SFA over DEA is

that it takes into account measurement errors and other noise in the data (Latruffe et al., 2004).

In several agricultural studies, SFA technique is used together with DEA and the results are compared with each other. One example can be given as Reinhard et al. (2000), which apply both DEA and SFA approaches to a sample of dairy farms in Netherlands in order to measure the environmental efficiency with the consideration of detrimental inputs. The study compares the results obtained from two methods, together with the discussions of strengths and weaknesses of both approaches in evaluating their case. In Iráizoz et al. (2003), DEA and SFA are applied to horticultural production farms in Spain. Tomato and asparagus production is evaluated separately with both techniques and both of them are found to be highly inefficient. Similarly, Latruffe et al. (2004) aims to measure and compare the technical efficiency through SFA and DEA approaches. A sample of Polish crop and livestock farms are evaluated separately. In this study, SFA findings are generally supported by DEA results. Livestock farms are found to be more efficient. Size- efficiency relationship is found to be positive. Soil quality, degree of integration with downstream markets and education are the variables that are indicated as important determinants of efficiency.

In addition to SFA technique, other similar stochastic approaches are applied together or compared with DEA. As an example, Sharma et al. (1999) apply stochastic efficiency decomposition technique following the Kopp and Diewert (1982) cost decomposition procedure to estimate technical, allocative and economic efficiencies. In the study, the results of both techniques are compared for a sample of swine producers in Hawaii. Results from both models reveal considerable

comparing results of different approaches can be given as Alene et al. (2006) which also apply a stochastic approach, stochastic frontier production function (SFP), as well as DEA and parametric distance functions (PDF). The study aims to measure the efficiency of different systems in crop production of Ethiopia and compare the performances of three methods. According to the findings of the study, SFP gave the lowest efficiencies. The results reveal that innovative cropping systems contribute to the farmers’ efficient use of land and other resources.

• DEA and Regression:A large number of studies can be found, which evaluate the agricultural efficiency and then investigate the factors underlying the efficiencies or inefficiencies through regression of efficiency scores over sets of various explanatory variables. The relationships between efficiency scores and different variables such as age of the farmer (Mathijs and Vranken, 2000; Dhungana et al., 2004,), education of farmer (Mathijs and Vranken, 2000; Dhungana et al., 2004; Galanopoulos et al., 2006), farm size (Helfland and Levine, 2004; Kleinhanß et al., 2007), gender (Mathijs and Vranken, 2000; Dhungana et al., 2004), land acquisition (Mathijs and Vranken, 2000; Helfland and Levine, 2004;), organizational forms (Mathijs et al., 1999), product specializations (Mathijs et al., 1999; Mathijs and Vranken, 2000; Helfland and Levine, 2004), risk attitude (Dhungana et al., 2004), subsidies (Kleinhanß et al., 2007) and technology (Helfland and Levine, 2004) are investigated through regression analyses following DEA. In addition, some studies focus on environmental aspects of the farms and investigate the relationship between efficiencies and environmental variables (Wossink and Denaux, 2006) or environment friendly behavior of farmers (Mathijs and Vranken, 2000).

• Bootstrapping Approaches: Simar and Wilson (1998) argue that ‘although the literature typically refers to DEA as being deterministic, efficiency is measured relative to an estimate of the true (but unobserved) production frontier. Since

statistical estimators of the frontier are obtained from finite samples, the corresponding measures of efficiency are sensitive to the sampling variations of the obtained frontier’. They advocate the bootstrapping introduced by Efron (1979) as a way to analyse the sensitivity of efficiency scores relative to the sampling variations of the estimated frontier. Building upon these discussions, Simar and Wilson (1998; 2000; 2007) propose a bootstrapping methodology allowing the construction of confidence intervals for DEA efficiency scores, which relies on smoothing the empirical distribution (Balcombe et al., 2008a). The approach is also adapted to the case of Malmquist indices in Simar and Wilson (1999). Bootstrapping approaches to DEA introduced by Simar and Wilson are applied widely in DEA literature to estimate and explain technical efficiency.

Bootstrapping approach to DEA is also applied in agricultural efficiency studies. Balcombe et al. (2006) dealing with technical efficiency of Australian dairy farms, Davidova and Latruffe (2007) and Latruffe et al. (2008a) evaluating a sample of crop and livestock farms in Czech Republic, Balcombe et al. (2008b) investigating the technical efficiency and factors behind it in Bangladesh rice farms and Monchuk et al. (2010) measuring the agricultural efficiency of Chinese regions are some examples of studies applying models developed by Simar and Wilson (1998; 2000; 2007). Moreover, the adapted models of bootstrapping to Malmquist Index approach is applied by Odeck (2009) to Norwegian grain farms and Balcombe et al. (2008a) to Polish crop and livestock farms.