Measurement of efficiency with DEA method

An important contribution was the work of ^{Farrell (1957)} who established the basic framework for studying and measuring the overall efficiency of the company. This theory is applied in practice mainly using two approaches: parametric and nonparametric approaches. For the first one, resorting the use of econometrics and, the second one, based on the Data Envelopment Analysis method (DEA). There are two basic models of DEA: 1) DEA-RCE model. Developed by ^{Farrell (1957)} and popularized by ^{Charnes et al., (1978)}, in which a production frontier is assumed constant returns to scale (CRS) and; 2) The DEA-RVE model (^{Banker et al., 1984}), which assumes a convex border production and therefore is more suitable for agricultural production systems.

Data

Information was obtained in 2010, from 30 bean farms located in the municipality of San Genaro Boconoíto, Sector Palaciera, Portuguesa State, Venezuela. As product, we used kilograms of beans (beans) harvested per farm, five inputs: number of hectares (ha) planted per farm and total expenditures in bolivars incurred by the concepts of soil preparation (plowing) of seed (seed), weed control (cmalezas) and harvest (harvest).The incorporation of costs as inputs is suitable according with ^{Castillo (2006)}. DEA oriented model products, which was resolved with Win4deap software was used (^{Coelli, 1996}).

Socioeconomic variables were identified: family labour (number), hired labour (number), age (years) and distance (km) from the farm to the population centre most important (Guanare), and others were discarded by their homogeneity. The Tobit regression was estimated with Stata (^{StataCorp, 2009}). The possible influence of other factors were also analysed in efficiency (soil-climate and proximity to roads) by the spatial distribution of scores TSG per farms (classified according if they xceeded or not the mean), determining the coordinates x and y. The Arcgis, software was used v. 9.2 (^{ESRI Inc., 2008}).

Efficiency estimation of farms producing beans

Farms bean threw an average of 850.7 kg ha^-1, lower value (p> 0.01) than the national average of 1 200 kg ha^-1 (^{Fedeagro, 2012}). Only occurred a perfect correlation between ha and labour, so the latter input was removed from the DEA model (^{Chediak and Rodríguez, 2011})

The average ETG of the farms was 81.2%, indicating that their bean production could increase on by 23.2% without increasing the resources currently applied and operating the most productive scale size. Moreover, the minimum value (ETG= 71.4%) reveals that less efficient farm production should increase 40.1% to reach the production level 2 group compared to efficient farms, representing 6.7% of the sample.

The average rate of pure technical efficiency (PTE= 86%) can be estimated that the production of inefficient farms should be increased by 16.3% to be efficient to scale established by the group of 7 farms with 100% of ETP representing 23.3% of the sample.

The average efficiency rating scale (SE= 95.1%) reflects that there are inefficiencies due to 36.7% (100% - 63.3%) of the farms are not operating, to their optimal sizes (measured by volumes of product). These inefficiencies of scale are attributed least above the optimum sizes (one farm which represents 3.3%) than under optimal sizes, which present 10 farms (33.3% of the sample) operating under increasing returns to scale (IRS). These farms are a group considered a structural problem of agriculture in some countries (^{Papageorgiou and Spathis, 2000}).

The inefficiency generated by the use of technology production is larger than the scale inefficiency, justifying the development and implementation of a plan of transfer of technology, but the technology gap is not as pronounced as reported in studies of other cultures (^{Ajibefun, 2008}; ^{Mulwa et al., 2009}; ^{Koc et al., 2011}). Finally, technology in farms with bean production adjusted to constant returns to scale (p> 0.05).

Second level analysis

Because the constant returns to scale were relevant and there are only two farms with 100% efficiency, the average of the ETG was used to form two categories (^{Castillo, 2006}): 1) level of less than average efficiency (ETG≤ 81.2%) and; 2) level above average efficiency (ETG> 81.2%). Each of the inputs and outputs were measured in total per farm and then averaged per group. The results indicated that there are no differences (p> 0.05) in amounts applied in production processes on farms discriminated by efficiencies inputs, but there were differences (p< 0.05) in bean production, which explains disparities in levels of efficiency compared two groups of farms.

The inputs and outputs of each level of efficiency were divided between the surfaces. The group with a level lower than the average efficiency emitted amounts per hectare slightly higher for concepts seed and weed control, but lower in heading harvest. On the other hand, presented a lower bean productivity. Importantly, the average productivity of bean producers sample was lower (850.7 kg ha^-1) (p< 0.01) than the national average (1 200 kg ha^-1) estimated for 2011 (^{Fedeagro, 2012})

The DEA model generated information to develop a plan of benchmarking to efficient technology transfer to less efficient farms. In short, for all farms evaluated, can increase aggregate bean production from 234 970 kg to 289 200 kg.

Socioeconomic determinants of efficiency in bean crop

Only family labour took effect (p<0.05) in the efficiency of farms producing beans, generating an increase of 5.1% TSG. However, due to the statistical evaluation, the model Tobit revealed problems of validity, Rho Spearman correlation, confirmed that none of the socioeconomic variables is related to the ETG, including the variable familiar MO (p=0.08) was applied by which it is discarded as a determining variable technical efficiency and recommends continued empirical testing.

Spatial distribution of ETG rates

ETG scores obtained by each farm is quite randomly distributed in the study area, so it is inferred that were not influenced by the distance to the road or soil-climatic variables, perhaps because the public technical assistance they received.

Conclusions

In the sample of farms bean, the overall technical efficiency (ETG) was 81.2%, broken down into pure technical efficiency (PTE) of 86% and scale efficiency (EE) of 95.1%. Similarly, the inefficiencies caused by technology are higher than those generated by a suboptimal size or scale production.

The technology of producing is set to constant returns to scale. In studies on the predominant type of technology on farms has not reached a consensus on their adjustment to variable or constant returns to scale.

According to the goals formulated in the plan for the sampling of farms, the aggregated output can get increase from 234 970 kg to 289 200 kg, representing an increase of 54 230 kg (23.1%). Considering that, the models are oriented in products, these increases were obtained with current levels of inputs (or a small reduction thereof in some cases) applied to production processes, and are not significantly larger because farms tend to be relatively homogeneous in terms of using technology due largely to receive technical assistance from public institutions. If achieving these increases of production, it would help to improve the food security of the country and also to improve the quality of life of the object of planning agricultural producers.

Socioeconomic and related environmental factors such as soil and climatic or close to access roads variables did not determine the levels of technical efficiency of the farms studied. The most likely cause of the findings of this research are not consistent with those reported by ^{Binam et al. (2003)}; ^{Rivers and Shively (2005)} and ^{Koc et al. (2011)}, among others, is that public technical assistance received by the producer group under study, minimizes the impact of their socioeconomic and environmental variables (soil and climate and distance from access roads) levels of efficiency of their operations.