The aim of this paper is to use the concept of the METAFRONTIER FUNCTION to study the determination of efficiency differentials and Technological Gap Ratio (TGR) on wheat production in Khorasan Razavi province. In this study, we used the METAFRONTIER FUNCTION and group frontier based on the concept of Stochastic Nonparametric Envelopment of Data analysis (StoNED). The data used in this study consisted of a sample of 435 wheat farms in 2011. The data samples collected from wheat farms are divided into three sizes namely small, medium and large farms. The results of estimating group frontier production FUNCTIONs indicate that the mean technical efficiency (TE) for small, medium and large farms are 0.426, 0.606 and 0.365, receptively. The figures were found to be mean TE for small, medium and large farms are 0.286, 0.239 and 0.248 when evaluated based on the METAFRONTIER production FUNCTION representing that the highest mean TE is devoted to small farms, while medium farms has the lowest mean technical efficiency. The average technological gap ratios for small, medium and large farms were 0.727, 0.463 and 0.725, respectively. Therefore, the medium farms frontier has the most distant to the METAFRONTIER, while the small and large farm frontiers have the closest.

Given the importance of the notion of Efficiency in the Country's Economic Growth, measuring the efficiency and the technology gap for various industries in order to achieve the best possible resource assignment, following the declared policy goals, is of particular importance for those countries, such as Iran, which are now at the early stages of the industrialization process. Hence, the present paper is devoted to determine the efficiency cost and the metatechnology ratio of the industrial activities in Iran. This is done for three groups with different levels of technology during 1995-2010; we use the cost frontier FUNCTION based on the likelihood ratio test between the Cobb-Douglas and Translog FUNCTIONs and also the Stochastic Frontier Analysis and the Meta-Frontier approach. The results indicate that the average percentage of the economic efficiency of these groups ranges from 59. 72 to 95. 26; the average meta-frontier ratio from 0. 5184 to 0. 9782, and also the average percentage of the Meta-Frontier Efficiency ranges from 30. 79 to 87. 37. The results also show that the average percentage of group and Meta-Frontier Economic Efficiency and also the average percentage of metatechnology ratio corresponding to the industries linked to Machinery Rank are better than those industries linked to agriculture, mining, energy and fuel. On the other hand, the growth process of the metatechnology ratio is clearer for the industries linked to mining, energy and fuel during the study stage.

This paper presents an analysis of technical efficiency and technology gap ratio (TGR) in greenhouse cucumber in Fars Province, Iran. Cucumber production was chosen for this study for the reason that greenhouse productions in this province mainly have focused on this product. The data used in this study was obtained from a random sample of 127 greenhouse s in Fars Province for 2010 to 2011. METAFRONTIER production FUNCTION model for firms was used within the parametric framework of stochastic frontier analysis (SFA). The frontier models are applied in the analysis of cross-sectional data by assuming a translog FUNCTIONal form. Results indicate that eliminating energy input subsidies has led to significant decrease in greenhouse cucumber production efficiency so that the mean technical efficiency declined from 98% to 67 % during 2010-2011. Furthermore, subsidies elimination has also led to decrease of the mean technology gap ratio in greenhouses from 0.92 to 0.87, in other words, it has caused more distance from efficient production frontier.

Estimates of technical inefficiency in agricultural production are suspect so long as variations exist in production technology among the sampled farmers. Traditional methods of dealing with these technological differences risk attributing "technology gaps" to technical inefficiency between farms, pointing to the need to undertake a METAFRONTIER analysis that allows technology gaps to be distinguished from technical inefficiency. Using farm-level data on the production of three different varieties of pistachio trees in Iran, we outline two criteria to justify its use: an inability in farmers to switch between production technologies except in the long term, and satisfaction of statistical tests on METAFRONTIER coefficients. The application of METAFRONTIER analysis enabled technical efficiency scores to be corrected for differences in production capacity imposed by tree variety. Results reveal that there is very little difference in technical efficiency between farms growing the different tree varieties. But they show that ignoring the production constraints imposed by variety choice could overstate the scope for farmers to improve their technical performance by adopting better farming practices. The results also indicate that it is misleading to compare the performance of different tree varieties on the basis of yield per hectare alone.

Seed is one of the most important agricultural inputs, which plays a key role in achieving optimal yield and quality of the product. Ever since mankind realized the role of the suitable seed in economic profit and food security, it has always made breeding efforts to provide cultivars with desired genetic characteristics. For the maximum effectiveness of other production inputs such as water, fertilizer and pesticides, access and use of new high-yielding and compatible cultivars is a necessity. In the present study, using the METAFRONTIER frontier FUNCTION, the technological gap ratio of certified seed of Hashemi rice variety was analyzed. The information of 531 farmers was used for the research. This information was obtained in 2018 using the cluster sampling method according to the size of the population. In this study, data envelopment analysis (DEA) model was used to estimate the technical efficiency relative to the group frontier, and the METAFRONTIER method was used to estimate the technological gap ratio (TGR). The results of the frontier production FUNCTION estimation showed that the technical efficiency for farmers who used certified seeds is 0.88 and for farmers who did not use certified seeds is 0.82. It means that these producers with a certain amount of inputs averagely produce about 88 percent and 82 percent of product respectively, which using the available input and the type of seed could be produced. The technical efficiency compared to the METAFRONTIER production FUNCTION was 0.82 in the group that used the certified seeds and 0.72 in the group that did not use this type of seed. The technological gap ratio for the above two groups was 0.93 and 0.86 respectively. In other words, farmers who used certified seeds had better technical performance and had a higher technological gap ratio. This is a promising point for policymakers in the agricultural sector that by promoting the use of certified seeds and taking necessary measures to encourage farmers to use this type of seed, the level of production can be improved.

The aim of this study was to investigate of energy technology gap ratio of main crops in Sari city in 2016. The energy technical efficiency and energy technology gap ratio indices were computed using three approaches; group frontier stochastic production FUNCTION, pooled frontier stochastic production FUNCTION and the METAFRONTIER FUNCTION. Data were collected from Agriculture Jihad Organization of Mazandaran. The results showed that in case of filling the gap between other units and units of efficient products, whit no change in technologies the average amount of energy production for soybeans, canola, alfalfa, barley, wheat and rice could be 19, 23, 35, 33, 39 and 28 percent increase. The results also showed that highest energy technology gaps ratio for the products studied was related to soybean (0.81) and canola (0.67). Thus it is suggested that researchers and policymakers should be more attention about environmental goals, especially ETGR to sustainable use of energy consumption to at least one of the goals in optimization of cropping pattern.

A characteristic of Data Envelopment Analysis (DEA) is to allow individual decision making units (DMUs) to select the factor weights which are the most advantageous for them in calculating their efficiency scores. This flexibility in selecting the weights, on the other hand, deters the comparison among DMUs on a common base. For dealing with this difficulty and assessing all the DMUs on the same scale, this paper proposes using a multiple objective linear programming (MOLP) approach based on scalarizing FUNCTION for generating common set of weights under the DEA framework. This is an advantageous of the proposed approach against general approaches in the literature which are based on multiple objective nonlinear programming.