# Abstract. Agricultural productivity in Africa from 1971 to 2000 is examined using the recently developed metafrontier function technique, for the purpose of studying differences in efficiency and technology gap across different regions of the continent. The results support the view that technology gap plays an important part in explaining the

The metafrontier framework proposed by O'Donnell et al. enables the evaluation of relative efficiencies for decision‐making units (DMUs) operating under heterogeneous technologies.

(J Prod Anal 21:91–103, 2004 ), the metafrontier production function allows for calculating comparable TE measures, which can be decomposed into group specific TE measures and technology gap ratios. The metafrontier model 24 makes it possible to calculate comparable technical efficiencies for agricultural farms that operate under different technologies. The main aim of this study was to compare tomato productivity of com-mercial and smallholder tomato farmers in the Nkomazi area, Mpumalanga, using a metafrontier analysis. The empirical results for the metafrontier analysis shows an average group technical efficiency (GE) score of 70.2% and average meta-technical efficiency of 56.7%. The community group recorded the highest efficiency score of 88.1% with respect to the group frontier, while the parish group showed highest efficiency score of 63.3% relative to the metafrontier.

However, if the three groups arenot exhaustive, then other input–output combinations may be feasi- be decomposed into two components: a component that measures the distance. from an input–output point to the group frontier (the common measure of. technical efﬁciency); and a component that Given $$X_{jit}$$, the metafrontier is defined as the upper boundary of the support of the distribution of $$f_{t}^{j} \left( {X_{jit} } \right)$$, i.e., $$f_{t}^{M} \left( {X_{jit} } \right) = \sup \left( {f_{t}^{j} \left( {X_{jit} } \right) \, \begin{array}{*{20}c} | \\ | \\ \end{array} \, G\left( {f_{t}^{j} \left( {X_{jit} } \right)} \right) < 1} \right)$$ where $$G\left( {f_{t}^{j} \left( {X_{jit} } \right)} \right)$$ is the distribution function of \(f_{t}^{j} … The metafrontier is defined as the area of an unlimited production technology set. In addition, group frontiers are proposed to be the areas of limited production technology sets. The metafrontier model is used to highlight heterogeneity among clusters of countries revealing catch up phenomena. The estimation procedure is based on the notion of stochastic ordering and relies on the solution of an optimization problem on the parameters’ posterior means.

An alternative metafrontier framework for measuring the heterogeneity of technology. Qunwei Wang (), Ye Hang, Jin-Li Hu and Ching-Ren Chiu. Naval Research Logistics (NRL), 2018, vol.

## Metafrontier generalized directional distance function is proposed. performance indicators using a meta-frontier generalized directional distance function.

function is the meaning of the metafrontier function of firms/units (Battese, Rao, & O’ Donnell, 2004). Several studies employ the metafrontier to be the main method in their research, emphasizing on the measurement of technical efficiency (TE) and technical gap ratio (TGRs).

### Feb 1, 2021 metafrontier analysis to estimate region level technical efficiency (TE) and technology gap ratio. (TGR) in the two main grain-producing regions

(TGR) in the two main grain-producing regions  We used an output-oriented data envelopment analysis metafrontier approach and the Tobit model to investigate smallholder and commercial farmers' technical   metafrontier estimated by Data Envelopment Analysis (DEA) was adopted to be the methodology. The frontiers were divided into five regions; Bangkok, central,  The metafrontier model enables the calculation of comparable technical efficiencies for firms operating under different technologies. The model also enables the  Keywords: China's grain production, county-level, metafrontier, stochastic production frontier, technical efficiency.

Agricultural productivity in Africa from 1971 to 2000 is examined using the recently developed metafrontier function technique, for the purpose of studying differences in efficiency and technology gap across different regions of the continent.
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This paper uses the concept of a metafrontier to compare the technical efficiencies of firms that may be classified into different groups. The metafrontier technique consists of enveloping the groups of frontiers estimated through another frontier, called metatechnology. This technique entails the estimation of the metatechnology and the frontiers of relatively homogenous groups (Rao et al., 2004).

Analogous to Battese et al. (J Prod Anal 21:91–103, 2004 ), the metafrontier production function allows for calculating comparable TE measures, which can be decomposed into group specific TE measures and technology gap ratios.
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### Empirical metafrontier studies based on stochastic frontier analy- sis have been presented by Bos & Schmiedel (2007), Lee & Hwang (2011) and Moreira & Bravo-Ureta (2010), among others. Meanwhile, this basic metafrontier framework has been ex- tended in several directions: one example is the transposition to a

metafrontier and revealed how a metafrontier could be computed using the DEA model. O'Donnell et al (2008) defined the metafrontier as two forms, convex and non convex metafrontier, and showed the specific function for the convex metafrontier model.

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### Results indicate that male-managed sorghum plots had the highest metafrontier technical efficiencies (MTEs) (61%, 56% and 15%) and technology gap ratios (TGRs) (98%, 92% and 20%) for Lira, Serere and Kumi districts, respectively compared to female and jointly managed plots.

Qunwei Wang (), Ye Hang, Jin-Li Hu and Ching-Ren Chiu. Naval Research Logistics (NRL), 2018, vol. 65, issue 5, 427-445 Abstract: The metafrontier framework proposed by O'Donnell et al.

## Jun 2, 2016 We therefore adopted the metafrontier approach to study the technical inefficiency and technological gaps of mango farmers in the different

The results obtained indicate, from a greater control of heterogeneity, through the segmentation of the sample of cities and the metafrontier methodology, that the composite index (IEC3) through the enveloping data analysis methodology (DEA) is more robust than that obtained with the arbitrary assignment of CCCM weights. The metafrontier of equation (3) is considered to be an envelope function of the stochastic frontiers of the different groups such that it is defined by all observations 2018-05-31 · We apply a stochastic metafrontier model to capture the different conditions in the health care systems in the countries within the European Union. By means of this approach, it is possible to detect performance differences in the European health care systems subject to different conditions and technologies relative to the potential technology available. Empirical metafrontier studies based on stochastic frontier analy- sis have been presented by Bos & Schmiedel (2007), Lee & Hwang (2011) and Moreira & Bravo-Ureta (2010), among others. Meanwhile, this basic metafrontier framework has been ex- tended in several directions: one example is the transposition to a 2013-11-01 · A more in-depth analysis of innovative plants requires a more deliberate examination. There are two types of innovative plants: group and metafrontier innovative power plants.

enables the evaluation of relative efficiencies for decision‐making units (DMUs) operating under heterogeneous technologies. The metatechnology ratio ( MTR ) constructed under the metafrontier framework helps estimate the gap between group frontiers and the metafrontier, with its score between 0 and 1. In other words, the metafrontier model is The use of the DEA methodology to construct the metafrontier considered as an envelope of all the possible group technologies. model is possible as long as we can identify separate frontiers for For example, if a particular output, y, can be produced using input different groups in the data set (O’Donnell et al., 2007). This paper uses directional distance functions to extend the non-parametric metafrontier approach to efficiency measurement proposed by O’Donnell et al.