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An Assessment of technical efficiency of the rainfed agriculture under water harvesting system in arid region: Case of the watershed of Oued Oum Zessar (South-Eastern Tunisia) Naceur MAHDHI, Mongi SGHAIER, Mohamed SALAH BACHTA Institut des Régions Arides de Médenine (IRA), Tunisie Email: naceur.mahdhi@ira.rnrt.tn,nmahdhi@yahoo.fr Abstract Because of its geographical situation between the Mediterranean and the Sahara, Tunisia is among the countries the least equipped in water resource in the Mediterranean basin. The potential water resources, including subsoil waters are limited to 4700 million m3, of which only 4000 million m3 are mobilized by hydraulic installations (Zahar, 2003). In arid region, and more precisely in the south-east of Tunisia, the harvest of surface waters constitutes an alternative resource in front of the scarcity and the weakness of the subsoil water resources. This water collected by a multitude of soil and water conservation (SWC) works, plays an important part in the operation of not irrigated agricultural systems of production, majority in the area (Sghaier et al., 2002). The aim of this paper is to estimate technical efficiency of the rainfed agricultural based on water harvesting in arid region. Technical efficiency for a sample of farms in the Oued Oum Zessar (south- eastern Tunisia) watershed has been evaluated. Both a non-parametric and a parametric approach to a frontier production are used and the differences in the results are discussed. Results show that rainfed farming efficiency is relatively satisfied with 74% and 70% of parametric and non-parametric approach. Key words: water harvesting system, technical efficiency, rainfed farming, arid region, watershed, Tunisia I. Introduction In most developing countries, particularly in the Middle East and North Africa, the agricultural sector occupies an important place in the strategies and models of development and that because of the importance of contribution of agriculture in gross domestic product, its participation in the creation of jobs and as well as its contribution to the balance of payments through exports of agricultural products and food. In Tunisia, the agriculture sector plays an important role in the economy, despite its relative decline during the last three decades. In arid zones rain-fed areas play an important role in the production of food in many countries of the region and the world. They cover more than 80% of the land area used for cropping throughout the world and produce some 60% of the total production (Harris et al, 1991). Located in North Africa, Tunisia is among the countries the least equipped in water resource in the Mediterranean basin. The rainfall regime is characterized by its scarcity, variability, torrential nature and poor distribution. It has a total land area of 16.4 million ha. Of this, the cultivable area is about 5 million hectare, while 92 % of cultivated area was planted in rainfed agriculture where two million hectares are grown under water harvesting techniques (WHT). In 2005, 37.2 % of cultivable area was planted with cereals, 36% with olive trees, 12% with fruit trees, 9% with forage crops (Min. Agr. 2006). In quantitative terms, the rainfed area contributes about 19.6 % of the total agricultural production and provided 11% of the gross national product in 2005 and 7.6% of total export earnings during the period (2000-2005). Agriculture is, however, responsible of about 16.3% of national employment. In arid region, most rainfed farming in the south-eastern of Tunisia are based on water harvesting techniques (WHT). This sector is, and will remain, an important component off the region’s agricultural production system. In the study area (Oum zessar watershed), rainfed agriculture grown under WHT play 1 an important role in rural development, but its productivity is, however, low compared with those in countries of the Mediterranean basin and severely limited by chronic rainfall deficits (Sghaier et al, 2002; Mahdhi et al, 2005). One way to support the sustainability of such a vulnerable system is by improving its competitiveness and efficiency. The efficiency, with the productivity and the competitiveness, constitute key parameters of the analysis of the farms (Bachta et Chebil, 2002). The study of production efficiency can provide some of the information needed for policy makers to improve the productivity of the rainfed agriculture sectors. The aims of this paper is to estimate and investigate the sensitivity of technical efficiency measures to estimation techniques using data from the rainfed agricultural grown under water harvesting techniques in Oum Zessar watershed (south-eastern of Tunisia). In this work a statistical parametric frontier and a non-parametric frontier are estimated. The present study analyses the extent to which DEA and the statistical deterministic frontier vary from one another in measuring technical efficiency, using data from the tunisian rainfed agricultural. The remainder of this paper is organized into four sections. The first of these describes the methods to be used in the estimation of the frontier productions functions. The next discussed the data and empirical model. The third section presents the results relating to technical efficiency and the comparison of the two methods used. The final section concludes the paper. 2. Methodology Efficiency refers to the global relationship between all outputs and inputs in a production process (Rodríguez Díaz et al., 2004b). The performance of a farm can be evaluated based on different efficiency measures, namely technical, allocative1 and economic efficiency. This study is limited to the calculation of technical efficiencies. The conventional definitions of efficiency used in the economics literature can be traced back to Farrell (1957). Farrell (1957) was the first to use frontier production functions to measure technical efficiency. The method involves estimating a frontier production function in order to calculate the maximum output that can be obtained by each production unit with a given combination of inputs. Units that are technically efficient will be located at the frontier, while those that are not will appear below the frontier, since they obtain less output than technically possible. The technical efficiency measure can be estimated as the relationship between the obtained output (Y) and what would be attained if the unit were located at the frontier (Y*), that is to say, 0 ≤ Y / Y * ≤ 1 . However, the frontier production function is unknown. In empirical work frontier production functions are obtained from available data, and technical efficiency estimates are based on empirical relations from sampled data. Higher efficiency levels may be theoretically possible. Several techniques have been used in the literature for the measurement of efficiency of production. These techniques can be broadly categorized into two approaches: parametric and nonparametric. The parametric stochastic frontier production function (Aigner et al., 1977; Meeusen and van den Broeck, 1977), the statistical deterministic production frontier, developed by Afriat (1972) and the nonparametric mathematical programming approach, commonly referred to as data envelopment (DEA), developed by Charnes, Cooper and Rhodes (1978). The main differences between the two approaches are that the stochastic and statistical methods use a parametric function to represent the production frontier, while DEA, which is based on a linear programming technique, is a non-parametric method. All three methods can also be classified as either stochastic or deterministic. The production frontier in DEA and the one suggested by Afriat (1972) are deterministic in the sense that they assign any deviations from the frontier, even those due to random factors, to inefficiency. On the other hand, the SPF allows the production frontier to be sensitive to random shocks by including a conventional random error term in the specification of the production frontier. As a result, only deviations caused by controllable decisions are attributed to inefficiency. Since none of the production frontier models used in empirical analyses of production efficiency is without its limitations, it is very important to make a careful choice of model. Among many authors, Coelli (1995) discusses the strengths and weaknesses of different types of production frontier models and applications in agricultural production. Given the different strengths and weaknesses of the parametric and nonparametric approaches, it is of interest to compare empirical performance of the two approaches using the same data set. 2 As is usual in the recent literature (Neff et al, 1993; Sharma et al, 1999; Wadud and White, 2000; Ferrier and Lovell, 1990; Kalirajan and Shand, 1999)we compared the technical efficiency measures obtained using two methods to estimate the frontier production functions. The main features of the two methods are described below 2.1 The statistical deterministic parametric frontier The statistical deterministic production frontier (Afriat 1972) representing Cobb-Douglas production technology characterised by variable returns to scale is specified as: n ln Yi = β 0 + ∑ β k ln X ki − µi i=1,2,.....n (1) k =1 Where Yi denotes output of the ith firm; Xi is a vector of functions of actual input quantities used by the ith firm; β k is a vector of parameters to be estimated; and µ is the error term which is assumed to be independently and identically distributed and has a non-negative mean and constant variance. Constant returns to scale in production is imposed via the following restriction on the parameters: n ∑β k =1 k =1 (2) With the problem of the use the Ordinary least square (OLS) to estimate this production frontier The proposed estimation technique is the corrected ordinary least squares (COLS) method. According to Greene (1980), while OLS provides best linear unbiased estimates of the slope parameters and appropriately computed standard errors, it does not provide an unbiased estimate of the intercept parameter β 0 . The OLS estimator of β 0 is biased downward. Due to this problem, it is possible for the estimated OLS residuals of the model to have the incorrect signs. Since the calculation of technical efficiency relies on these residuals being non-positive, Greene (1980) suggests a correction for this biasedness by shifting β 0 , the OLS estimator of upward by the largest positive OLS residual (e*). This two-step procedure is known as the corrected ordinary least squares (COLS) method. The unbiased estimator of the intercept parameter is given by: * β 0 = β 0 + e* (3) This correction makes all the OLS residuals non-positive, implying that the estimates of ε i are non- th negative and none of the farms is more than 100 percent efficient. Technical efficiency (TE) of the i farm is calculated by using the following equation: TEi = exp(− µi ) = exp(ei − e* ) (4) * Where ei is the OLS residual for the Ith farm and e is as defined above. 2-2 Nonparametric approach Data envelopment analysis (DEA) was developed by Charnes, Cooper, and Rhodes (1978, 1979, 1981) based on M.J. Farrel's contribution to productive efficiency. The data envelopment analysis technique uses linear programming methods to construct a non-parametric frontier. The technique also identifies efficient production units, which belong to the frontier, and inefficient ones, which remain below it. Data envelopment analysis (DEA) uses a non-parametric piecewise linear production frontier in estimating technical efficiency. A DEA model may be either input-oriented or output-oriented. Both output-oriented and input-oriented DEA models produce the same technical efficiency estimate for a farm under the assumption of constant returns to scale in production. In deciding on the orientation of a DEA model one should also consider over which variables decision making units (DMUs) have most control. If DMUs have more control over output variables than input variables, the DEA model should be output-oriented; otherwise, the model should be input-oriented. Agricultural farms, such as rainfed agriculture farms, usually have more control over their inputs than their 3 outputs. Input-oriented models were chosen in this study to reflect the reality where the main aim is not to increase production but to use different resources more efficiently (Rodríguez Diaz et al., 2004a). Consider the situation with n firms or decision making units (DMUs), each producing a single output by using m different inputs. Here, Yi is the output produced and Xi is the (m × 1) vector of inputs used by the ith DMU. Y is the (1× n) vector of outputs and X is the (m × n) matrix of inputs of all n DMUs in the sample. The technical efficiency (TE) measure under constant returns to scale (CRTS), also called the global technical efficiency (GTE) measure, is obtained by solving the following DEA model: m in θ iC R S C R S θ i , λ s u b je t to i) Y i ≤ Y λ ii) θ i X i ≥ X λ (5) iii) λ ≥ 0 Where θi is a TE measure of the ith DMU under CRTS and λ is an n × 1 vector of weights attached to each of the efficient DMUs. A separate linear programming (LP) problem is solved to obtain TE score for each of the n DMUs in the sample. If θ =1, the DMU is on the frontier and is technically efficient under CRS. If θ ≺ 1 , then the DMU lies below the frontier and is technically inefficient. The CRTS or global technical efficiency (GTE) measure can be decomposed into its pure technical efficiency (PTE) and scale efficiency components by solving a variable returns to scale (VRTS) DEA n model, witch is obtained by imposing the additional constraint, ∑λ i =1 j = 1 on Eq. (5)(Banker et al., 1984). Let θiVRS denote the TE index of the ith DMU under variable returns to scale (TEVRS). Because the VRS analysis is more flexible and envelops the data in a tighter way than the CRTS analysis, the VRTS TE measure ( θ VRS ) is equal to or greater than the CRS measure ( θ CRS ). Using the relation ship between PTE and TE computed above, the scale efficiency (SE) for a farm is computed as: θiCRS TEi SEi = = (6) θiVRS PTEi Where SEi =1 indicates scale efficient farm that is operating at a point of CRS. A value SEi <1, indicates the two technologies (CRTS and VRTS) do not coincide, and the farm is not operating at a point of CRS. 3. Data and empirical procedures 3.1 Data The data used in this paper come from a random sample of farms interviewed in the Oum Zessar watershed (South-east Tunisia) in 2004. The data refer to 214 rainfed agricultural farms where olive trees growing under water harvesting techniques as a main fruit trees. 4 Rainfed agriculture production features multiple outputs and inputs. For the purpose of efficiency analysis, output is aggregated into one category and inputs are aggregated into four categories. The basics statistics are shown in table 1. The output (Y) is measured by the average production of olive trees per farm expressed in tunisian dinars (TD). Table 1 Basic statistics for the data used Average Standard deviation Y (TD) 467,69 9,41 X1 (ha) 4,75 4,6 X2 (hours per year) 130 82,26 X3 (TD) 89,5 134,2 X4 WHT (no.) 6 4,74 a Number of observations=214; 1 TD= 1.3 Dollars Y: average productions. X1: cultivated land. X2: amount of family and hired labor used. X3: others variable inputs (represents the total of all variable expenses, except hired labour). X4: SWC works. Y: total production of fruit trees (TD) The inputs included in the estimation of the frontier production functions are aggregated into four categories, namely, land, labour, other variable inputs and soil and water conservation works. These inputs variable are described below. The first input is the Land (X1), witch is calculated in hectares of utilised agricultural area. The second is Labor (X2), witch is calculated in terms of number of hours worked per year. The third is the other variable inputs (X3), witch represents the total of all variable expenses, except hired labour expressed in Tunisian dinars (TD). Finally, we consider the number of water harvesting techniques (X4) by farmer. 3.2 Empirical models Tow models are considered in this study. These are the statistical deterministic production frontier and DEA. In the statistical deterministic production frontier, a Cobb-Douglas production function is used to represent the production technology used by rainfed agricultural farmers. In defence of this choice, the following can be said. The Cobb-Douglas function has been the most commonly used function in the specification and estimation of production frontiers in empirical studies. It is attractive due to its simplicity and because of the logarithmic nature of the production function that makes econometric estimation of the parameters a very simple matter. Under the parametric approach, the Cobb-Douglas deterministic production frontier is specified as follows. lnYi = β 0 + β1 lnX i1+ β 2 lnX i 2 + β3 lnX i3 + β 4 lnX i 4 + µi (7) Where I refers to the ith farm in the sample; Y is output and Xs are inputs variables, defined in the previous section; β k are parameters to estimated; and µi is the term error, defined in Section 3.1. Note that the production frontier in Eq. (7) represents VRS technology and corresponding frontier CRS can be n obtained by imposing the restriction that the sum of output elasticities of inputs equals one (i.e., ∑β k =1 k =1 ) Under the nonparametric approach, CRS and VRS as presented in Section 3.2 are estimated for the same output and inputs variables as for the deterministic parametric frontier. 4. Empirical results 4.1. Parametric frontier results The corrected ordinary least squares (COLS) estimates of the parameters of the statistical deterministic production frontier (Eq.7) were obtained using the Shazam software Version 9.0. These results are presented in table 1. 5 Table 1 Estimated Cobb-Douglas production frontiers VRS model CRS model Estimated t-ratio Estimated t-ratio parameter parameter intercept 3.688 13.27* 4.089 16.43* ln (land) 0.183 2.34** 0.188 2.403** ln (Labor) 0.115 1.33 0.0476 0.699 ln (Other variable input) 0.185 2.33** 0.13 2.118** ln (number of WHT) 0.634 9.83* 0.633 9.820* 2 R - adjusted 0,595 0.593 * Significant at the 1% level. ** Significant at the 5% level. All the inputs, except labour, were statistically significant in the production process and explain about 59% of the variation in the total production of rainfed agriculture. Land and the number of water harvesting techniques (WHT) showed the greatest elasticity. We can conclude that these two inputs, land and WHT have a major influence on output in rainfed agriculture production. The frequency distributions and summary statistics of the estimated technical efficiency indices for the sample rainfed farms from the parametric approach are presented in Table 2. The average overall technical efficiencies for the CRTS and the VRTS DEA approaches are 0.715 and 0.745 respectively, indicating that substantial inefficiencies occurred in farming operations of the sample farm households. These means indicates that either output can be increased on average by 26% with the same amount of inputs as before, or the current level of output can be produced using 20% less inputs an average than are applied by farmer. Under the observed conditions, about 1% of farms were identified as fully technical efficient under both returns to scale specifications. Table 2 Frequency distributions of technical efficiency estimates from the DEA and the COLS, under both returns to scale specifications Efficiency score COLS (VRS) COLS (CRS) DEA (VRS) “PTE” DEA (CRS) “GTE” N° % of N° % of N° farms % of N° farms % of farms farms farms farms farms farms 0-10 0 0 0 0 13 6 4 2 10-20 0 0 0 0 15 7 3 1 20-30 0 0 0 0 16 7 2 1 30-40 0 0 1 0.5 27 13 6 3 40-50 5 2 4 2 30 14 11 5 50-60 18 8 24 11 12 6 29 14 60-70 49 23 69 32 10 4.6 32 15 70-80 81 38 76 36 4 2 58 27 80-90 49 23 32 15 1 0.5 48 22 90-100 9 4 6 3 0 0 16 7 100 3 1.4 2 1 86 40 5 2 Total 214 214 214 214 Average score 0.745 0.715 0.698 0.628 6 4.2 Data envelopment analysis results Both the CRTS and the VRTS DEA models for overall technical efficiency (equation 5) are estimated using the program DEAP (Coelli, 1996). Table 2 gives the frequency distribution of the efficiency estimates obtained by the DEA methods. The average overall technical efficiencies for the CRTS and the VRTS DEA approaches are 0.628 and 0.698 respectively, indicating that substantial inefficiencies occurred in farming operations of the sample farm households. Under the observed conditions, about 2 % and 40 % of farms were identified as fully technical efficient under the CRTS and VRTS specification respectively. The large differences between the CRS and VRS measures further indicated that many farmers did not operate at an efficient scale and that adjusting the scale of operation could improve the efficiency. The scale efficiency index for every farm was obtained by the equation SE=(GTE/PTE), as the efficiency scores estimated under the variable return to scale frontier (PTE) are equal to or greater than those calculated under the constant return to scale assumption (GTE). The summarised statistics for the three estimated measures of efficiency for rainfed agriculture are presented in Table 3. Table 3 Basic statistics for GTE, PTE and SE levels a b Average S.D. GTE 0.628 0.2 PTE 0.698 0.17 SE 0.90 0.06 a GTE: global technical efficiency; PTE: pure technical efficiency; Se: scale efficiency b S.D., standard deviation Rainfed agricultural production showed a global technical efficiency (GTE) level of 0.63, which means that the same amount could be produced with an approximate 37% reduction in the factors used. Under variable return to scale, the estimated pure technical efficiency was greater but not by a very wide margin, indicating that scale efficiency must be close to 1. The decomposition of the technical efficiency measure produced estimates of 30.2% pure technical inefficiency and 10 per cent scale inefficiency. By eliminating scale inefficiency the farms can increase their average technical efficiency level from 62.8% to 69.8% 4.3 Comparison parametric and DEA results The two approaches used here to measure the technical efficiency measure for the sample rainfed agricultural farms are based on different production frontiers. The parametric approach is based on a statistical deterministic production frontier and nonparametric data envelopment analysis is based on a deterministic frontier. The distribution of technical efficiency scores from each technique are presented in Table 2 while the distributions are presented in Figure 1 and 2. A comparison of the distributions of TE estimates from different models shows that the distribution is relatively symmetric in the COLS model, while it is skewed to the left in the DEA model. This fact is also obvious from Figures 1-2 that represent the distributions of TE estimates in Table 2. However, the DEA technical efficiency measures show significantly higher variability than the COLS TE measures. The longer and fatter tail of the distribution associated with the DEA model indicates that there is more variability in the TE scores derived under the DEA approach relative to the COLS approach. In contrast to efficiency scores in the COLS model, the PTE estimates of the DEA models are clustered around the upper end of the PTE distributions, indicating that most rainfed agricultural farms in Ou Zessar Watershed are near to or at full technical efficiency. 7 90 80 70 number of firm 60 50 COLS( VRS) 40 COLS (CRS) 30 20 10 0 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100 100 technical efficiency Figure 1 Histograms of the TE estimates from the COLS models 100 90 80 70 60 PTE 50 GTE 40 30 20 10 0 0-10 10-20 20- 30 30-40 40-50 50-60 60-70 70-80 80-90 90-100 100 T echnical ef f ici ency Figure 2 Histograms of the TE estimates from the DEA models From Table 2, it can be seen that the mean technical efficiency of Rainfed Agricultural grown under water harvesting techniques is sensitive to model choice. Under the assumption of constant returns to scale, the mean TE of the rainfed agricultural varies from 62.8% to 71.5% while under the assumption of variable returns to scale it varies from 69.8% to 74.5%. The DEA model produces the smallest mean technical efficiency while the COLS model produce higher mean technical efficiency for the rainfed agricultural. However, comparing the distribution of scores may be misleading. While the overall distributions of the technical efficiency scores for the COLS and CRTS DEA models were similar, the efficiency scores of individual rainfed farms estimated using the different methods varied considerably. A number of farms that 8 were estimated to be the least efficient using the COLS model were found to be efficient using the DEA models (Figure 3). Conversely, some farms that appeared efficient in the COLS results were estimated to be inefficient in the DEA results. CRS DEA_CRS VRS DEA_VRS Figure 3. Scatter plots of individual scores Under the assumption of CRTS and VRTS, the COLS models has a higher mean technical efficiency for the rainfed farms than the DEA models, it is interesting to compare the efficiency levels for these two methods. A statistical normal test has been conducted in order to test whether the mean technical efficiencies obtained from the two models are significantly different from one another. These results are reported in Table 4. Table 4 Test results for difference between DEA technical efficiency and COLS efficiency scores Test Test statistic Level of Critical value Decision significance CRTS:COLS-GTE 1.11 5% 1.97 Unable to reject H0 VRTS:COLS-GTE 3.07 5% 1.97 Reject H0 VRTS:COLS-PTE 4.77 5% 1.97 Reject H0 The tests reject the null hypothesis that mean technical efficiencies from any two models are the same under both scale assumptions, except for the special case of COLS production frontier and Global technical efficiency (TE) under the assumption of CRTS where the test fails to reject the null hypothesis at the 5% level of significance. Therefore, we conclude that COLS technical efficiency is significantly higher than DEA technical efficiency under VRTS, while no difference is found across the two methods under CRTS. To assess the overall consistency of the two methods in ranking individual farms in terms of efficiency, the spearman rank correlations between different measures of efficiency are presented in table 5. Table 5. Spearman rank correlation coefficients COLS DEA CRTS VRTS CRTS (GTE) VRTS (PTE) COLS (CRTS) 1 COLS (VRTS) 0.99 1 GTE 0.99 0.99 1 PTE 0.909 0.909 0.909 1 9 The correlation between the scores for the individual boats confirms that the different techniques produce substantially different rankings of efficiency (Table 3). Under both scale assumptions, the TE estimates from the COLS and DEA models are the most highly correlated. Since the correlation coefficients between the TE estimates from the three models are significantly different from zero and greater than 0.5, it can be concluded that the two models are consistent in their ranking of farms in terms of technical efficiency. 5- Conclusion This paper set out to compare the empirical performance of two popular approaches to estimation of technical efficiency in production: corrected ordinary least squares regression (COLS), and data envelopment analysis (DEA). The comparison has focused on measuring the technical efficiency of rainfed farms in south-eastern Tunisia under two scale assumptions: constant returns to scale (CRTS) and variable returns to scale (VRTS). The main points arising from the results of this study can be summarised as follows: In relation to the production function, the two most important inputs in the rainfed sector are land and water harvesting techniques, because in rainfed production these are the inputs with higher partial elasticity of output. From an efficiency analysis point of view, the results obtained in this paper show that upper average efficiency of rainfed farms in the Oum Zessar watershed only reaches 74.5%. This implies a production level substantially smaller than they could have achieved if they had used productive factors more efficiently. The results so far indicate a wide difference in efficiency scores between farms and a sensitive to the choice of production frontier estimation method. Under the assumption of constant returns to scale, the mean TE of the rainfed agricultural varies from 62.8% to 71.5% while under the assumption of variable returns to scale it varies from 69.8% to 74.5%. The DEA model produces the smallest mean technical efficiency while the COLS model produce higher mean technical efficiency for the rainfed agricultural under both scale assumptions. DEA efficiency scores at constant returns to scale are also estimated in order to analyse the scale efficiency of each rainfed farms. The major finding that 97.6% farms are not technically efficient and 29% of farms have efficiency scores below the average level 62.8%, compare with an average scale efficiency score of 0.9, indicating that managerial rather than scale inefficiency is the major problem for Tunisian rainfed agriculture. Considering the methods used to estimate the frontier production function, we found strong similarities between the two estimates for the technical efficiency of rainfed farms. The two models are more consistent in their ranking of rainfed farms in terms of technical efficiency under the assumption of CRTS than under the assumption of VRTS. This is illustrated by the high Pearson correlation coefficients and by the high Spearman rank correlation coefficients found between the corresponding rankings. What this analysis does not consider and needs to be the focus of further work is identifying the reasons why particular farms are efficient and others are not. In relation to technical efficiency, it is unlikely that there are going to be significant differences between farmers in terms of the production technology employed here. Thus, it is all very well establishing that there is a significant gap between those who operate technically efficiently and those who do not, but to really understand why the gap exists requires further research of socio-economic characteristics. This topic has been addressed by other researchers. Unfortunately, the data set used here is limited as there are no socio-economic data such as the age or the educational level of farmers. References Afriat P., 1972. 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