Previous studies (Wouterse, 2010, Omondi, and Kelvin, 2013, Adama, 2014), measuring technical inefficiencies have specified a non-**stochastic** or deterministic **frontier** **model** of Cobb Douglas **production** **function**. According to (Kumbhaker and Lovell, 2000), this **model** does not take account the possible influences of measurement errors and other noises up on the shape and positioning of the estimated **frontier**. Alternatively, any deviation from the **frontier** will be taken as inefficiency. Application of this **model**, especially in cases where there is high probability of measurement risk, will exaggerate the inefficiency estimates as compared to the models which decompose the error term into two components, e.g. the **stochastic** **frontier** **production** **function** approach. The **stochastic** **frontier** approach allows for random disturbances, such as weather conditions, the effects of pest and diseases, and measurement errors in the output variables (Kumbhaker, 2001). A number of studies estimating the **stochastic** **frontier** have mainly been implemented with cross-sectional data and not within the context of panel data and had tended to explicitly **model** inefficiency as a **function** of country-specific explanatory variables (Burhan et al 2009). The major objective of these studies was to examine the effects of particular factors on the efficiency of **production**, without paying attention to random disturbances. However, random disturbances can have broad-reaching impacts on **production** output (Omondi and Kelvin (2013).

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Many researchers have used various approaches to evaluate sea-port efficiency. Annual firm level surveys have been employed as indicators of sea-port operational efficiency, but “there was almost no information on how port efficiencies evolve over time from these studies” [11, p. 3]. A number of studies have used data on inputs, out- puts and **production** **function** theory, by means of data envelopment analysis (DEA), to estimate the most effi- cient **production** **frontier** across a set of sea-ports [6,12, 13]. The approaches using this method have the advan- tage of economies of scale derived from econometric evidence but the drawback is that they typically assume constant return to scale [11]. To address the issue of error estimation and statistical confidence, another approach, econometric estimation of cost functions, was developed by [11]. The method, however, has “difficulties with data requirements, particularly measurement of labor, capital and other requirements” [11, p. 5] which limit its appli- cation to many sea-ports at a time.

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Farm level technical efficiency and its determinants in wheat **production** in the state of Bihar has been studied using **stochastic** **frontier** **production** **function** **model**. The average productivity of wheat was reported 28.43 q/ha which was below the national average of 30.33 q/ha during 2016-17. The resource inputs were found inelastic and not being properly utilized. All the resource inputs were found positive and significant at 1 per cent and 5 per cent level of probability except machine labour used which was negatively significant, indicating overuse of machine labour or costly machine labour. The mean input efficiency in **production** of wheat in the state was estimated to be 94 per cent, emphasizing that efficiency may be enhanced by 6 per cent. The factors influencing efficiency were identified as education, family size and landholding size. The mean technical efficiency was found to be 0.94 indicted that optimal and sustainable use of resource inputs may further raise the input use efficiency in wheat **production** by 6 per cent and consequently boost up the income of the wheat cultivators in the state.

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To estimate the technical efficiency of maize **production** among fluoride affected and non affected locales of Tamil Nadu. A multi-stage sampling method involving a combination of purposive and random sampling procedures was employed in drawing up the samples for collecting primary data. The sample size is about 120. **Stochastic** **frontier** **production** **function** is used to estimate technical efficiency of maize. The result of **stochastic** **frontier** **production** **function** indicated that FYM, Potassium, machine power, irrigation and management index have significant influence on yield of maize in less fluoride affected locale, while, seed rate, nitrogen, phosphorous, machine power and irrigation are significantly influence the yield of maize in moderately fluoride affected locale, in case of highly fluoride affected locale, seed rate, nitrogen, phosphorous, potassium and irrigation are significantly influencing the yield of maize, while, nitrogen, potassium, irrigation and management index are significantly influences the yield of maize in non affected locale. The study suggests that awareness of fluoride contamination and averting measures must be disseminated to the farmers.

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Two m ajor criticism s have been levelled against the statistical approach to m easuring **production** efficiencies. First, the sam pling distributional assum ptions artificially im posed on the one sided-error term used to characterize inefficiency are som ew hat restrictive. Moreover, alternative distributional assum ptions can lead to substantially different results for the estim ated technical efficiencies; m ak ing it difficult to provide an economic and practical justification of the choice of a p articu lar distribution. W ithin the spectrum of inefficiency sam pling d istri butions proposed in th e literatu re, the half- or tru n cated norm al has received a relatively wider applications th an others such as gam m a and exponential. Q uite often th e choice of th e distributions is based on ease of em pirical estim ation. Second, th e specification of th e **stochastic** **frontier** **production** **function** in the statistical approach assumes th a t th e effects of technical inefficiency on input prod u ctiv ity (or elasticity) are th e sam e for each input w ith the resultant neu tral shift of th e **frontier** **production** **function** from the ‘average’ and firm-specific realized **production** functions. In other words, the **frontier** and the other pro duction functions have identical slope coefficients (input elasticities) bu t different intercepts so th a t th ey m erely represent neutral shifts from one another.

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The technical efficiency of wheat farms that operate under a given **production** technology, which is assumed to be defined by a **stochastic** **frontier** **production** **function** **model**, are not comparable with those of farms operating under different technologies. Battese and Ro (2002) presented a **stochastic** metafrontier **model** by which comparable technical efficiencies can be estimated. However, the **model** of Battese and Ro (2002) assumes that there are two different data-generation mechanisms for the data, one with respect to the **stochastic** **frontier** that is relevant for the technology of the farms involved, and the other with respect to the metafrontier **model**. This study presents a modified **model** that assumes that there exists only one data generation process for the farms that operate under a given technology. The metafrontier **function**, defined in this study, is an overarching **function** of a given mathematical form that encompasses the deterministic components of the **stochastic** **frontier** **production** functions for the farms that operate under the different technologies involved.

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In this study, we use a stochastic frontier production function along with an inefficiency model as specified by Battese and Coelli [39] in order to measure technical change, technical e[r]

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The possible way to improve **production** and productivity with a given input mix and available technology is to improve efficiency of resource use. For this purpose examining the technical efficiency of the **production** process is very crucial. Thus, the aim of this paper is to analyze the technical efficiency of rice **production** in Fogera District of Ethiopia. To do so, **stochastic** **frontier** approach is employed on a data which is collected from 200 sample households in 2015/16 **production** year. The sampling techn iques used to get those 200 sample households is a multistage sampling where in the first stage five Kebeles 1 were purposively selected, in the second stage two Gotes 2 randomly selected from each Kebeles and in the third stage 200 households were selected using simple random sampling technique. Doing so, it was found that except manure all the variables in the Cobb -Douglass **stochastic** **frontier** **model** which includes; land, fertilizer, oxen, seed and labor are found to be positively and sign ificantly related to rice **production**. The average technical efficiency score predicted from the estimated Cobb-Douglas **stochastic** **frontier** **production** **function** is found to be 77.2% implying that there is a room for rice yield increment by improving the resource use efficiency of the households. The study also revealed that; provision of extension service, training on rice product improvement, experience on rice farming; agrochemical and education tend to be positively and significantly related to technical efficiency while hou sehold size is negatively and significantly related. Thus, strengthening extension service provision and training on rice yield increment, campaigns to disseminate rice farming experiences and increasing the supply of agrochemicals are crucial to improve the technical efficiency of rice **production** in the study area.

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TE has value between 0 and 1 where 1 implies a fully efficient farm and 0 a fully inefficient farm. Thus, TEi indicator is interpreted as a measure of managerial efficiency, that is, an expression of the farmer’s ability to achieve results comparable to those shown on the **production** **frontier**. The parameters of the **stochastic** **frontier** **production** **function** and the inefficiency **model** were estimated using the computer program **Frontier** 4.1 (Coelli, 1996). Two models were estimated for this study. The first **model** which is the traditional response **function** of Ordinary Least Square (OLS) assumes that the inefficiency effects are absent. It is a special form of the **Stochastic** **Frontier** **Production** **Function** (SFPF) **model** where the total output variation due to technical inefficiency is zero that is, γ= 0 (Jondrow et al., 1982). The second **model** is the general **frontier** **model** where there is no restriction here γ≠ 0. Using the generalized likelihood ratio test, the two models were compared for the presence of technical inefficiency effects which is defined by the test statistic, chi-square, χ 2 (Greene, 1980).

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At least since the early 1990s, the problem of Africa’s debt was a recurring theme in the development debate and many suggestions for debt relief have now been implemented. However, a thorough solution is hampered by the existence of multiple ways of scaling debt. This paper provides a framework for comprehensively measuring indebtedness and gives therefore a basis for setting objective principles for debt reduction measures. The paper uses a **stochastic** **frontier** **production** **function** approach and the technical efficiency computation procedure to develop an indebtedness index for 46 African countries. The results indicate an indebtedness index across countries ranging from a minimum of 3.6 (South-Africa) to a maximum of 92 (Zambia), with an average of 69. Countries, which have experienced extended civil wars, are generally less indebted, while countries with more corrupt governments have generally contracted more multilateral debt. The paper ends by raising a number of implications for a better approach of debt management in Africa.

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However, across years, the methodology as developed by Farrell has known a larger utilization leading to some major improvement. From those major changes, the **stochastic** **model** was developed, allowing to measure for the first time technical, allocative and economic efficiency, using maximum likelihood measurement method. Aigner et al. (1977), Meeusen and Van (1977) were among the first to develop the **stochastic** **frontier** **production** **function**. Aigner et al. (1977) extended this analysis method to agriculture in the United State (US). Battese and Corra (1977) applied this method to analyse a pastoral zone in Eastern Australia. Meeusen and Van (1977) extended this method to analyse 10 manufacturing industries in France. And more recently, empirical analyses were conducted by Battese and Coelli (1993), Beloume (1999), Ojo (2004) and Nuama (2006). The method used in this paper is based on Battese and Coelli (1995), and Battese et al. (1996) work. According to this specific method, the **stochastic** **frontier** encompasses inefficiency effects and any other parameters related to **production** or cost **function** measured simultaneously. 2.3.3. The efficiency analysis method

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countries. reardon and Barrett (2000), Sartorius and Kristen (2007), Demircan et al. (2010) and caberera et al. (2010) have found that small dairy farmers are gradually becoming less profitable and loosing their market share due to a tighter alignment of the supply chain producing for international markets. Burki and Khan (2008) analyzed the effects of the supply chain on the productive/technical efficiency and found that building the supply chain management practices has a strong positive effect on the productive efficiency. Sharma and gulati (2003) and Kumar and Jain (2008) analyzed the farm level efficiency for dairy farmers in india using the **stochastic** **frontier** **production** **function** approach. Binam et al. (2004) analysed the factors affecting the technical efficiency among small- holder farmers in the slash and burn agriculture zone of cameroon. however, there seems to be a lack of studies where the technical efficiency of farmers following the modern supply chain management practices has been measured and compared with non-followers of the modern supply chain practices. Further, the influence of some farm and farmers specific characteristics and socio-economic features on the inefficiency has not been examined; which is undoubtedly very significant for policy makers. in this background, the present paper investigates the technical efficiency along with the technical inef- ficiency effects on milk **production** of the member and non-member dairy farmers in india.

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The maximum likelihood estimates of the **stochastic** **frontier** **production** **function** and inefficiency **model** results are presented in Table 1 and 2. The estimate for parameters of the **stochastic** **frontier** **production** **function** indicates that the elasticity of output with farm size was positive and approximately 0.634 and it was statistically significant at 1% level. This implies that a one percent increase in area under tomato **production** will raise output of tomato by 0.634% this shows that land is a very important factor in tomato **production**. This finding is at tandem with the findings of Eyo and Igben (2002); Maurice et al., (2005); Odoh and Folake (2006), that land has positive sign and statistically significant.

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nitrogen, phosphorous, potash, plant protection chemicals, machine hours, land size values, farmyard manure, human labor are being used at suboptimum level and there exists the possibility of enhancing the yield of onion by increasing their use. The **stochastic** **frontier** **production** **function** resulted that, the coefficients of inputs like bulb, plant protection chemicals, human labour and machine hours were significant at 1% respectively and the sample farmers were technically efficient with 78% in onion cultivation. Thus this result has indicated that bulbs, plant protection chemicals human labour and machine hour were the significant inputs in onion cultivation. Hence concerted efforts will be taken to train the farmers in the optimal use of inputs towards reaping the full benefit from onion cultivation. The results suggests that farmers could increase output through more intensive use of seed material, potash, plant protection chemicals, human labour and machine hours inputs given the prevailing state of technology. This could be achieved through development of awareness of agricultural practices by the government as well as removal all distributional bottlenecks, which affect the availability and prices of improved seeds and fertilizers at the grass root. In the long term, higher technical efficiency could be achieved by improving farmers’ educational status through adult education and literacy campaigns. Also, extension agents should be adequately trained and equipped to help the farmers imbibe the culture of sound agronomic practices that would ensure increased onion **production** in the study area.

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The 3-year average of the estimated efficiency was around 0.60, which was lower than 0.896 reported by Jacobs, Smith, and Street (2006), 0.78 by Kawaguchi (2008), and 0.79 by Takatsuka and Nishimura (2008) [8-10]. This discrepancy could be attributed to differ- ences in the nature of sampled hospitals, the functional form of estimation models, and inclusion of a quality indicator in our **model**. Jacobs, Smith, and Street (2006) used a simple linear cost **function** with 4-year panel data of 185 samples from public hospitals in the United Kingdom [8]. Kawaguchi (2008) analyzed 5-year panel data of 862 municipal hospitals in Japan with a Cobb– Douglas cost **function**, accounting for patient character- istics and proxy indicators of care quality [9]. Takatsuka and Nishimura (2008) investigated the effects of introdu- cing a new ordering system on efficiency with 5-year panel data of 408 municipal hospitals using a translog **production** **function** [10]. When we removed the quality indicator from our **model**, the 3-year average efficiency increased to 0.744, a level similar to that reported in the previously published studies described above. Thus, we speculate that previous studies may fail to discriminate the efficiency of quantity **production** from the quality of **production**. Additionally, Mutter et al. (2008) reported

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Nonetheless, the parametric specification is attractive for the **production** **frontier** **function** because it is easy to compute and the economic interpretation of the pro- duction process can fit into the **production** theory well. Hence, the parametric SF **model** is still dominating the area of productivity and efficiency analysis. We note that all these procedures are based on the assumed parametric form of the **production** **frontier** **function**. If the parametric assumption on m( · ) is not adequate, the conclu- sions may not be valid and the inference drawn may be misleading. Thus, testing the form of the **production** **frontier** **function** is essential in the SF analysis. There are many regression theories (see, for example, Gonz´alez-Manteiga and Crujeiras (2013) for a review) could be used to test the form of functions being assumed in economic theories. However as far as we know, there is no paper explore the testing theory for the SF **model**. In this connection, we aim to fill into the gap in this paper to test whether the **production** **frontier** **function** can be described by some known parametric functions.

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efficiency measurement. Thus, a Monte Carlo analysis for **stochastic** distance **function** **frontier** **model** was developed to test the asymptotic properties. The technology for the framework of **stochastic** distance **function**, used to overcome the criticisms related to the **stochastic** **frontier** approach, is specified as a translog **function**. Then, the basic method to estimate the **stochastic** **frontier** is provided and the maximum likelihood **function** is also given. In the Monte Carlo experiment, 1000 replications are set for analysis. The results show that, except for the scenario with equal outputs, **stochastic** distance **function** **frontier** will yield biased estimators even with large sample size. The 2-output **model** will give better estimators than 3-output **model**. An increasing sample size will improve the relative performance of ML estimations for **stochastic** distance **function** **frontier**. Therefore, the Monte Carlo analysis indicates the result that the **stochastic** distance **function** **frontier** is probably biased for multi-output **production**.

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© 2015 Tehranian A et al.; licensee Iran University of Medical Sciences. This is an Open Access article distributed under a Cre- Background and Objectives: Social Security Organization (SSO) is the second largest organization to the Ministry of Health and Medical Education (MOHME) in providing health care services in Iran. In recent years the gap between the SSO’s resources and expenditures has shown an unprecedented growing trend due to the rapidly increasing demand. Continuation of this trend may lead to financial imbalance in the following years, which would negatively impact access of public to health care services. This study, thus, seeks to explore factors affecting the efficiency of SSO’s health care services in quest for solutions to alleviate the potentially critical situation ahead. Methods: A microeconomic analysis was carried out by panel **stochastic** **frontier** approach (**SFA**) method. Cobb- Douglas **production** **function** was estimated based on maximum likelihood estimation (MLE), using 7-year panel data derived from the yearbooks of SSO (2008-2015). The annual admission rate was selected as the output variable and it was assumed to be a **function** the number of physicians, nurses, active beds, paraclinical and other staff, and the bed restoration interval. Calculation was carried out using **Frontier** version 4.1 software.

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sible with the conventional linear-regression approach. In an application to economic growth, Kumbhakar and Wang (2005a) employ the **stochastic** **frontier** approach and **model** growth convergence as countries’ movements toward the world **production** **frontier**. A country may fall short of producing the maximum possible output because of technical inefficiency, and the phenomenon of technological catch-up is observed if the country moves toward the world **production** **frontier** over time. By making u i a **function** of time and other macro variables,