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Application of Stochastic Frontier Production    Function to Separate the Effect of Random Variation in Output from    Inefficiency in the Agricultural Production of African CountriesAuthor(s): Kalu Ukpai  Ifegwu and Joshua Olusegun    Ajetomobi

Application of Stochastic Frontier Production Function to Separate the Effect of Random Variation in Output from Inefficiency in the Agricultural Production of African CountriesAuthor(s): Kalu Ukpai  Ifegwu and Joshua Olusegun Ajetomobi

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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Sea Port Operational Efficiency: An Evaluation of Five Asian Ports Using Stochastic Frontier Production Function Model

Sea Port Operational Efficiency: An Evaluation of Five Asian Ports Using Stochastic Frontier Production Function Model

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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Productivity and Resource Use Efficiency in Wheat: A Stochastic Production Frontier Approach

Productivity and Resource Use Efficiency in Wheat: A Stochastic Production Frontier Approach

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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Technical Efficiency of Maize Production in Fluoride Affected Locales, Tamil Nadu: A Stochastic Frontier Approach

Technical Efficiency of Maize Production in Fluoride Affected Locales, Tamil Nadu: A Stochastic Frontier Approach

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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Production frontiers and efficiency measures : concepts and applications

Production frontiers and efficiency measures : concepts and applications

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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A Metafrontier Production Function for Estimation of Technical Efficiencies of Wheat Farmers under Different Technologies

A Metafrontier Production Function for Estimation of Technical Efficiencies of Wheat Farmers under Different Technologies

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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Impact of Economic Liberalization on Technical Efficiency of Firms: Evidence from India’s Electronics Industry

Impact of Economic Liberalization on Technical Efficiency of Firms: Evidence from India’s Electronics Industry

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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Analysis of technical efficiency of rice production in fogera district of Ethiopia: A stochastic frontier approach

Analysis of technical efficiency of rice production in fogera district of Ethiopia: A stochastic frontier approach

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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Relationship between plot size and technical efficiency of cassava farms in oyo state of nigeria: a stochastic frontier analysis

Relationship between plot size and technical efficiency of cassava farms in oyo state of nigeria: a stochastic frontier analysis

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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On measuring indebtedness of African countries: A stochastic frontier debt production function

On measuring indebtedness of African countries: A stochastic frontier debt production function

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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Technical and economic efficiency of rice production in the Kou valley (Burkina Faso): Stochastic frontier approach

Technical and economic efficiency of rice production in the Kou valley (Burkina Faso): Stochastic frontier approach

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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Technical efficiency and supply chain practices in dairying: The case of India

  Technical efficiency and supply chain practices in dairying: The case of India

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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Analysis of Technical Efficiency of Tomato Production in Adamawa State, Nigeria

Analysis of Technical Efficiency of Tomato Production in Adamawa State, Nigeria

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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Estimation of Resource Use Efficiency and Technical Efficiency of Small Onion Farmers in Tamil Nadu: A Cobb-Douglas and Stochastic Frontier Approach

Estimation of Resource Use Efficiency and Technical Efficiency of Small Onion Farmers in Tamil Nadu: A Cobb-Douglas and Stochastic Frontier Approach

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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Efficacy of a numerical value of a fixed effect estimator in stochastic frontier analysis as an indicator of hospital production structure

Efficacy of a numerical value of a fixed effect estimator in stochastic frontier analysis as an indicator of hospital production structure

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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Dynamics of innovation and efficiency in banking system: An application of SFA and meta frontier method

Dynamics of innovation and efficiency in banking system: An application of SFA and meta frontier method

Stochastic Frontier Analysis (SFA) is a parametric approach in modern benchmarking models that indicates the relationship between cost and inputs prices and outputs. The prominent feature of SFA is its stochastic form that makes it different from other deterministic approaches which consider only the inefficiency error term. Aigner et al. (0222) firstly developed SFA in production function and provided a definition of disturbance term in frontier function which is the sum of symmetric normal and half-normal random variables. Also, Meeusen and Broeck independently (0222) proposed a composed error term (an efficiency measure and noise error term) in a Cobb-Douglas production function. According to Bogetoft and Otto (4101), SFA method specifically supposes that the source of deviations from the cost frontier function is not only the efficiency term (such as managerial performance) but also the noise term on the value of cost such as the effects of luck, weather, measurement problems, etc. So, the cost frontier function will have an extra variable denoted by v i . In other words, following Hasan and Marton
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Specification Testing of Production Frontier Function in Stochastic Frontier Model

Specification Testing of Production Frontier Function in Stochastic Frontier Model

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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A Monte Carlo Analysis for Stochastic Distance Function Frontier

A Monte Carlo Analysis for Stochastic Distance Function Frontier

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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Estimation of Production Function of Direct Health Care Services Delivered by Iranian Social Security Organization

Estimation of Production Function of Direct Health Care Services Delivered by Iranian Social Security Organization

© 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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Stochastic frontier models

Stochastic frontier models

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,

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