Stochastic frontier production function

The paper applied the stochastic frontier production function to separate the effect of random variation in output from inefficiency in the agricultural production of African countries. The general Cobb-Douglas and translog functional forms were tested for adequate functional form. A Quasi-translog production frontier function was specified using a balanced panel data of 26 African countries, drawn from Food and Agriculture Organization covering the period 1961-2009. The parameters in the Quasi translog stochastic frontier production function were estimated by the maximum-likelihood method using FRONTIER 4.1. The stochastic frontier incorporates stochastic output variability by means of a two-part error term. In order to separate deviations away from the frontier production function into random variation and inefficiency, a distribution assumption for both parts of the error term was imposed and the error term of the stochastic frontier calculated. The test result suggests that the random term has a truncated normal distribution. Out of the five input variables used, land, labour and livestock significantly influence the agricultural production of the panel of African countries. Furthermore, the agricultural production function operated at a technical regress in a panel of African countries, implying that there is a possibility to increase production by improving the use of input resource. It was observed that 92.4% of the variation in output was due to technical inefficiency. While 7.6 % of the variation in output is explained by the stochastic random variation, implying that the agricultural industry stochastic random error is important in explaining the total variability of agricultural output produced. This was not unexpected in the African agricultural production where random shocks or measurement error are assumed to be vital sources of variation in output.

sided error term (v) account for random variation in profit attributed to the factors outside the farmer‟s control (random effects, measurement errors, omitted explanatory variables and statistical noise). The one-sided component (u) is a non-negative error term accounting for the inefficiency of the farm. Thus represents the profit shortfall from its maximum possible value that will be given by the stochastic profit frontier. However, when u= 0, it implies that farm profit lies on the efficiency frontier (i.e. 100% profit efficiency) and u < 0 means that the farm profit lies below the efficiency frontier. Both v and u assumed to be independently and normally distributed with zero mean and constant variance.

The stochastic disturbance term ( ) consists of two independent elements: “v” and “u”. The symmetric two sided error term (v) account for random variation in profit attributed to factors outside the farmer’s control (random effects, measurement errors, omitted explanatory variables and statistical noise). The one-sided component ( ) is a non-negative error term accounting for the inefficiency of the farm. Thus represents the profit shortfall from its maximum possible value that will be given by the stochastic profit frontier. However, when u = 0, it implies farm profit lies on the efficiency frontier (i.e. 100% profit efficiency) and u < 0 implies that the farm profit lies below the efficiency frontier. Both v and u are assumed to be independently and normally distributed with zero mean and constant variance.

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.

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.

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.

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.

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.

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.

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.

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.

This study employed a Cobb-Douglas stochastic frontier production function to measure the level of technical efficiency and its determinants in small-holder cocoyam production in Anambra state, Nigeria. A Multi-stage random sampling technique was used to select 120 cocoyam farmers in the state in 2005 from whom input-output data were obtained using the cost-route approach. The parameters of the stochastic frontier production function were estimated using the maximum likelihood method. The study found farm size, labour and fertilizer to be positively and significantly related to output at 5% level of significance. Socio economic determinants influencing technical efficiency directly were farming experiences and credit access at 5% level of significance. Age and farm size were negatively and significantly related to technical efficiency at 5% level of significance. The test of significance using ANOVA showed that there were significant differences in the technical efficiencies among zones.

Several agricultural e ffi ciency analyses have been car- ried out in the Ethiopian context, of which the studies by Gebreegziabher et al. (2004), Seyoum et al. (1998) and Haji (2007) stand out. Seyoum et al. (1998) estima- ted the stochastic frontier production function for maize farmers in eastern Ethiopia, distinguishing between par- ticipants and non-participants in a project that pro- motes high-input maize technologies (Sasakawa-Global 2000 project). They established that project farmers are technically more e ffi cient than those who remained outside the project. The study by Haji (2007) es- timated technical, allocative and economic e ffi ciency levels for mixed farmers in eastern Ethiopia who are predominantly engaged in growing vegetables. Using non-parametric data envelopment analysis they revealed technical, allocative and economic e ffi ciency of 91, 60 and 56 %, respectively. Finally, using a similar meth- odology, Gebreegziabher et al. (2004) found 80 % tech- nical e ffi ciency among farmers in northern Ethiopia in producing commonly grown crops in the region. They used the value of overall crop output (in birr) as a de- pendent variable.

The objective of this study is to analyze the impact of economic liberalization on technical efficiency of firms in the electronics hardware industry. Technical efficiency refers to the ability of a firm to minimize use of inputs in the production of a given output vector, or the ability to obtain maximum output from a given input vector. We have estimated Translog stochastic frontier production function in order to measure technical efficiency of firms. In this approach the best-practice production frontier has been estimated and then how far short an indi- vidual firm falls below this frontier has been considered. A firm is considered to be technically efficient if it is on the frontier [3]. This study has explored whether the firms in India’s electronics hardware sector have expe- rienced an improvement in technical efficiency during the period of economic liberalization. This study has also tried to identify the determinants of technical efficiency for a firm operating in this sector. This paper has ex- amined whether technical efficiency of firms is dependent on imports of technology, capital-goods and raw ma- terials. This study has further analyzed whether there is a significant difference in technical efficiency between foreign firms and domestic firms and between domestically owned private and public sector firms. This paper has also examined whether size of the firm has any significant influence on its technical efficiency.

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.

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.

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).

This paper made use of technical, allocative and economic efficiency indices to determine socio- economic factors that have influence on technical and allocative efficiencies. With regard to stochastic frontier production function, the results showed that the coefficient of variables as farm size, quantity of fertilizer used, years of experience and literacy are significant, reflecting their influence on the production level. All selected variables pertaining to cost function proved to be significant. Concerning the determinants of efficiency, the years of experience and the size of the household of an individual producer had a negative impact on their allocative efficiency. Furthermore, the evolution of technical, allocative, and economic efficiency levels reveal that the average of producers are allocatively more efficient than they are technically and economically. The 74.43% of the level of economic efficiency is an indication that producers can save up to 25% without necessarily having to reduce the level of production.

The stochastic frontier model was first proposed by Aigner et al. (1977) and Meeusen and van den Broeck (1977) in the context of production function estimation. The model extends the classical production function estimation by allowing for the presence of technical inefficiency. The idea is that although the production technology is common knowledge to a group of producers, the efficiency in using that technology in the production process may vary by producers, with the degree of efficiency depending possibly on factors such as experience, management skills, etc.. Given the technology, a fully efficient producer(s) may realize the full potential of the technology and obtain the maximum possible output for given inputs, while less efficient producers see their output fall short of the maximum possible level. Therefore, the underlying technology defines a frontier of production, and actual outputs observed in the data fall below the frontier because of the presence of technical inefficiency.

In our analysis, we used a large casemix database based on Japanese diagnosis-related grouping called the Diag- nosis Procedure Combination (DPC) [13]. The DPC was introduced to the Japanese social insurance system in 2003 for reimbursement of 82 special-function hospitals, consisting of main branches of university hospitals, and two national centers specializing in cancer and cardio- vascular diseases [13]. The system has been extended to a wider spectrum of acute-care hospitals, and an add- itional 359 hospitals participated in 2006. Owing to lim- ited data availability, we used a balanced panel dataset collected between 2005 and 2007 from 127 hospitals. The participating hospitals submitted anonymous data of discharged cases to a research group funded by the Ministry of Health, Labour and Welfare. The collection and use of data were approved by the Internal Review Board of the institute that the last author was affiliated with. The sample hospitals had an average of 600 beds, a relatively large number for Japanese hospitals.