The changing food demands by the teeming urban population, job search, and sector profitability have made vegetable production indispensable as it contributes to increased incomes and livelihoods of urban dwellers.This study investigated the current level of productive efficiency (technical and allocative) of vegetable farmers in the Kumasi Metropolis using cross- sectional data obtained from 135 sampled farmers using a semi-structured questionnaire. Data analysis was conducted using the **stochastic** **frontier** **approach** to estimate firm-specific technical efficiencies and the factors that influence efficiency levels. The results show that inefficiency exists among the sampled vegetable farmers as they currently achieve an average technical efficiency score of 66.7%. Allocative efficiency estimates for land and labour revealed that both factors of production are over utilised by farmers. The age of the farmer is the main socio- economic determinant of technical efficiency.The study recommends that farmers be educated on the correct use of inputs by extension agents. The government policy of recruiting community extension agents under the ‘planting for food and jobs’ programme is in line with addressing inefficiency in the production sector and should be promoted.

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The banking sector in New Zealand is characterised by the dominance of foreign-owned banks, and in particular from Australia. The objective of this study is to examine the efficiency performance of foreign-owned banks relative to domestically owned banks, with major focus on the determinants on the differences of foreign banks’ efficiency. The parametric **stochastic** **frontier** **approach** (SFA) is employed to extend the existing bank efficiency studies that used the non- parametric **approach**--Data Envelopment Analysis (DEA). Ten major banks which have continuously operated over the period 2002 to 2011 were selected and both industry- and bank- specific characteristics are tested using quarterly data for 40 quarters with the consideration of macroeconomic conditions. The one-step SFA **approach** of model is used in order to obtain the cost and profit efficiency scores and the inefficiency effects simultaneously to avoid any bias on the results.

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Study attempts to measure the efficiency level and its determinants of a sample of microfinance institutions operating in India by applying **stochastic** **frontier** **approach** for unbalanced panel of 40 microfinance institutions for the 2005-08. It has been found that mean efficiency level of microfinance institutions is quite low but it increases over the period of study. Age of microfinance institutions is positive determinant of efficiency level but size does not matter much. Higher outreach is associated with higher efficiency which negates the general perception of trade off between outreach and efficiency. Microfinance institutions operating in southern states are more efficient than their counterparts. It has been found that regulated microfinance institutions are less efficient.

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Z daných predpokladov taktiež vyplývajú silné a slabé stránky metód. V tejto štúdii je použitý parametrický prístup a konkrétne metoda **Stochastic** **Frontier** **Approach** (SFA). Táto metóda umožňuje odlíšiť náhodné chyby od neefektívnosti. Efektívnos ť pomocou tejto metódy môžeme merať pomocou Cobb-Douglasovej produkčnej funkcie, nákladovej a ziskovej funkcie, čo vlastne znamená riešenie dvoch optimaliza č ných úloh – minimalizácia nákladov a maximalizácia zisku. V tejto práci bude využitá Cobb-Douglasova produkčná funkcia (CDPF).

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Econometrically, several approaches can be applied to measure technical efficiency, which include the nonparametric data envelopment analysis (DEA) and the parametric **stochastic** **frontier** **approach** (SFA). This paper utilizes the parametric SFA which allows for decomposing the error term into two components: the inefficiency term and the random error terms. The DEA **approach** suffers from two major criticisms (Lovell, 1993; Coelli et al., 1998). First, the DEA **approach** assumes away measurement error, which implies that all deviations from the **frontier** are solely due to the inefficiency. Therefore, by making such assumption, the DEA **approach** leads to an upward bias in estimation of the inefficiency. Second, as a nonparametric technique, it is difficult to conduct statistical hypotheses tests regarding the existence of inefficiency and the structure of the production technology (Coelli et al., 1998). In light of these two limitations of the DEA **approach**, this study uses the SFA to model for the cross sectional and time series data in this study.

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Idiong (2007) estimated the farm level technical efficiency in small-scale swamp rice production in cross river state of Nigeria using **stochastic** **frontier** **approach** and found an average technical efficiency score of 77% implying better scope to enhancing the resource use efficiency. The study also shown that, years of schooling, membership to associations and access to credit are found to be the major determinants of technical efficiency. Bamiro and Janet (2012) employed **stochastic** **frontier** **approach** to analyze the technical efficiency of swamp rice and upland rice production in Osune Sate, Nigeria and estimated an average technical efficiency of 56% and 91% respectively, which showed that efficiency improvement is possible in the swamp rice production. The study revealed that volume of credit have negative effect on technical efficiency of upland rice while females are found to be more efficient compared to males in the swamp rice production. Kadiri et al. (2014) revealed that paddy rice production is technically inefficient in the Niger Delta Region of Nigeria. The study further indicated that, marital status, educational level and farm size are the major determinants of rice production in the study area.

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The present paper seeks to deal with the issue of technical and economic efficiency of rice producers in the Kou valley, located in the region of the high basins in the western part of Burkina Faso. The **stochastic** **frontier** **approach** was used to estimate the production function, from a Cobb- Douglas **stochastic** **frontier** function and its dual which allow the estimation of the technical, allocative and economic efficiencies. The determinants of efficiency were simultaneously assessed along with the **frontier** functions through the **FRONTIER** 4.1 software. The data used herein are from a survey encompassing 130 rice producers, randomly chosen. Results show that farm size, fertilizer used, years of experience and literacy are the explicative factors of rice production in the Kou valley. The costs of the different production factors significantly contribute to explain the total production cost, and that is in concordance with the economic theory. The technical, allocative and economic efficiencies of producers are, on average, 80.15%, 92.7% and 74.43% respectively. A 25% improvement of rice production is possible if producers optimize their economic efficiency. Keywords: Technical efficiency, allocative efficiency, economic efficiency, rice, Kou valley, Burkina Faso

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This paper aimed at a statistical analysis of competition for tourists between regions within Baltic states (Estonia, Latvia, Lithuania) and estimation relative efficiency levels of regions. We apply a modern **approach** called Spatial **Stochastic** **Frontier** and corresponded to spatial modification of a **stochastic** **frontier** model. We specify two alternative spatial **stochastic** **frontier** models – distance and travel-time based to identify an influence of existing transport network on research results.

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Among six square parameters only the coefficient of irrigation square is statistically significant and has positive sign. It means that an increase in irrigation cost will increase boro rice production at an increasing rate. Other square parameters are statistically insignificant. From Table 3 it is also found that among the interactive variables ‘farm size*irrigation’ and ‘labor*fertilizer and pesticide’ are significant at 1% level and have also positive sign. Besides, ‘farm size*labor’ and ‘fertilizer and ‘pesticide*ploughing’ are significant at 10% significance level and have negative and positive sign, respectively. Moreover, coefficients of other interactive variables are statistically insignificant indicating no significant meaning in explaining boro rice production. The estimated value of γ is found as 0.97, which means that 97% of the total variation in rice output is due to technical inefficiency. It means that about 97% of the discrepancies between observed output and the **frontier** output are due to technical inefficiency.

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Time series data is prone to trend, cycles and seasonality (Greene, 2003). To ensure that the estimates from the data are not biased, the series must be stationary, meaning the mean and variance must be constant throughout the experiment time while the covariance must depend only upon the time periods between two values (Maddala, 1992). A **stochastic** trend is manifested in a series if the series moves upward and downward as a result of **stochastic** effects meaning its mean is a function of time. To detrend or test for stationarity of data in the series, Augmented Dickey-Fuller (ADF) test was used because it takes into account the cointegration problem (Greene, 2003; Maddala, 1992). Data was further subjected to normality, serial correlation and heteroscedasticity tests. Durbin’s alternative and Breusch-Godfrey test were used to test for autocorrelation and where serial correlation was detected, the data was transformed through lagging. Jarque-Bera’s test was used to test normality because it shows consistent result irrespective of the number off observations. It shows robust results because of the its asymptotic characteristic. Normality of the error term is necessary for the efficiency and consistency of the estimates to hold.

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Hailin Liao et al. [4] applied a **stochastic** **frontier** ap- proach to sector-level data within manufacturing and examined total factor productivity (TFP) growth for eight East Asian economies during 1963-1998, using both sin- gle country and cross-country regression. The analysis focuses on the trend of technological progress (TP) and technical efficiency change (TEC), and the role of pro- ductivity change in economic growth. The empirical re- sults reveal that although input factor accumulation is still the main source for East Asian economies’ growth, TFP growth is accounting for an increasing and impor- tant proportion of output growth, among which the im- proved TEC plays a crucial role in productivity growth.

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Specifically, with respect to M&As, there has been a growing number of studies examining the potential gains to be made from mergers in the bank sector based on the strategic fit of two banks (Shi, Yongjun, Emrouznejad, Xie, & Liang, in press; Gattoufi, Amin, & Emrouznejad, 2014). The underlying idea is that, in order to decrease the high failure rate of M&A activities, a bidder bank should try to identify suitable target banks prior to an M&A is to determine whether the prospective partner can offer synergies and the necessary relevant attributes to complement their operations (Wanke et al., 2017, 2016). The need to predict M&A outcomes has drawn the attention of many researchers (Dietrich and Sorensen, 1984; Pasiouras and Gaganis, 2007; Powell, 2001; Gale and Shapley, 1962), including those focused on efficiency measurement (Chow and Fung, 2012). As regards efficiency measurement, this is often done by assessing the impact of contextual, business- related, variables of the bidder and target banks in terms of the individual efficiency levels of the potential merged banks and their impacts upon the efficiency **frontier** (Wanke et al., 2017, 2016).

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From the econometric point of view, the estimation of electricity cost functions is mostly carried out using panel data. Several panel data estimators have been proposed and used for this purpose. Of particular interest are the clustering and non-clustering methods recently developed to deal with unobserved heterogeneity across firms. 4 The non-clustering **approach** includes the panel data **frontier** models introduced by Greene (2005), where unobserved heterogeneity is captured through a set of firm-specific intercepts (more details can be found in Section 3). The clustering **approach** can be viewed as a two-stage procedure where the original sample is first split into a number of mutually exclusive groups (classes), and then separate efficiency analyses are carried out for each class/sub-sample. Thus, the clustering **approach** allows the estimation of different technological characteristics for firms belonging to different groups. In this sense, Agrell et al. (2013) advocate using the so-called latent class model to split the sample as this **approach** is specifically designed to cluster firms by searching for differences in production or cost parameters. Moreover, the simulation analyses carried out by Llorca et al. (2014) show that the latent class **approach** outperforms other somewhat more arbitrarily and less robust procedures of splitting a sample of observations, such as cluster analysis. 5

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So far, as outlined in the literature review, no other study examines the impact of stocks and flows and their interactions on labor market matching by applying a **stochastic** translog **frontier**. However, to enable a comparison with studies considering solely the stocks, I also estimate the Battese and Coelli specification for the stock-stock matching model (1) in Table 4.2. Similar to the studies of Fahr and Sunde (2006) for Germany, Hynninen (2009) for Finland and Ibourk et al. (2004) for France, the stocks of unemployed and vacancies turn out to be signifcantly positive. However, in contrary to Ibourk et al. (2004), the interaction of stocks of unemployed and vacancies exhibits with a coefficient of 0.4 and a t-value of 32.62 a highly significantly positive impact on the hiring rate. Furthermore, the findings of Ibourk et al. (2004) suggest a concave behavior of the vacancy stock. As the coefficient of the quadratic term of the vacancy rate v 2 is 0.11 significantly positive in Table 4.2, I do not find support for their results. The results for the stock-flow model (2) barely differ from those obtained by the estimation of the stock-flow specification (T L) without the modeled inefficiency term in Table 4. The significantly positive impact of the stock-flow interactions on the hiring rate remains unchanged as opposed to the either not significant or negative impact of the stocks and flows taken seperately.

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In this paper, parameters are analysed using maximum likelihood estimates with single step **approach** by following (Battese and Coelli 1995). For the present study, Cobb-Douglas production **frontier** using cross sectional data with half-normal distribution (Kaur et al. 2010; Shantha et al. 2012; Dhehibi et al. 2014; Singh et al. 2016) is employed. The general form is,

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To evaluate efficiency of vegetable production, we can use farm-level data for each of 12 regions of Albania and later by pooling regional results we can have an assessment for the country as a whole. We don't have such data, so we use an opposite or aggregate **approach**; to evaluate efficiency of vegetable production we use aggregate (regional level) data. Each region is considered a cross-section and for each of them we collected the necessary data for 9 out of 10 years of the period 2006-2015. From the methodological point of view, there are a number of approaches and methods that can be used to evaluate efficiency. DEA (Data Envelopment Analysis), which is a non-parametric method, quantile regression, propensity score matching, and SFA (**Stochastic** **Frontier** Analysis), which is a parametric and econometric method. In our research we use SFA. The key point in SFA is that the residual term in a production econometric model is composed of two components, inefficiency component, and the error component. So its basic assumption is that all firms are not equally efficient. Based on this, the econometric model according to SFA would be:

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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,

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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Once TE scores are obtained using a translog production function, we apply a **Stochastic** **Frontier** **Approach** (Greene, 2005), specifically a true fixed effect model (TFE) as it has some advantages over other SFA models for panel data. First, it considers not only the technical inefficiency component, but also the fact that random shocks may affect the production **frontier**. Second, it allows us to control for heterogeneity, avoiding the strong assumption under which inefficiency is constant over time. In fact, a time-invariant inefficiency term leads to overestimated inefficiency and hence a downward bias of the estimated TE scores (Greene, 2005). Third, it permits the inclusion of the unobserved heterogeneity that is assumed to be correlated to the explanatory variables, allowing it to overcome the issues characterizing time-invariant efficiency panel data models (see Pit and Lee, 1981).

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Following Farrell (1957), many different methods have been considered for the estimation of efficiency. Two major approaches that are widely used are the Data Envelopment Analysis (DEA) which involves mathematical programming, and the **Stochastic** **Frontier** Analysis (SFA) which uses econometric methods. This study adopts the **stochastic** **frontier** **approach** as it is preferred because of the inherent stochasticity involved (Aigner et al. 1977; Meeusen and Van den Broeck 1977). The SFA specifies output variability by a non-negative random error term (u) to generate a measure of technical inefficiency as consid- ered also by advocates of the deterministic **approach** (Afriat 1972; richmond 1974; greene 1980) and a symmetric random error (v) to account for effects of exogenous shocks beyond the control of the analysed units which embodies variation in weather conditions, diseases, poaching etc, measurement errors and any other statistical noise. For a cross sectional data, the SFA model expressed in accordance with the original models of Aigner et al. (1977) and Meeusen and Van den Broeck (1977) has the form:

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