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THE EFFICIENCY OF LARGE AND MEDIUM SCALE OF THE FOOD AND BEVERAGE INDUSTRIAL PRODUCTION IN EAST JAVA: DATA ENVELOPMENT ANALYSIS (DEA) AND STOCHASTIC FRONTIER ANALYSIS (SFA) APPROACHES

This study aims to estimate the technical efficiency of food and beverage industry in East Java in 2011 to 2013 using micro data at the company level. Stochastic Frontier Analysis (SFA) and Data Envelopment Analysis (DEA) are used to estimate technical efficiency. The output variable was the value of production, while input variables were capital, labor, raw material, and energy. The Likelihood Ratio test dictates that the Translog production function is more appropriate for use in this study. The estimation results show that the efficiency of food and beverage companies in East Java by using SFA has decreased significantly by 3.02%, whereas with the DEA method, the average technical efficiency has increased by 0.583% compared to the beginning of the year in 2011. In addition, there is difference in the efficiency value between SFA and DEA. The technical efficiency value of SFA calculation is greater than that of DEA. The dissimilarity is caused by the difference of specification in both methods related to the interaction between uncaptured variables in the DEA method. The results of this policy have implications on the government’s obligation to pay attention to the food and beverage industry in order to suppress the company’ various operating costs, such as maintenance for old machines, which has an impact on on technical efficiency or improve the ability of labor in terms of machinery utilization. Therefore, in the following year, the performance of the food and beverage industry as the largest sub-sector in manufacturing is able to show the progress.


Introduction
According to Wasiaturrahma and Ajija (2017), East Java is one of the provinces in Indonesia which has a higher rate of economic growth than the average national economic growth during the last five years. With an average growth of 6.7%, East Java is able to contribute to Indonesia's GDP of 15% per year. The contribution of East Java Gross Regional Domestic Product occupies the second highest position after Jakarta which contributes about 17% per year.
According to the data of Central Bureau of Statistic of Indonesia, Gross Regional Domestic Product (GRDP) of East Java has received a large contribution from the manufacturing sector. In 2014, the sector contributed to the Gross Regional Domestic Product (GRDP) 28.9 %. Compared to other sectors, such as agriculture which reached 13.56% by 2014, manufacturing industry has stabilized to become the largest contributor since 2000.
The manufacturing industry sector consists of various subsectors that will produce output from the production process. Central Bureau of Statistics noted that The East Java manufacturing industry output in 2014 reached 445 Trillion Rupiah. The amount was contributed by the food and beverage subsector of 27.41 percent to the total output of manufacturing industries in East Java. The contribution of the food and beverage subsector to the East Java manufacturing sector has continued to increase since 2010, which contributed 26%. Meanwhile the food and beverage subsector is stable as the largest contributor to the output of manufacturing industries in East Java. Therefore, the food and beverage industry has become one of the leading sub-sectors in East Java.
The food and beverage subsector is classified by the Central Bureau of Statistics based on the company scale, i.e., large and medium scale. The classification is based on the amount of labor used in each company. The Central Bureau of Statistics (2017) stated that by 2013, companies in the food and beverage subsector account for 31% of the total output of the manufacturing companies in East Java. These percentages indicate that the role of large and medium enterprises in the food and beverage subsector is vital in an effort to increase economic growth in East Java.
However, even though Food and Beverage industry of East Java become the leading sub-sector among the others, yet evidently, Food and Beverage industry as particular has fluctuate performance due to its large independency toward the price of input, notably labor, machine, and material. For instance, the data of Central Bureau of Statistic in 2013, Food and Beverage industry in East Java show the great decrease of labor productivity by 29 percent, much greater than the decreasing productivity in the 2015. Furthermore, external factor such as exchange rate also affected to the performance of this sub-sector in East Java. For instance, the depreciation in 2013 reached 24 percent, the greatest along 2010 to 2016. It implicates that, in 2013, there was great significant downward economic trend of Indonesia that might affect to the Food and Beverage industry of East Java performance.
The existence of a significant food and beverage subsector in improving the economic performance of East Java as well as its high independency performance toward various variables indicates evaluations need to be undertaken. Evaluations will provide insight for improvements on various factors in the food and beverage subsector, so the economic benefits of this subsector may improve. These evaluations can be done aggregately across large and medium-sized companies or even the micro size companies. In the end, the more detailed and thorough economic evaluation is the more efficient and effective the policy planning will be. In addition to spatial outreach, various calculation methods are also undertaken to ensure that the output produced is able to illustrate the industry condition more accurately as well as to provide key indicators that may affect industry performance (Lindberg, Tan, & Yan, 2015).
Currently, industry performance evaluation has evolved and varied as an effort to improve the benchmark indicators that have implications for development policies. One of the indicators used is technical efficiency that describes input contribution proportionally in generating output (Timothy J Coelli, O'Donnell, & Battese, 2005). The way in which technical efficiency evaluating the performance of entities is quite straightforward since there are considerable explanations of the correlation between input and output. Hence, this reason become the urgency of this study in evaluating the Food and Beverage Industry of East Java. The evaluation was conducted in various researches such as Saptana, Supena, & Purwatini (2004) which tested the efficiency and competitiveness of farming and sugarcane industry in East Java, as well as Susilowati & Tinaprilla (2012) which tested the technical efficiency of sugarcane farming in Indonesia. In addition, Cullinane, Wang, Song, & Ji (2006) examined the technical efficiency of ports in the world by expanding estimated output results with Stochastic Frontier Analysis (SFA) and Data Envelopment Analysis (DEA).
This research attempts to calculate the efficiency score by using two methodologies, Stochastic Frontier Analysis (SFA) and Data Envelopment Analysis (DEA). Two methods are utilized due to the comparison will be able to generate multi perspective and more accurate depiction of the Food and Beverage Industry of East Java and conducted policy afterwards. Furthermore, there are a few number of research which empowered both SFA and DEA. Hence, this study contributes in diversifying the use of performing estimator of the regional economy. In the end, following the result of calculation, Food and Beverage Industry as the largest contributor for East Java's economy will possess precise measurement and significantly encourage various positive sign, such as capital inflow and investment.udi ini. Pembahasan hasil akan didiskusikan pada bagian 4 dan bagian akhir akan ditutup dengan kesimpulan dan implikasi kebijakan.

Production Theory
The notion of production can be attributed to a functional illustration called the production function (Pindyck & Rubinfield, 2001). Nicholson & Snyder (2008) define the function of production as a function that reflects the technical knowledge of the company about the utilization of inputs that have in producing the output. The definition, according to Bradley (2010) will aim to determine the level of output gained by the variation of factors of production.
The production function consists of various types. Two of them are the Cobb Douglas and Transcendental Logarithmic (Translog) production functions. The Cobb Douglas production function is understood as a linear homogeneous function with a substitution elasticity of 1 of each factor of production (Douglas 1976). Cobb's Douglas production function is illustrated as follows: Where P is the total production, L is labor, K is capital (including machine, equipment, and building), α and β are the degree of elasticity in every factor of production. Based on equation 1, it is seen that the relationship of K and L is direct and non-existent interaction variables between variables that can affect production levels.
The production function of Transcendental Logarithmic (Translog) is a production function of Cobb Douglas generalization. This production function is more flexible in explaining the relationship between output and input (Boisvert, 1982 andKonishi &Nishiyana, 2002). This production function accommodates the interaction variables of the main variables that can not be applied to Cobb Douglas. The Translog production function is illustrated in equation 2.

/ / /
Where y is the output, α0 is an efficiency parameter, xi is the input i, xj is the input j, and Ln is the natural logarithm. Translog production function is often written in logarithmic equation to form a linear equation (Boisvert, 1982). Equation 2 shows that there are variables xi and xj as a form of interaction between variables in influencing the dependent variable. Therefore, this production function is referred to as a function flexible production.

Technical Efficiency
Efficiency is understood terminologically in the Oxford Dictionary as the maximum production condition obtained by the low cost. In addition, Koopmans (1951) defines the concept of efficiency in a more technical way that connects between the input and output that is the condition when the output increase reduces the output in the lowest quantity or the increment of at least one input. Timothy J Coelli, O'Donnell, & Battese (2005) define the concept of efficiency to be the technical efficiency illustrated in Figure 1. Based on figure 1, the line q is the frontier line. The frontier line is derived from the optimum (efficient) production standard points, for example at points B and C. While at point A, production levels are not technically efficient because they are outside the frontier line. The firm at point A must reduce the quantity of input x to be efficient because with the input level of x1 at point A, the firm can produce the same output (y1) if the firm produces with input at x2 (this condition is called technical inefficiency) . This condition is called input ori- The Efficiency of Large and Medium Scale of the Food and Beverage Industrial Production in East Java: Data Envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA) Approaches ented. In addition, to achieve efficient conditions, the company at point A can also increase its output to the frontier line (point B). This is because, with the same level of input usage x1, the company can still increase its output from y1 to y2 (frontier line), thus, the company can achieve efficient conditions. This condition is referred to as output oriented.

Data Envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA)
Estimation of technical efficiency is related to the method used. The method can be classified into 2 types namely parametric and non-parametric. In the parametric method, one of which is Data Envelopment Analysis (DEA). Data Envelopment Analysis (DEA) is a type of non-parametric method associated with productivity and was first discovered by (Charnes, Cooper, & Rhodes, 1978). This method requires modeling in a linear program derived from the specification of the variables used. Non-deterministic DEA modeling causes this model to measure efficiency without statistical noise (Sari, Khalifah, & Suyanto, 2016). The impact is that the specification used should be in accordance with empirical research so that the output calculations performed describe the actual conditions. The DEA illustration is shown in figure 2. The DEA concept estimates the lag between the potential output and the actual output. In FIG. 2, points A ', B', C, and D are the efficient production levels owned by each firm A ', B', C, and D, while at points A and B are the production levels owned by each firm A and B. However, the problem occurs when at point A ' which is an efficient point, similar to point C, in fact uses fewer x2 inputs than firm C. In other words, firm C can produce the same output as firm A' using less X2 input. This condition is called the slack input which can be found through the DEA approach (Timothy J Coelli, O'Donnell, & Battese, 2005).

Figure 3: The Concept of SFA
Source: Battese (1992) Stochastic Frontier Analysis (SFA) is a parametric method that also deals with productivity calculations. This method is proposed by (Aigner, Lovell, & Schmidt, 1977) and (Meeusen & Broeck, 1977). Similar to DEA, the SFA method estimates full production capacity (full capacity) or the so-called frontier (Lei, 2013). However, the difference with DEA is the presence of statistical noise as well as the parameters that appear as a benchmark of the significance of the specification used, so that in SFA the level of accuracy variables used can be measured. In addition, the SFA will distinguish the calculations between technical efficiency, technological progress, and total productivity factor (TFP) (Lloyd & Zhang, 2000). The SFA concept illustration is shown in figure 3. Figure 3 describes the concept of SFA according to Battese (1992) illustrated in the production activity of two firms i and j. Company i uses the input with the value xi and produces the output of Yi, but the frontier of the output is in Yi * which exceeds its ideal value, so the value of Vi which is statistical noise is positive. Conversely, firm j uses inputs of xj and achieves production Yj with the ideal output position at Yj *, so Vj is negative. In the SFA approach, the value of V will be aggregated so that it will describe the statistical noise value of all firms under test.

Data and Variable
This study uses secondary data Manufacturing Industry food and beverage sub-sector derived from the Indonesian Central Bureau of Statistics (BPS). BPS defines the manufacturing industry as an economic field of activity that converts raw materials mechanically, chemically, or manually into finished / semi-finished goods. Therefore, in the presence of the process, the value of goods initially does not worth.
The classification of the manufacturing industry is divided by the number of workers. Large scale is a company that has a workforce of more than 100 people. Medium scale is a company that has a workforce of 20 to 99 people. The workforce is a group of workers with certain skills that work with predefined system.
The data of this research is taken from the annual survey of large and medium manufacturing industry companies (IBS) conducted by the Central Bureau of Statistics. The advantage of data used in this research is firm data (5 digits) Classification of Indonesian Business Standards (KBLI) so it will show the calculation output of each company in East Java. The number of observations used is 2433 with the details of 811 companies over a period of 3 years. This number is selected with the sorting company which have complete value in each variable. This study decide to eliminate the company which has empty value in certain variable. Since according to the data of BPS, the number of Food and Beverage companies in East Java in 2011-2013 reached 1630, 1689, and 1724 respectively. Therefore, the number of sample of this study is quite representative for more than 50 percent of total Food and Beverage companies in East Java and this balance panel data is appropriately able to be analyzed.
The companies being tested are those that have been in the food and beverage industry for 3 years (2011)(2012)(2013) in East Java. Period of 2011 to 2013 is chosen as consideration of those period as the downward trend of national economy, notably in 2013. Moreover, the limited access of the national survey of industry for the forward years also become the limitation of this study. Hence, the performance of efficiency score trend will viewed in 2011 and 2012 before the downward economy occurred.
145 Ajija, S. R, dkk The Efficiency of Large and Medium Scale of the Food and Beverage Industrial Production in East Java: Data Envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA) Approaches The existence of the relationship between input and output on the SFA and DEA estimates requires that the corresponding variable be present. This research uses variable value of manufactured goods (in rupiah) as output, fixed capital (in rupiah) variable, amount of labor (per person), fuel used (in rupiah), and raw materials) (in rupiah) as inputs. These variables according to Evan & Hunt (2009) are the development of a classical production function that initially consists only of capital and labor. These variables are also the core variables in the manufacturing production process according to the Central Bureau of Statistics in Indonesia. The descriptive statistics of the data used in this study are presented in Table 1 below.

Method
The method used in this research is Data Envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA) used to estimate the technical efficiency level of food and beverage companies in East Java. The first method to be used is SFA as determinants of the suitability of variables used significantly affect the output. Then, the DEA method is used as a computation of the calculation results using the SFA method.
Where Y is the value of the goods produced, K is the value of fixed capital, L is the amount of labor, M is the raw material, E is the energy used, t is the time period (year), v is the statistical noise of the equation, u is the inefficiency parameter, i is the i-th observation, and Ln is the natural logarithm. This research uses technical efficiency effect (TE effect) method which will describe the determinants of the technical efficiency level that is produced. Research by (Battese & Coelli, 1995); (Kneller & Stevens, 2003); (Kumbhakar & Wang, 2005); (Becerril-Torres, Alvarez Ayuso, & Moral-Barrera, 2010) is used for the TE effect specification. The TE effect specification is as follows.
Where U is technical efficiency, T is time, and W is statistical noise from the TE effect equation. Cobb Douglas production function is also used in this equation as an alternative to the production function of Translog. The Cobb Douglas production function is formed by ignoring the parameters β5, β6, β7, β8 , β9, β10, β11, β12, β13, and β14 in equation (3). The production function of the Translog and Cobb Douglas will be tested with the Likelihood Ratio test in FRONTIER 4.1 application to determine the production function according to the data characteristic used. The LR test calculation formulation is as follows.
Where λ (H0) and λ (H1) are log likelihood function values in the null hypothesis (Cobb Douglas) and alternative hypothesis (Translog). After the value is known, the parameter λ compared with χ2 with degrees of freedom is equal to the number of parameters involved in the restriction. If the calculation of λ likelihood count is greater than χ2 table then H0 is rejected so as to accept H1 (Translog production function is used).
The calculation of technical efficiency on the SFA method uses a formulation of (Farrell, 1957) with the following specifications.
Technical efficiency is calculated based on the level of production achieved relative to the maximum production level. The technical efficiency will be worth between 0 (very inefficient) to 1 (very efficient).
Specification Data Envelopment Analysis used in this study using the assumption of maximization ie each company is assumed aims to maximize its output. Therefore, DEA-BCC (Banker, Charnes, Cooper) output oriented was used in this study. In addition, DEA VRS (variable return to scale) is used in this study. The model is as follows. -Where θ is the radial when the input reduction estimates the technical efficiency (parameter efficiency), λ is the matrix that describes each Decision Making Unit (DMU). (Banker, Charnes, & Cooper, 1984) states that efficiency occurs when θ is worth 1 and all positive and negative slacks are zero.

Selection of Production Function and Technical Efficiency Calculation
Selection of production function is performed to select the appropriate production (4) The Efficiency of Large and Medium Scale of the Food and Beverage Industrial Production in East Java: Data Envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA) Approaches function. The selection is done by using Likelihood Ratio test according to the formulation in equation (5) by using application FRONTIER 4.1. The LR test decides the production function of Translog as an appropriate production function because the value λ = 1982.38 (greater than χ2 table) and significant at 1% level. The results of the calculation of the two production functions using Maximum Likelihood are presented in Table 2. Based on the calculations performed, the parameters on the Translog function are almost entirely significant at the 1% level except in beta13 (labor and energy interaction variables). The values of γ and σ2 are 0.9526 and 2,164, respectively, which are defined as the variance distribution of Vit and Uit. The γ value of 95.26% indicates the proportion of error rate on Uit. The significant result of this parameter shows the variables can be used for SFA analysis and technical efficiency calculation.
Calculation of technical efficiency of food and beverage companies by SFA method is done with application FRONTIER 4.1. The calculation is presented in Table 3 (classified by district / city and in average). Based on calculations by SFA method, Sidoarjo regency has the largest number of food and beverage companies in the observation of 107 companies. This number means that the company has survived for 3 years in a row, so it can be recorded in this research. The average technical efficiency score in the food and beverage industry in East Java for 3 years decreased. In 2011 the average reached 85.58% with the highest level of technical efficiency occurred in Bojonegoro Regency of 88.47%, while the lowest efficiency is owned by Blitar regency which is equal to 74.09%. In 2012, the average technical efficiency decreased by 3.31% to 82.27% with the highest technical efficiency in Pamekasan Regency of 88.83%, while the lowest technical efficiency of 70.79% was by Ngawi Regency. In the following year, there was an average technical efficiency of 0.29%. This year, Magetan Regency had the highest technical efficiency of 89.64%, while Ngawi Regency still has the lowest technical efficiency of 70.43%. The technical efficiency level of the above 33 districts is summarized in Table 4. Based on Table 4, districts/municipalities that have consistent food and beverage companies in the top 10 within 3 years are Mojokerto and Pamekasan districts. Sidoarjo Regency which has the largest number of companies in this study in fact has the greatest efficiency level of the 16th in 2011 and 11 in the next 2 years. The city of Surabaya, as the capital of East Java province in 2011 was ranked the 8th largest, but decreased in 2012 to rank 15 and increased again to become the 7th largest. The changes that occurred at the level of efficiency shows the level of great competition between companies described in the operational policies of each company to improve efficiency. As a comparison, the calculation of technical efficiency with Data Envelopment Analysis (DEA) was also done. The results are presented in Table 5. Based on Table 5, the technical efficiency of beverage and food companies in East Java with DEA method has increased slightly. In 2011 the average reached 53.79% with the highest level of technical efficiency occurring in Magetan Regency which amounted to 77.65%, while the lowest efficiency was by Pasuruan at 29.51%. In 2012, there was an average increase of technical efficiency by 0.66% to 54.45% with the highest technical efficiency occurring in Magetan Regency of 78.35%, while the lowest technical efficiency was 29.75% in Mojokerto City. In the following year, the decline occurred at an average of technical efficiency of 0.081%. This year, Magetan Regency is still the district with the highest technical efficiency of 77.65%, while Pasuruan has the lowest technical efficiency at 29.69%. The technical efficiency level of 33 districts / cities with the DEA method above is shortened in Table 6. Based on Table 6, the districts / cities consistent with the top 10 highest technical efficiency scores are Magetan Regency, Batu City, Nganjuk Regency, Gresik Regency, Bojonegoro Regency, Madiun Regency, Malang Regency, Sampang Regency, Sumenep Regency and Pamekasan Regency. The results show that the technical efficiency calculation with DEA shows the stability of the technical efficiency level in each district / city. This stability is due to the limited specification of the DEA compared to the SFA which uses many specifications and interactions on the variables (see equation 1), so that any changes to the variables will affect the technical efficiency. While in the DEA method, the specification is only done on the main variables without any interaction between the variables, so the efficiency is more stable but lower. As a comparison of the technical efficiency spreads of the SFA and DEA methods,  Based on Figures 4 and 5, the technical efficiency level of beverage and food companies in East Java with the SFA method is larger at the 70% to near 100% efficiency range. There is only one company that has technical efficiency of less than 30%. When using the DEA method, the spread of technical efficiency values tends to be more evenly in the range of 0 to close to 100%. This diffusion difference is caused by differences in specifications in both methods resulting in higher technical efficiency in SFA. There is interaction between the main variables on the SFA method impact on higher technical efficiency because there are more variables that can explain and contribute to the level of technical efficiency. While in the DEA, the specification is used only on the main variable, so the number of explanatory variables is less, so the technical efficiency is not as big as the SFA method.
The technical efficiency of the food and beverage industry in East Java based on the SFA method shows a significant decrease in 2011 to 2013. The decrease is similar to that of Darmawan (2016) which found that there was a negative growth trend in the food and bev-erage industry in East Java in 2009 to 2010, so the negative growth trend was expected to continue until 2013. Puspitasari (2011) mentioned that the negative trend of efficiency was caused by the cost of procurement input, so the cost is not proportional in generating output. This has implications for large and medium scale food and beverage industry research in East Java Increasing competition among food and beverage producers demands every producer to produce various product variants. However, limited production machinery or old machinery, for example, has an impact on the increasing cost issued for input (Suyanto, 2009);(Bank Indonesia, 2006). Therefore, technical efficiency trends allegedly continue to occur prior to the government's revitalization policy (Yasin, 2017).
Study of Minh et. al. (2011) found that the exchange rate influence the rate of efficiency score. As mentioned in the introduction section in this study, Indonesia had large depreciation of exchange rate in 2013 which might implicate to the performance of Food and Beverage industry in East Java. Since some raw materials of Food and Beverage industry require to be imported, such as salt and flavor, the great depreciation might also affect the rate of efficiency score.
The results of technical efficiency calculations using DEA show different trends with the use of SFA methods. It is indicated that SFA trends occurring in SFA are derived from interactions between Translog variables not found in the DEA method. For example, the interaction between capital and labor in generating output which in the empirical production process must occur, but the interaction is unable to be quantified by the DEA method. These induced interactions resulted in a downward trend in efficiency of the SFA method. This is seen in the technical efficiency level of the smaller DEA method compared to the SFA method due to differences in assumptions and specifications on both methods (Cullinane, Wang, Song, & Ji, 2006).
The different trend of efficiency score is a salient finding of this study. As aforementioned justification, the different trend occurred due to DEA is unable to capture the interaction between main variable, such as labor and capital, since this interaction may create the negative trend of efficiency score which captured by SFA. Hence, it is important to revolve around the interaction of labor and capital in conducting policy. For instance the use of machine involving the labor that might have downward performance compared to a machine which produce by itself in generating a product that have upward performance may implicate into the large amount of firing. As consequence, improving ability of labor in the use of machine is a must and become the appropriate policy following the result of this study.

Conclusion
The results show that the SFA method produces a greater efficiency level than DEA. Both methods also show different technical efficiency trends. These results have implications for the existence of interaction allegedly occurred between variables which have a greater contribution in generating production output than the main variable used in the DEA method. In addition, the limitations of the specifications on the DEA method also have an impact on the low technical efficiency, although these variables have been confirmed in significance with the SFA method. However, the diffusion of technical efficiency in the DEA method is more even compared to the SFA whose technical efficiency is dominated in the range above 70 %.