DO: 0.55/vjbsd-05-000 Visegrad ournal on Bioeconomy and Sustainable Develoment /05 EFFCENCY OF BOMASS PRODUCTON METHODOLOGCAL APPROACHES Tatiana Svetlanská, Natália Turčeková,* zabela Adamičková Slovak University of Agriculture in Nitra, Slovakia The article investigates methodological aroaches towards economic efficiency, which may be alicable in case of biomass roduction with emhasis on agricultural biomass roduction energy cros. The selected methods are: arametric stochastic frontier analysis (SFA) and nonarametric data enveloment analysis (DEA), which are suitable for efficiency measurement in agriculture. The study is organized in four sections. ntroduction rovides brief reort on issues related to biomass roduction and term efficiency. Both methods (models) are shortly described in the material and methods chater. n this art, bio-economy efficiency is shortly deicted as a modification of environmental efficiency. The results and discussion art elains limitations of models, inuts and oututs in terms of biomass roduction. The conclusion sums u the alication of models. The results suggest the use of SFA on sector level and the use of DEA on farm level or regions basis. Keywords: efficiency, biomass, inuts, oututs, roduction ntroduction The imortance of biomass as a source for roduction of renewable energy has been increasing in ast few years. The EU has released regulations for biofuels and biomass, namely the EU Energy and Climate Change Package and Fuel Quality Directive which contains mandatory goals for 00. One of the most imortant goals is 0 ercent share for renewable energy in the EU total energy mi. n accordance with these regulations, the eectations of the Euroean Commission are to reach heat and ower roduction to account for nearly 45 ercent of the renewable energy use in 00 from solid biomass and about twelve ercent from liquid biomass. As for the share of the rimary energy roduction of renewable energy from the forestry, the sector of agriculture has grown more raidly. Desite of this fact, forestry has the major contribution to renewable energy roduction from biomass. The EU Energy and Climate Change Package also includes economic and social criteria. Economics of biomass roduction is rather a wide issue that may include modeling of biomass suly and demand for instance by Sharma, ngalls, ones and Khanchi (03), a artial equilibrium model through OSCAR made by Sourie, Rozakis (00), and various erformance measurements. From the ersective of society, when technology interacts with the environment, it is essential that erformance measurement considers the full imact of the roduction rocess (Antle et al., 005; Weaver, 996; Weaver et al., 996). n this article, the main focus is ut on economic efficiency measurement methodology aroaches, roosals and limitations. Economic efficiency is often illustrated by roduction frontier. The roduction frontier itself refers to state of technology in industry and shows the maimum outut that can be achieved from given inuts. However, it is necessary to distinguish terms efficiency and roductivity. The efficient decision making unit (DMU) oerates on roduction frontier. Efficiency is therefore bounded to current state of technology. Productivity imrovement is attained by either imroving the state of technology or imroving rocedures. Thus roductivity growth can be achieved by efficiency imrovement. The roductivity growth of biomass roduction is discussed in many other ublications, for eamle Vance et al. (04). From early literature we can assume that economic efficiency consists of technical efficiency and allocative efficiency. Technical efficiency is related to the ability of the DMU to roduce maimum outut from given inuts or the minimum feasible amounts of inuts to roduce a given level of outut. The former definition is referred to as outut-oriented TE, while the latter definition is referred to as inut-oriented TE (Watkins, 03). The allocative efficiency refers to the ability to use the set of inuts in otimal roortions, given their ertinent rices (Farrell, 957). Economic efficiency is then calculated as the ratio of the minimum ossible costs and the actual observed costs for a DMU and is the reflection of both efficiencies. One could argue that the relevant measure of efficiency of energy cro roduction can be simly the energy roduced from a ton of biomass cro harvested for eamle. n fact, such indicators do not consider any other inuts used for roduction of that ton such as labour, costs for rocessing, fuels etc. The main roblem of efficiency measurement is the clarification of all relevant inuts as it requires more than one factor of roduction. The objective of our study was to outline some of the relevant methods for efficiency measurement ossibly alicable in terms of biomass roduction. There are several methods generally alicable for economic efficiency measurement. We will further discuss arametric stochastic frontier analysis aroach (SFA), non-arametric data enveloment analysis aroach (DEA), and a relatively new tye of efficiency measurement roosed by Zúniga (0), known as bio-economy oriented efficiency. Material and methods Stochastic frontier roduction function Cobb-Douglas form This aroach was develoed as an adjustment of deterministic frontier estimators roosed by Aigner and Chu (968), who used Cobb-Douglas roduction function in logarithmic form for n DMUs: ln y i = F( i ; β i ) U i () i,,..., n y i features outut of i-th DMU i stands for vector of inut quantities used by DMU β the vector of unknown arameters to be estimated Efficiency of Biomass Production Methodological... Svetlanská, T., Turčeková, N., Adamičková, Download. vol. Date 4, 05, /3/8 no. :50 PM. 6
/05 Visegrad ournal on Bioeconomy and Sustainable Develoment 3 U i F(.) reresents non-negative variable indicating technicanefficiency in roduction denotes aroriate function (Cobb-Douglas) Aigner, Lovell and Schmidt (977) created the estimation of a stochastic frontier roduction and added a symmetric error term to the non-negative error in () to rovide: ln y i = F( i ; β i ) + V i U i () i =,,..., n V i is an indicator of random errors indeendent of the U i. The arameters of such defined model are assumed to be estimated by maimum likelihood (assumes normal distribution for V i N(0, σv ), and half-normal or eonential distribution for U i with mean u i and variance σ. According to Mburu et al. (04), variances of random errors σ v and those of technical and allocative inefficiency effects σu might be eressed through the overall variance: v u σ =σ +σ And thus technical (allocative) inefficiency can be eressed by the σu ratio γ=. σ Dual forms of technology Coelli (995) claims there are three main reasons for dual forms of roduction technology as cost or rofit function; it is necessary to consider behavioral objectives as cost minimization; the need to account for multile oututs; redict technical and allocative efficiency in the same time. Based on these imlications, Mburu et al. (04) further worked with equations above by subtracting v i from (): ln Y = y v= F( ; β ) U i i i i i i Y i the observed outut of i-th DMU adjusted by stochastic noise v i. For this level of outut, the technically efficient inut vector for the i-th X DMU X i is constructed as a solution of (4) and the ratios X = k i X i (i >) and k i denotes the ratio of observed inuts. The dual cost frontier can be then derived and written in form: i i i ln C= f( P ; α, Y ; α) C i reresents minimum cost of observed level of outut for i-th DMU P i an inut rices vector for i-th DMU α the vector of arameters to be estimated The revious methodology assumes n DMUs observed in one oint at time. When the data are observed in different time eriods, it is vital to use anel data version of revious equations. This is a subject of a study conducted by authors Pitt and Lee (98) or more recently Greene (005). Data enveloment analysis efficiency measurement DEA models attemt to measure efficiency involving multile inuts and oututs. Cooer, Seiford and Zhu (0) stress the relevance of DEA in case (3) (4) (5) of unknown relationshis between inuts and oututs. Podinovski, 004 argues that in DEA models, the efficiency of the DMUs can be measured by solving mutually dual linear rogramming roblems. One of them refers to the enveloment model and the other one to the multilier model. These models can be constructed either as outut oriented (maimization) or inut oriented (minimization). They are also based on different return to scale assumtions. Seminal aer by Charnes et al. (978) rooses original model CCR (Charnes Cooer Rhodes) built under the assumtion of constant return to scale. Banker et al. (984) made a modification of CCR model assuming variable returns to scale, known as BCC (Banker Charnes Cooer) model. Given the data on K inuts and M oututs for each of N DMUs, for the i-th DMU inuts and oututs are reresented by vectors i and y i. Then, we can assume that KXN is the inut matri and MXN is the outut matri, which reresent data of all N DMUs. Coelli (995) constructs DEA model urose of which is to build a non-arametric enveloment frontier over the data oint in a way that all observed oints lie on or below the roduction frontier. DEA in ratio form: u yi mauv, (6) v i u y j subject to:, j =,,..., N v j u, v notation u is an Ml vector of outut weights and v is a Kl vector of inut weights. The roblem of such formulation is infinite number of solutions. One ossible solution is to imose constraint v i = and thus create LP model: subject to: v i = m y j v j 0, j =,,..., N m, v ma m, v (m y i ) (7) Change from u and v into μ and v illustrates the transformation and this form is called multilier of the linear rogramming roblem. Enveloment form of this roblem can be derived using the duality in linear rogramming: min θ, l θ (8) subject to: -y i + Yl θ i Xl l θ a scalar indicating efficiency and λ is N vector of constants. The enveloment form is generally referred because of fewer constraints. The value of θ stands for efficiency score of i-th DMU and will vary between 0 and. The value of indicates technically efficient firm as a oint on the roduction frontier according to Farell (957). The linear rogramming roblem must be solved N times for each DMU in the samle Watkins (03) secifies technical, allocative and economic efficiency of rice roduction for n farms through DEA model which might be aly for any kind of agricultural roduction, in form: TE = min θ, l θ n n n i (9) Efficiency of Biomass Production Methodological... Svetlanská, T., Turčeková, N., Adamičková, Download. vol. Date 4, 05, /3/8 no. :50 PM. 6
4 Visegrad ournal on Bioeconomy and Sustainable Develoment /05 subject to: ij θ n 0 l= i stands for farm for inut K for outut non-negative weight for i-th farm ij an inut j used by farm i an amount of outut k roduced by farm i y ik The economic efficiency score for n farm can be clarified by first solving the cost minimizing linear rogramming model: subject to: l= i MC n minimal total cost for farm n is the rice of inut j for farm n (0) the cost minimizing level of inut j in farm n at given inut rice and level of outut Economic efficiency for each farm is then calculated as follows: yik ynk 0 ij yik ynk n = min l i MC EE the actual total cost observed for farm n 0 n = () Unlike in general DEA formulation by Coelli (995) resented by equations (7) and (8), Watkins (03) works under variable returns to scale assumtion. Variable returns to scale are eressed by constrain l= i. Bio-economic oriented efficiency Bio-economic oriented efficiency (BE) is roosed by Zúniga (0), whose study is based on Coelli s et.al. (007) environmental efficiency measure. The environmental efficiency incororates material balance condition into roduction models. Material balance condition may be elained by the balance of nutrients and thus the difference between nutrients in inuts and nutrients in oututs. The ollution is reduced for eamle by reducing the nutrients content in inut vector which causes reduction of nutrients balance. n this case, the materials contents of inuts are analogous to the inut rices in a standard cost efficiency calculation, and hence arametric and non-arametric techniques are alicable in order to estimate the efficiency scores. Given a fied outut vector, Zúniga defines the environmental efficiency as the ratio of the smallest technically feasible bio economic balance over the observed bio economic balance and can be written in form: a e minimum nutrient content a observed nutrient content () BE can be estimated by estimating cost efficiency in DEA models where the vector of nutrient contents of the inuts is used instead of rices. Hence it is ossible to use reviously described methods. Results and discussion Be a e BE = = B a The methods used for erformance measurement may vary deending on the nature of research. n order to measure economic efficiency of biomass roduction it is vital to use more than one measure as each of the methodologies described reviously is based on different assumtions. SFA methodology The main reason why SFA is a useful method for economic efficiency measurement of biomass roduction is its wide alicability in agriculture. The model of stochastic frontier estimation can be written in a form that suorts behavioural objectives such as cost minimization (5). The cost minimization is the imortant assumtion in dual frontier models. n our study we stated the eamle of Cobb-Douglas functional form of roduction function, which was commonly used in emirical estimations of frontier models. The logarithmic transformation enables a model to be linear in the logs of inuts and therefore alicable in econometric estimation. The terms of inefficiency and random errors has aeared. Random errors are simly measurement errors which may occur but they are not taken into consideration in case of non-arametric methods. n case of inefficiency, the DMU is labelled inefficient when oerating below the oint on roduction frontier. The inefficiency and random error comonents are solved by making assumtions about their distributions. The random error term has usually normal distribution and the inefficiency term has usually a half-normal distribution. The arameters of the two distributions are estimated and can be used to estimate DMU s secific inefficiency. The estimation method used in stochastic frontier models is ML estimation, which estimates unknown arameters of models by setting the arameters values that maimize the likelihood function. The SFA ermits conducting of hyothesis testing in regard to the degree of inefficiency and roductions structure. The roblem with SFA is that it does not account for multile oututs and cannot measure technical and allocative efficiency in the same time. The main criticism of this method is based on distribution assumtions. Efficiency of Biomass Production Methodological... Svetlanská, T., Turčeková, N., Adamičková, Download. vol. Date 4, 05, /3/8 no. :50 PM. 6
/05 Visegrad ournal on Bioeconomy and Sustainable Develoment 5 DEA methodology DEA has become widely used in sector of agriculture just in the last decade. As discussed in the revious section, DEA models can be constructed either as outut (maimization) or inut (minimization) oriented. For outut-oriented models, a DMU is not efficient when there is a ossibility to enlarge outut without increasing any inut and without decreasing any other outut. Moreover, in the inut oriented models, a DMU is not efficient if it is ossible to decrease any inut without enlarging any other inut and without decreasing any outut. This methodology uses mathematic rogramming, in our case linear rogramming, and thus can deal with many variables. Furthermore, it is effectively alicable in case of multile oututs. n order to measure economic efficiency of biomass roduction, it is reasonable to construct the model under the assumtion of variable return to scale, as we did in (9), (0) and (), when measuring on multile country bases, considering the fact that many industries are not erfectly cometitive. Constant return to scale constrain is alicable under the assumtion of constant size of DMUs. DEA models are focused on measuring relative efficiency asects of selected units. t is based on the variances of individual DMU comared to ideal DMU lying on the roduction frontier. The researchers can construct DEA in order to evaluate and interret the efficiency from certain oints of view and rovide emhasis on many different subjects such as environment, sustainability, subsidies etc. The roblem of DEA is that it does not account for random errors or uts random error equals zero. On the other hand, the modes free to distribution assumtions. When comaring DEA and SFA aroach, it is necessary to stress that none of them is a suerior method. Both methods have limitations as described earlier. BE methodology Bio-economy oriented efficiency is the methodology derived from environmental efficiency aroach. Model of BE can be formed on basis of linear rogramming using the reviously described methods. The main idea is to involve material balance condition into roduction model. Material balance condition elains content of nutrients in inuts. The descrition of BE in revious section is based on Zúniga aroach that combines DEA aroach with Malmquist total factor roductivity methodology. Data oututs, inuts n order to calculate economic efficiency of biomass there are different ossibilities for data selection. Let us assume roduction of biomass cros such as corn, sugar beet, sunflower etc. Oututs the most commonly used outut in case of agriculture is agricultural roduction in either monetary or hysical units. The outut is eressed by total amount of roduction in monetary units (relevant currency) or total revenue of the DMU. Physical units in terms of agricultural roduction are tons, or in case of biomass cro it could be renewable energy roduced in ktoe (kilotonne of oil equivalent). nuts decision about inut set deends on toic of research related to biomass roduction. The most aroriate in this case aear to be initially labour, land and caital as any measurement of roductivity. Labour in case of biomass cro roduction might be considered through number of workers in bioenergy sector or alternatively labour hours. Land is measured in hectares utilized for biomass-agricultural roduction. Caital factor can be considered in many ways of which we assume book value of machinery and inventory the most aroriate. Costs are notably one of the most imortant inut data. For biomass cros roduction it is vital to searate costs into inut of seed, fertilizer, esticides, energy consumtion. The last category of inuts is imortant in terms of environmental efficiency. Environmentally related inuts are for eamle nitrogen, hoshorus, otassium surlus. nut and outut data may be found in corresonding database such as FADN (Farmers Accountancy Data Network). Conclusion The article dealt with the aroriate efficiency measurement in terms of biomass roduction. We can conclude that none of the roosed methodologies is suerior and therefore it is desirable to use combination of BE with either SFA or DEA. DEA seems to be more relevant in cases based on farm or region basis. t is also vital to use DEA in case of wider comarison. On the sectoral level, the use of SFA is considered more aroriate because of ossible measurement errors and missing variables which might lay an imortant role when it comes to efficiency. DEA requires a large number of observations to be relevant methodology of measurement. On the other hand, it does not require measurement unit s equivalence. Hence, we can conclude that the considered alication has significant influence on the used methodology. n the resented article we assumed energy cros roduction in regard to efficiency measurement. The biomass roduction is undoubtedly related to bioeconomy issues, thus we adduced the modification of environmental efficiency. The use of BE is adequate in resect of interaction between technology and environment which is certainly the case of biomass roduction. Any of described methods can suffer from incorrectly selected or measured inut data. Poorly measured inuts might have a significant imact over the technical efficiency measurement and influence the overall or economic efficiency. The crucial role of any conducted research on efficiency evaluation is selection of suitable data set. Efficiency measurements of bioenergy sector is imortant from the oint of fulfilling the goals set by the Euroean Commission to increase the share of renewables in total energy mi and thus decrease the deendence on fossil fuels. There are many conflicting oinions on cultivation of agricultural cros as feedstock for energy uroses as it otentially reduces their nutritional aim. Desite criticism, biomass and waste from agriculture has become imortant sources in the field of bioenergy esecially in the EU states. Acknowledgements This work is co-funded by the Euroean Community under the roject 60080: Building Research Centre Agrobiotech. References AGNER, D.. CHU, S. F. 968. 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