MODELING MILK COST IN ESTONIA: A STOCHASTIC FRONTIER ANALYSIS APPROACH

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1 MODELING MILK COST IN ESTONIA: A STOCHASTIC FRONTIER ANALYSIS APPROACH Estonan Unversty of Lfe Scences ABSTRACT. Ths paper presents a formulaton of stochastc fronter models for mlk cost n Estona. Two dstnct models of mlk cost were nvestgated. A balanced panel of 45 Estonan farmers observed durng the perod 2001 to 2006 was used. For the models parameter estmaton a computer program FRONTIER Verson 4.1 was used. The results for varous specfcatons were compared and dscussed. The results from stochastc fronters model analyss were compared wth the results of OLS. Predcted cost effcences of the Estonan farmers were compared under the dfferent model specfcatons. Ths analyss demonstrated that stochastc fronter analyss (SFA) can be mplemented for parameter estmaton of econometrc models and for predctng the cost effcency of mlk cost n Estonan farms. Keywords: stochastc fronter analyss, cost (economcal) effcency, panel data, mlk cost Introducton Estona s one of the new members of the European Unon. The EU enlargement means for East European countres a lot of changes n ther agrculture. These changes are at the poltcal, economcal and techncal level. Ths means that nformaton systems on agrculture (databases, models etc) have to move along wth those changes. Consequently, the economc models n Estona have ether to be created, developed or renewed, and must be harmonsed wth the European requrements. Hopefully, we can use new nformaton technology to lead such evolutons. We recognse that there s a varaton n the behavoural characterstcs of the agrcultural producton systems over tme as well as between countres. The dverse nature of agrcultural producton systems and agrfood markets across the EU poses a challenge to anyone seekng to develop a model that can be used to analyse polcy at EU and member state level. Improvng the compettveness of Estonan agrculture s the prorty objectve of agrcultural polcy. The outcome and mpacts of those polcy actons wll strongly depend on developments of the agrcultural world markets. The dary sector s the most compettve commodty of Estonan agrculture. Consequently, the need to make Estonan dary farms more compettve s obvous. At the Estonan Unversty of Lfe Scences (Insttute of Economcs and Socal Scences), we have nvestgated the possbltes of some new Data Mnng (DM) methods and have some experence n mplementng algorthms used n DM packages. We have used varous methods for estmatng the parameters of econometrc model of gran yeld and mlk cost. We have used Bayesan statstcal methods n Põldaru and Roots (2001b), neural networks n Põldaru and Roots (2003), prncpal components method n Põldaru and Roots (2001a), decson trees and rules CART (Classfcaton And Regresson Trees) n Põldaru et al. (2003b), assocaton rules dscovery n Põldaru et al. (2003a), fuzzy regresson n Põldaru et al. (2004a); and support vector machnes regresson (Põldaru et al., 2004c; Põldaru et al., 2004d; Põldaru et al., 2005) for estmatng the parameters of econometrc model of gran yeld and mlk cost. Recently Journal of Productvty Analyss publshed specal ssue dscussng the productvty and effcency problems of countres that mght be movng from command economes to market economes (L et al., 2008). In recent decades, the nterest of econometrcans for new models and methods has ncreased substantally, ncludng the stochastc fronter analyss (SFA). The stochastc fronter analyss (SFA) was prevously used to model agrcultural producton (Coell, Battese, 1996; Hadr, Whttaker, 1999), gran producton (Battese, Broca, 1997; Põldaru, Roots, 2004b), mlk producton (Renhard, et al., 2000; Lawson et al., 2004; Abdual, Tetje, 2007), meat producton (Sharma et al., 1997) and wool producton (Fraser, Horrace, 2003). Recently an extensve overvew of emprcal studes of techncal effcency n farmng was publshed (Bravo- Ureta et al., 2007). In ths paper we consder SFA as a method for econometrc model parameter estmaton and as an nstrument to predct economcal effcences of mlk producton n Estonan farms. Next we nvestgate the possble use of two dstnct models of mlk cost. The study dffers from prevous studes because t dscusses the effcency of mlk producton n the country that s movng from command economes to market economes. In ths study we use the approach that s generally preferred n effcency analyses of agrcultural performance, where data nose mght be a sgnfcant ssue (Coell, 1995). Two specfc econometrc models were specfed. The frst model (MI) s a neutral stochastc fronter model where farm specfc neffcency explanatory varables are assumed to be ndependent of the nput varables n the producton functon. The frst model s relatvely correct (almost all essental ndependent varables are ncluded n the model, the coeffcent of determnaton, R 2, s hgh, almost all parameter estmates are sgnfcant and acceptable from economc pont of vew). The parameters of the frst econometrc model

2 26 (MI) were prevously estmated mplementng ordnary least square regresson (OLS) method. The second model (MII) s a modfed stochastc fronter model where farm specfc neffcency explanatory varables are assumed to account for cost neffcency n producton, ndependent of the nput varables n the producton functon. For the both stochastc fronter models two alternatves are consdered: a) analyss of cross-secton data and b) analyss of panel data. The model parameters for dfferent varants of ndependent varables specfcaton were estmated. For the model parameter estmaton, a computer program FRONTIER Verson 4.1 was used (Coell, 1996). The results for varous specfcatons were compared and dscussed. The results from stochastc fronters model analyss were compared wth results of prevous analyses. The data s a balanced panel of 45 Estonan mlk producers drawn from FADN (Farm Accountancy Data Network) observed durng the perod 2001 to Ths paper s organzed as follows. The next secton descrbes the fronter cost models used. Secton 2 descrbes the data for the emprcal analyses. Secton 3 presents and dscusses the results. Secton 4 summarzes and gves conclusons. Stochastc fronter models for mlk cost n Estonan farms In ths paper the standard stochastc fronter cost functon models (M I) for panel (or cross-sectonal) data was used. Ths frst model s descrbed more thoroughly n Battese and Coell (1992). The model may be expressed as: K 0 + β j j=1 ( V U ) Y t = β x jt + t + t (1) where: Y t s the mlk cost of the -th farm n the t-th tme perod; x jt s the j-th nput quantty of the -th farm n the t-th tme perod; β s K x 1 vector of unknown parameters; the V t are random varables whch are assumed to be ndependent dentcally dstrbuted normal random va- 2 N, σ ), and ndependent of the U t ; rables (d ( ) 0 V U t ( U ( ( t T ))) = exp η (2) the U are non-negatve random varables whch are assumed to account cost of neffcency n mlk cost 2 N µ σ ; model and are assumed to be d ( ), U η s a parameter to be estmated usng panel data. The parameterzaton of Battese and Corra (1977) who 2 2 replaced σ V and σ U wth = σ V σ U and γ σ U / ( σv + σ U ) σ + = s followed. (2a). The cost (economcal) effcency of a gven farm (at a gven tme perod) s defned by Battese and Coell (1992) as the rato of ts mean cost (mlk cost) to the correspondng mean cost f the farm utlzed ts levels of nputs most effcently (as the rato of mnmum feasble cost to observed expendture). The measure of cost (economcal) effcency relatve to the cost fronter (1) s defned as: where, * * ( U, X )/ E( Y U = 0 X ) CE = E Y, (3) * Y s the cost (mlk cost) of the -th farm, whch wll be equal to Y when the dependent varable s n orgnal unts and wll be equal to exp ( Y ) when the dependent varable s n logs. CE wll take a value between one and nfnty n the cost functon case. The mposton of one or more restrctons upon ths model formulaton can provde a number of the specal cases of ths partcular model whch have appeared n the lterature. Settng η to be zero provdes the tme-nvarant model (varant MI-2). Furthermore, restrctng the formulaton to a full (balanced) panel of data gves the producton functon assumed n Battese and Coell (1988). The addtonal restrcton of µ equal to zero reduces the model to varant MI-1. The restrcton of T=1 return to the orgnal cross-sectonal (varant MI-1), half-normal formulaton of Agner, Lovell and Schmdt (1977). Obvously a large number of permutatons exst. For example, f all these restrctons exceptng µ=0 are mposed, the model suggested by Stevenson (1980) results. Furthermore, f the cost functon opton s selected, we can estmate the model specfcaton n Hughes (1988) and Schmdt and Lovell (1979) specfcaton, whch assumed allocatve effcency. These latter two specfcatons are the cost functon analogues of the producton functons n Battese and Coell (1988). There are obvously a large number of model choces that could be consdered for any partcular applcaton. For example, does one assume a half-normal dstrbuton (varant MI-4) for the neffcency effects or the more general truncated normal dstrbuton (varant MI-3). If panel data are avalable, should one assume tme-nvarant or tme-varyng effcences? If such decsons must be made, t s recommended that a number of the alternatve models be estmated and that a preferred model be selected usng lkelhood rato tests. The second model (MII) s descrbed more thoroughly n Battese and Coell (1992). The model may be expressed as: K 0 + β j j=1 ( V U ) Y t = β x jt + t + t (4) where Y t, x t, and β are as defned earler; the V t are random varables whch are assumed to be d N(0,σ 2 V ), and ndependent of the

3 Modelng mlk cost n Estona: a stochastc fronter analyss approach 27 U t whch are non-negatve random varables whch are assumed to account for cost neffcency n producton and are assumed to be ndependently dstrbuted as truncatons at zero of the N(m t,σ 2 U ) dstrbuton; where: m = δ or m t = δ 0 + δ j ztj (5) t z t P j= 1 where z tj s the j-th nput quantty of the -th farm n the t-th tme perod (varables whch may nfluence the effcency of a frm); and δ s an 1 P vector of parameters to be estmated. Ths model specfcaton also encompasses a number of other model specfcatons as specal cases. If we set T=1 and z t contans the value one and no other varables (.e. only a constant term), then the model reduces to the truncated normal specfcaton, where δ 0 (the only element n δ) wll have the same nterpretaton as the µ parameter n frst model MI (varant MI-2). It should be noted, however, that the model defned by (4) and (5) does not have the model defned by (1) as a specal case, and nether does the converse apply. Thus these two model specfcatons are non-nested and hence no set of restrctons can be defned to permt a test of one specfcaton versus the other. Data In ths study we utlze data descrbng the producton actvtes of 45 hghly specalsed dary farms (Decson Makng Unts DMU) that were n the Estonan Farm Accountancy Data Network (FADN) all of the perod. The FADN s a stratfed random sample. Stratfcaton s based on economc farm sze, age of the farmer, regon, and type of farmng. We have a total of 270 observatons n ths balanced panel, and so each farm appears 6 tmes n the panel. The perod 2001 s chosen because detaled nformaton at each farm s avalable from 2001 onwards. A panel contans more nformaton than does a sngle cross secton. Consequently t s to be expected that access to panel data wll ether enable some of the strong dstrbutonal assumptons used wth cross-sectonal data to be relaxed or result n estmates of cost effcency wth more desrable statstcal propertes. The fundamental problem s that n a sngle cross secton we get to observe each producer only once, and ths severely lmts the confdence n our cost effcency estmates. In the selecton of ndependent varables we must address the trade-off between usng techncal detals by applyng more nputs and addng the rsk of multcollnearty on the one hand, and dmnshng the nputs and sacrfcng potentally useful nformaton on the other hand. Note that we use the prelmnary analyss to select varables that have a sgnfcant nfluence on mlk cost functon. The lnear cost functon defned n equatons (1) and (4) s estmated usng ordnary least squares regresson. At ths step, we dentfy nputs expected to have a sgnfcant nfluence on cost functon before the fronter producton functon s estmated usng maxmum lkelhood estmaton. The dependent varable s a mlk cost per kg of mlk output (Y), and ndependent varables are average mlk yeld per cow (x 1 ), labour nput per 100 kg mlk (x 2 ), total feed cost per 1 kg of mlk (x 3 ) and number of mlkng cows n herd (x 4 ). The characterstcs of the selected data are summarsed n Table 1. Table 1. Data summary statstcs Defntons of varables Measure Characterstcs Y-mlk cost per kg of mlk output x 1 average mlk yeld per cow kroons kg x 2 - labour nput per 100 kg mlk hours x 3 - total feed cost per 1 kg of mlk kroons x 4 - number of mlkng cows n herd Years All panel Mean St.dev Mnmum Maxmum Mean St.dev Mnmum Maxmum Mean St.dev Mnmum Maxmum Mean St.dev Mnmum Maxmum Mean St.dev Mnmum Maxmum

4 28 One feature of the sample s that the mean value of dependent varable (mlk cost per kg of mlk output) s changng. In the years average mlk cost wth fluctuatons ncreased from 2.90 kroons to 4.70 kroons per kg and then decreased to 4.62 kroons per kg n Nearly analogously changes the mean value of ndependent varable x 3 total feed cost per 1 kg mlk. At the same tme mean values of other ndependent varables are changng wth almost constant trend. The average mlk yeld per cow (x 1 ) ncreased from 5,530 kg per cow n 2001 to 6,516 kg n The total labour nput x 2 (hours per 100 kg mlk) has decreased essentally (from 4.19 hours n 2001 to 2.68 hours n 2006). Consequently, the labour nput decreased 1.6 tmes. The average number of mlkng cows n herd, x 4, ncreased from 114 cows n 2001 to 134 cows n Ths ncrease s moderate as compared to decrease of labor nput. Consequently, the mlk producton n Estonan farms s not obtaned a stable state. Table 1 show, that the most crtcal s the year Ths stuaton may be explaned by the features of movng from the socalst economc system to market economes: The process of movng from command economes to market economes n Estona s not ended yet. Begnnng from 2004 Estona s one of the new members of the European Unon. Before 2004 the prces (ncludng prces of nputs for mlk producton) ncreased. At same tme the effcency of mlk producton s rsng (labour use decreases). After 2004 the economc stuaton changed. Consderng crcumstances descrbed before, one addtonal ndependent varables was ncluded n the mlk cost model: the trend varable x 5. Results and dscusson The fronter functons (1) and (4) are estmated for several alternatve models. To derve our preferred functonal form we estmated sx specfcatons (four alternatves for MI and two alternatves for MII). The specfcatons for MI alternatves are presented n Table 2. Table 2. Descrpton of model MI specfcatons Defnton of specfcaton MI-1 MI-2 MI-3 MI-4 Descrpton of the specfcatons mu µ Parameters eta η cross-sectonal, halfnormal neffcency, tmenvarant model cross-sectonal, truncatednormal neffcency, tmenvarant model y 0 1 panel-data, truncatednormal effcency y y 6 panel-data, half-normal effcency, tme-nvarant model The specfcatons for MII alternatves are presented n Table 3. Table 3. Descrpton of model MII specfcatons Defnton of specfcaton MII-1 MII-2 Descrpton of the specfcaton mu µ eta η T Parameters del0 δ 0 del1 δ 1 T del2 δ 2 panel-data, truncatednormal y 0 6 y y y panel-data, truncatednormal y 0 6 y y 0 The specfcatons and maxmum-lkelhood estmates of the parameters n the mlk cost stochastc fronter functon defned by equatons (1) and (4) for alternatve specfcatons are gven n Table 4. Table 4. Maxmum-lkelhood estmates for parameters of stochastc fronter producton functon of mlk costs for dfferent model specfcatons Parameter Alternatves of specfcaton Varable OLS MI-1 MI-2 MI-3 MI-4 MII-1 MII-2 Intercept β Mlk yeld β Labour nput β Feed cost β Number of cows β Trend β Sgma-squared σ Gamma γ Mu µ Eta η Ineffcency Average u Mnmum u mn Maxmum u max R

5 Modelng mlk cost n Estona: a stochastc fronter analyss approach 29 Table 4 also reports the parameters OLS estmates for alternatve MI and presents result summares of the results of varous MI and MII alternatves. Summary characterstcs for varous alternatves are: sgma-squared σ 2, gamma γ, mu µ, eta η, and summary characterstcs of cost (economcal) economcal neffcency (mnmum, mean and maxmum) and coeffcent of determnaton R 2. The coeffcents of the exploratory varables β n the mlk cost model (the stochastc fronter cost functon) are of partcular nterest to ths analyss. Next we analyse the parameter estmates n Table 4. The results n Table 4 ndcate that the OLS estmates (OLS) and SFA estmates (MI-1 and MI-2) are smlar, whereas the estmates for feed cost (β 3 ) are essentally equvalent. The estmates for ntercept (β 0 ), labour nput (β 2 ), number of cows (β 4 ) do not dffer essentally. Comparng the sgns of parameter estmates for dfferent mode specfcatons, one should conclude that only once the sgn s changng. In the case of ndependent varable mlk yeld per cow (β 1 ). The estmates of other ndependent varables for all varants have the same sgn postve or negatve. Consequently the SFA models are robust. It s mportant to note that the estmate sgn for mlk yeld per cow (β 1 ) s postve for OLS, and sgn s negatve for all SFA alternatves. The economc theory and practce assert that the model parameter should be negatve for the varable mlk yeld per cow. Consequently, n the case of OLS the estmate for ndependent varable, mlk yeld per cow, s not adequate and SFA are preferred. Comparng the parameter estmates for models MI and MII, one should conclude that parameter estmates practcally do not dffer. The models parameters sgns for all specfcatons (varants) are the same. Fnally t may be concluded that the OLS and SFA estmates don t dffer sgnfcantly. Next we analyse the summary characterstcs for SFA models n Table 4. Frst, we analyse the characterstcs for model MI (see equaton (1) and Table 2). Comparng the summary characterstcs n Table 4 t may be concluded that the characterstcs dffer n dfferent cross-sectonal data (MI-1 and MI-2) and panel data (MI-3 and MI-4) models. Comparng the estmates of sgma squared, σ 2 (σ 2 s calculated usng equaton (2a)), for model MI varants, one should conclude that estmates dffer. In the case of alternatve MI-4 (panel data, half-normal neffcency dstrbuton, tme-nvarant model) the value of σ 2 s mnmal (σ 2 =1.012) and n the case of alternatve MI-2 (cross-sectonal data, truncated-normal neffcency dstrbuton, tme-nvarant model) the value of σ 2 s maxmal (σ 2 =2.771). The values of σ 2 n Table 4 dffer approxmately 2.7 tmes. Comparng the estmates of sgma squared, σ 2,for model MII varants, one should conclude that estmates do not dffer. The values of parameter gamma, (γ), do not dffer substantally. The value of the parameter gamma, (γ), n estmated model MI-2 s maxmal. It mples that the predcted varance of neffcency (see equaton (2a)) s estmated to have a value hgher approxmately by a factor of 30 than the estmated value of varance of random varable V. That dfference s essental. The value of the parameter gamma, (γ), n estmated model MII-2 s mnmal. It mples that the predcted varance of neffcency s estmated to have a value hgher approxmately by a factor of 7.5 than the estmated value of varance of random varable V. Consequently, n dfferent varants the neffcency component nvolve dfferent amount of nformaton. Because the estmates for the parameter, η, s negatve, the neffcency of mlk cost for Estonan farmers tend to decrease over tme, accordng to alternatve MI-3. The values of the coeffcent of determnaton, R 2, are relatvely hgh. The mnmal value (0.479) and maxmal value (0.668) of R 2 n Table 4 does dffer. Thereby n cases of alternatves MI-4 (R 2 =0.668) and MI-3 (R 2 =0.612) the values of R 2 are hgher than n cases of alternatves MII-2 (R 2 =0.497) and MII-1 (R 2 =0.500). But at the same tme the values of R 2 for SFA models are lower than for OLS model (R 2 =0.707). Next we analyse the cost neffcency characterstcs n Table 4. It should to be mentoned, that cost neffcency s measured n unts of dependent varable (n unts of mlk cost). Consequently neffcency n Table 4 s measured n kroons per kg of mlk output. The average value of neffcency, u, for dfferent model varants does not dffer substantally. The average neffcency ranges between (MI-1) and (MI-2) for cross-secton models, and ranges between (MI-4) and (MII-2) for panel data models. Consequently, Estonan farmers on an average have a reserve to reduce mlk cost approxmately by 80 cents. It should to be noted, that neffcency s producer (farmer) specfc characterstc. Comparng the neffcency varablty characterstcs (mnmum and maxmum) n Table 4 t may be concluded that the characterstcs dffer n dfferent cross-sectonal data and panel data models. In the case of MI the neffcency ranges between and n alternatve MI-2 and, between and n alternatve MI-3. The predcted neffcences for model MI-2 exhbt less varablty than n MI-3. In the case of MI-3 mnmal neffcency equals (a reserve to reduce mlk cost s only by 4 cents) and the maxmal neffcency equals (a reserve to reduce mlk cost s very large by 3.23 kroons). The last value s authentc (s not astonshng), whle the two maxmal values of mlk cost n Table 1 are equal to 8.14 and Specfc analyss shows that n present case the actual mlk cost s equal to It should to be noted, that the same farm s most neffectve n all model varants. Consequently, there are reserves. In the case of most effectve farm (U=0.038) the actual mlk cost s equal to 1.96 kroons per kg of mlk output. So low was mlk cost n year For the varants MII-1 and MII-2 the varablty of neffcency s practcally the same. Next we analyse the dstrbutons of neffcency for consdered alternatve models. The Fgure 1 shows the hstograms of cost neffcency for dfferent model varants.

6 30 Fgure 1. Hstograms of cost neffcency for dfferent model varants As ndcated n Table 4, n three varants (MI-1, MI-4 and MII-1) half-normal dstrbuton for random varable U (neffcency) was assumed (parameter µ=0). As seen from Fgure 1, hstograms for those varants have asymmetrc character wth maxmum at zero. Consequently, n those cases the estmates of neffcency have half-normal dstrbuton. For other varants (MI-2, MI-3 and MII-2) the truncated normal dstrbuton was assumed. Fgure 1 shows, that hstograms for those varants have asymmetrc character wth maxmum approxmately at estmated value of parameter µ (see Table 4). For example, for varant MI-3 the estmated µ=0.319 and from the hstogram we can fnd approxmately the same maxmum value. Next we compare estmates of economcal effcency (cost neffcency) for consdered alternatve models. For that purpose we check the robustness of our cost (economcal) effcency results. A smple test of whether the rank of farms (DMU-s) s robust to dfferent model specfcaton s to estmate the Spearman Rank Correlaton coeffcent between the varous model alternatves (Frazer and Horrace 2003). We estmated cost (economcal) effcency for all the model alternatves and derved the rank of the farms (DMU-s). Then, rank correlaton coeffcent was estmated for all pars of model alternatves; the results are reported n Table 5. Table 5 provdes also rank correlaton coeffcents between ranks of farms (DMU-s) for dfferent model alternatves and ranks of farms obtaned usng OLS model. For the OLS model the rank of the farms (DMUs) was derved usng regresson resduals. The model

7 Modelng mlk cost n Estona: a stochastc fronter analyss approach 31 alternatves n Table 4 are grouped. The two frst models (MI-1 and MI-2) use cross-sectonal data and four last models (MI-3, MI-4, MII-1 and MII-2) panel data. Table 5. Spearman rank correlaton coeffcents Model varant OLS Model varants MI-1 MI-2 MI-3 MI-4 MII- 1 MII- 2 OLS MI MI MI MI MII MII As we can see from the estmates n Table 5, there s a very strong postve relatonshp across the varants of models estmated. So n the case of usng crosssectonal data, there s practcally functonal relatonshp across models (MI-1 and MI-2). In the case of usng panel data, there s very strong relatonshp across models (MI-3, MI-4) and (MII-1, MII-2). Thus, despte a dfference between the dfferent model specfcatons, we are able to assume that the order (rank) of effcent/neffcent DMU-s tend to be the same across model alternatves. Comparng the rank correlaton coeffcents between ranks of farms (DMU-s) for dfferent model alternatves and ranks of farms obtaned usng OLS model n Table 5, t may be concluded that the correlaton coeffcent dffer n dfferent cross-sectonal data and panel data models. So n the case of usng crosssectonal data, there s very strong relatonshp across models (MI-1 and MI-2) and OLS model, but n the case of panel data models there s a relatvely dense relatonshp across models (MI-3 and MI-4) and OLS model. In the case of model MII there s also a relatvely dense relatonshp across varants (MII-1 and MII-2) and OLS model. Hence, cost effcency rankngs are farly robust to model specfcaton for ths partcular data set. These results are consstent wth the exstng fndngs n the fronter lterature (Kumbhakar and Lowell (2000) and Frazer and Horrace (2003)). Conclusons In ths paper we have estmated the stochastc fronter cost functon for a panel of mlk cost data n Estonan farms and have estmated the cost (economcal) effcency of mlk producton n Estonan farms. By comparng the OLS, MI and MII models we may deduce: In the case of model MI (the neffcency dstrbutons mean value s constant), the OLS and SFA parameter estmates do not dffer sgnfcantly; the coeffcent of determnaton, R 2, for SFA models s lower than for OLS models. For the cross-sectonal data models the effcency scores are relatvely hgh (neffcency scores are relatvely low) n the varant MI-2. The rank correlaton coeffcents for all pars of model alternatves are very strong. For the panel data models MI-3 and MI-4 the predcted effcency scores exhbt practcally the same varablty as n cross-sectonal data models and tend to decrease over tme. In the case of panel data the SFA models the analyss gves some new nformaton. In the case of model MII (the neffcency dstrbutons mean value s dfferent), the OLS and SFA estmates also do not dffer sgnfcantly. The coeffcent of determnaton, R 2, for SFA models s lower than for OLS model. The effcency scores exhbt practcally the same varablty than n the model MI. Ths analyss has demonstrated that SFA can be mplemented for parameter estmaton of econometrc models and predcted effcency scores gve new addtonal nformaton about mlk producton n Estonan farms. Ths analyss showed that Estonan farmers on an average have a reserve to reduce mlk cost per kg of mlk output approxmately by 80 cents. Regardless of functonal form used, the effcency nformaton that emerges from the analyss s lmted to producer-specfc estmates of the cost of neffcency. Wth a sngle-equaton model, and wthout nput quantty or nput cost share data, t s not possble to decompose these estmates nto estmates of the cost of nput orented techncal neffcency and the cost of nput allocatve neffcency. A decomposton requres addtonal data and a smultaneous equaton model. Consequently, sngle-equaton cost fronter models are easy to estmate, but they generate lmted nformaton. If all that s desred s producer-specfc estmates of cost effcency, sngle-equaton models are adequate for the task. References Abdula, A., Tetje, H Estmatng techncal effcency under unobserved heterogenety wth stochastc fronter models: applcaton to northern German dary farms. European Revew of Agrcultural Economcs, 34, p Agner, D.J., Lovell, C.A.K., Schmdt, P., Formulaton and Estmaton of Stochastc Fronter Producton Functon Models. Journal of Econometrcs, 6, p Battese, D. E., Corra, G.S., Estmaton of Producton Fronter Model: Wth Applcaton to the Pastoral Zone of Eastern Australa. Australan Journal of Agrcultural Economcs, 21, p Battese, G.E., Coell, T.J., Predcton of Frm- Level Techncal Effcences Wth a Generalsed Fronter Producton Functon and Panel Data. Journal of Econometrcs, 38, p Battese, D. E., Coell, T.S., Fronter Producton Functons, Techncal Effcency and Panel Data: wth Applcaton to Paddy Farmers of Inda. Journal of Productvty Analyss 3, p

8 32 Battese, D.E., Broca, S.S., Functonal Forms of Stochastc Fronter Producton Functons and Models for Techncal Ineffcency Effects: A Comparatve Study for Wheet Farmers n Pakstan. Journal of Productvty Analyss, 8, p Bravo-Ureta, B.E., Sols, D., Lo pez, V.H.M., Marpan, J.F., Tham, A., Rvas, T., Techncal effcency n farmng: a meta-regresson analyss. Journal of Productvty Analyss, 27, p Coell, T Recent developments n fronter modellng and effcency measurement. Aust. J. Agrc. Econ. 39, Coell, T., A Gude to FRONTIER Verson 4.1: A Computer Program for Stochastc Fronter Producton and Cost Functon Estmaton. CEPA Workng Paper 96/07, Coell, T., Battese, G.E., Identfcaton of factors whch nfluence the techncal neffcency of Indan farmers. Australan Journal of Agrcultural Economcs, 40, p Frazer, I.M., Horrace, W.C., Techncal Effcency of Australan Wool Producton: Pont and Confdence Interval Estmates. Journal of Productvty Analyss 20, p Hadr, K., Whttaker J., Effcency, envronmental contamnants and farm sze: testng for lnks usng stochastc producton fronters. Journal of Appled Economcs, 11, p Hughes, M.D., A Stochastc Fronter Cost Functon for Resdental Chld Care Provson. Journal of Appled Econometrcs, 3, p Kumbhakar, S.C., Lowell, C.A.K., Stochastc Fronter Analyss. Cambrdge Unversty Press, Cambrdge, 333 p. Lawson, L.G., Agger, J.F., Lund, M., Coell, T., Lameness, metabolc and dgestve dsorders, and techncal effcency n Dansh dary herds: a stochastc fronter producton functon approach. Lvestock Producton Scence, 91, p L, S., Smar, L., Wlson, P.W., Zelenyuk, W., Introducton for Journal of Productvty Analyss specal ssue on transtonng economcs. Journal of Productvty Analyss, 29, p. 77. Põldaru, R., Roots, J., 2001a. On the Implementaton of the Prncpal Component Regresson for the Estmaton of the Econometrc Model of Gran Yeld n Estonan Countes. Problems and Solutons for Rural Development, Internatonal Scentfc Conference Reports (Proceedngs) (ed Kozlnsks, V.). Latva Unversty of Agrculture. Jelgava, p Põldaru, R., Roots, J., 2001b. Bayesan Statstcs BUGS n the Estmaton of the Econometrc Model of Gran Yeld n Estonan Countes. Agrculture n Globalsng World, Proceedngs volume II of Internatonal Scentfc Conference (ed. J. Kvstk). EAA No. 15/2001,Tartu, p Põldaru, R., Roots, J., The Estmaton of the Econometrc Model of Gran Yeld n Estonan Countes Usng Neural Networks. VAGOS, No. 57, Akademja, Kaunas, p Põldaru R., Roots J., Ruus R., 2003a. A Perspectve of Usng Data Mnng Assocaton Rules n Rural Areas., Transactons of the Estonan Agrcultural Unversty, No 218, Perspectves of the Baltc States Agrculture under the CAP Reform, September, Proceedngs of Internatonal Scentfc Conference (ed Kerner, Ü.), Tartu, p Põldaru R., Roots J. Ruus R., 2003b. A Perspectve of Usng Data Mnng n Rural Areas. VAGOS, No. 61, Akademja, Kaunas, p Põldaru R., Roots J. Ruus R., 2004a. Usng Fuzzy Regresson n Rural Areas. Economc Scence for Rural Development Possbltes of Increasng Compettveness, Proceedngs of the Internatonal Scentfc Conference No 7 (eds. Strks, V., Zandere, E.). Jelgava, p Põldaru R., Roots J., 2004b. Modellng Gran Yeld n Estonan Countes: A Stochastc Fronter Analyss Approach. Data Envelopment Analyss and Performance Management, Proceedngs of the 4th Internatonal Symposum of DEA 5th 6th September 2004 Aston Busness School Aston Unversty UK, p Põldaru R., Jakobson R., Roosmaa T., Roots J., Ruus R., Vra A-H., 2004c. Support Vector Machne Regresson n Estmatng Econometrc Model Parameters. Informaton Technologes and Telecommuncaton for Rural Development, Proceedng of the Internatonal Scentfc Conference Jelgava, Latva, 6 7 May, Jelgava, p Põldaru R., Roots J., Vra A.-H., 2004d. The estmaton of the econometrc model of mlk yeld per cow: a support vector machne regresson approach. Operatons Research 2004 Internatonal Conference, Tlburg Unversty, Netherlands, 1 3 September, Tlburg, p Põldaru R., Roots J., Vra A.-H., Estmatng econometrc model of average total mlk cost: a support vector machne regresson approach. Economcs and Rural Development, 1, p Renhard S, Lovell C, Thjssen G., Envronmental effcency wth multple envronmentally detrmental varables; estmated wth SFA and DEA. European Journal of Operatonal Research, 121, p Schmdt, P., Lovell, C.A.K., Estmatng Techncal and Allocatve Ineffcency Relatve to Stochastc Producton and Cost Fronters. Journal of Econometrcs, 9, p Sharma, K.R., Leung, P.S., Zalesk, H.M., 1997 Productve effcency of the swne ndustry n Hawa: stochastc fronter vs. Data envelopment analyss. Journal of Productvty Analyss, 8, p Stevenson, R.E., Lkelhood Functons for Generalsed Stochastc Fronter Estmaton. Journal of Econometrcs, 13, p

9 Modelng mlk cost n Estona: a stochastc fronter analyss approach 33 Pma tootmskulude (omahnna) modelleermne Eests: stohhastlse pranalüüs meetodl Kokkuvõte Antud artkls kästletakse Eest ettevõtete pma arvutuslke tootmskulude (oma)hnna mudel koostamst stohhastlse pranalüüs meetodl. Artkls antakse lühülevaade stohhastlse praanalüüs meetod olemusest ja kasutamsvõmalustest tootmskulude modelleermsel. Töös kästletakse kahte ernevat pma arvutuslke tootmskulude (omahnna) mudelt. Mudelte parameetrte hndamseks on koostatud vastav andmestk, ms kujutab endast tasakaalustatud andmepaneel 45 ettevõtja kuue aasta ( ) andmetest. Andmestku koostamsel on kasutatud põllumajanduslku raamatupdamse andmebaas (FADN) andmed. Mudel parameetrte ledmseks (hndamseks) kasutat tarkvarapakett FRONTIER (versoon 4.1). Kahe erneva mudel jaoks koostat kokku 6 ernevat varant. Artkls võrreldakse ja analüüstakse ernevate varantde parameetred ja efektvsusnätajad. Stohhastlse pranalüüs meetod abl letud mudel parameetrd on võrreldus klasskalse regressoonanalüüs tulemustega. Analüüs nätas, et stohhastlse pranalüüs meetodt on võmalk kasutada ökonomeetrlse mudel parameetrte hndamseks, ga ettevõtja jaoks reservde kättenätamseks pma tootmskulude vähendamseks nng ettevõtjate majanduslku tegevuse hndamseks (prognoosmseks).