Efficiency Measurement in Greek Dairy Farms: Stochastic Frontier vs. Data Envelopment Analysis

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1 Internatonal Journal of Economc Scences and Appled Research 1 (2): Effcency Measurement n Greek Dary Farms: Stochastc Fronter vs. Data Envelopment Analyss A.M. Theodords Arstotle Unversty, School of Agrculture, Department of Agrcultural Economcs Thessalonk, Greece A. Psychoudaks Correspondng Author Arstotle Unversty, School of Agrculture, Department of Agrcultural Economcs Thessalonk, Greece E-mal: psychoud@agro.auth.gr Abstract Parametrc Stochastc Fronter Analyss (SFA) and non-parametrc Data Envelopment Analyss (DEA) have become very popular n the analyss of productve effcency. Ths paper undertakes a comparson of the SFA and the constant returns to scale (CRS) and varable returns to scale (VRS) output-orented DEA models, based on a sample of 165 dary farms n Greece. However, the am of ths paper s not only to compare estmates of techncal effcency obtaned from two approaches, but also to produce effcency data about the farms studed, whch have mplcatons for agrcultural polcy to mprove dary producton. The results ndcate that there s a potental for ncreasng producton n the dary farms through mproved effcency. Keywords: Data Envelopment Analyss, Stochastc Fronter Analyss, Dary Farms JEL classfcaton: Q18, D24, Q12 Many thanks to Dr. Trotman for readng the paper and gvng me valuable correctons concernng the use of Englsh language. 53

2 Theodords A.M. and Psychoudaks A. 1. Introducton Effcency measurement has been the concern of researchers wth an am to nvestgate the effcency levels of farmers engaged n agrcultural actvtes. Based on Farrell s (1957) poneerng artcle, several approaches to effcency measurement have been developed. Among these, Stochastc Fronter analyss (SFA) models and Data Envelopment Analyss (DEA) models have proved an extremely useful tool n measurement of the techncal effcency of producton unts. The stochastc fronter approach was ntated by Agner et al. (1977) and Meeusen and van der Broek (1977), whle DEA approach was proposed by Charnes et al. (1978). Many authors n economc lterature have dealt wth the two approaches. Comprehensve revews can be found n Kumbhakar and Lovell (2000), Seford and Thrall (1990), Fred et al. (1993), Coell, Rao and Battese (1998), Bravo-Ureta and Pnhero (1993), Coell, (1995), Cooper et al. (2000). The man advantage of non-parametrc DEA s that t does not requre specfcaton of the functonal form of the producton functon. Furthermore, DEA smultaneously utlzes multple outputs and multple nputs wth each beng stated n dfferent unts of measurement. DEA focuses on revealed best practce fronters rather than on central-tendency propertes or fronters and t generates a set of peer unts wth whch a unt s compared. However, several propertes that represent strengths n one capacty may act as lmtatons n another. DEA s determnstc and attrbutes all the devatons from the fronter to neffcences,.e. at frst sght, the method does not have any statstcal foundaton; t s not possble to make nference about estmated DEA parameters, senstvty, asymptotc propertes, etc. Recently, bootstrap technques have been appled n order to obtan measures of statstcal precson n the DEA estmates (Smar and Wlson, 2000a, 2000b, Löthgren and Tambour, 1999). In contrast, the parametrc stochastc fronter approach treats devatons from best-practce as comprsng both random error (whte nose ) and neffcency. SFA also assumes a structure for the best-practce fronter and then fts a curve. An advantage of the econometrc approach s that t allows for formal statstcal testng of hypotheses and the constructon of confdence ntervals (Hjalmarsson et al., 1996). The man drawback of the approach s that t requres a pre-specfcaton of the functonal form and an explct dstrbutonal assumpton for the techncal neffcency term. The man purpose of ths study s to compare techncal effcency measures from SFA and DEA models and to test f there are sgnfcant dfferences n the estmates of effcency. A few studes (Hjalmarsson et al., 1996; Kaltzandonakes and Dunn, 1995; Bjurek et al., 1990; Wadud and Whte, 2000; and Sharma et al., 1997) have compared emprcal performance of the two technques. As t concerns the dary sector, there exst many studes whch apply one of the two methods (Kumbhakar and Hjalmarsson, 1993; Tauer and Mshra, 2003; Cuesta, 2000; Bravo-Ureta and Reger, 1991; Kumbhakar and Hesmat, 1995; Weersnk et al., 1990; Manos and Psychoudaks, 54

3 Effcency Measurement n Greek Dary Farms: Stochastc Fronter vs. Data Envelopment Analyss 1997; Hallam and Machado, 1996 and Lujt and Hllebrand, 1991), but there s only one (Renhard, 1999), at least to our knowledge, comparatve study of SFA and DEA approach concernng the dary sector. Furthermore, ths study contrbutes to the exstng lterature wth the use of data from Greek dary farms. For the purpose of ths paper, the analyss s lmted to techncal effcency. A Cobb-Douglas stochastc fronter producton functon and constant returns to scale (CRS) and varable returns to scale (VRS) output-orented DEA models are estmated. The analyss s based on farm accountng data from Greek dary farms, whch have not been studed before. The paper s organzed as follows: Secton 2 descrbes the Stochastc Fronter Analyss and Data Envelopment Analyss models. Secton 3 descrbes the dary data. Secton 4 contans the emprcal results and ther mplcatons. Secton 5 concludes the paper. 2. Theoretcal Models 2.1 Stochastc Fronter Model The stochastc fronter producton functon can be expressed as: y = f( x; β ) exp{ v u} = 1, 2,3,..., n (1) where y s scalar output, x s a vector of nputs, and β s a vector of parameters to be estmated. The frst error component, v, s assumed to be ndependently and dentcally dstrbuted (d) and symmetrc, dstrbuted ndependently of the u and captures the effects of statstcal nose. The second error component, u 0, s ntended to capture the effects of techncal effcency component and t s assumed to be ndependently and 2 dentcally dstrbuted truncatons (at zero) wth mean, μ, and varance, σ u. The techncal effcency of the th farm, denoted by TE, can be estmated as: TE = exp( u ) (2) The predcton of techncal effcences s based on the condtonal expectaton of gven the values of v u (see Jondrow et al. (1982) and Battese and Coell (1988)). Ths method allows a drect comparson between the results from the stochastc fronter approach and DEA. Coell (1995) suggests that the stochastc fronter method s recommended for use n agrcultural applcatons, because measurement error, mssng varables and weather, are lkely to play a sgnfcant role n agrculture. More detals and further approaches can be obtaned from books edted by Fred, Lovell and Schmdt (1993), Coell, Rao and Battese (1998) and Kumbhakar and Lovell (2000). 2.2 Data Envelopment Analyss The non-parametrc approach to effcency measurement obtans techncal effcency e u 55

4 Theodords A.M. and Psychoudaks A. estmators as optmal solutons to mathematcal programmng problems. Charnes et al. (1978, 1979, 1981) formulated the Data Envelopment Analyss (DEA) methodology, whch defnes a non-parametrc fronter and measures the effcency of each unt relatve to that fronter. Assumng that there are n decson makng unts (DMUs), each producng sngle output by usng m dfferent nputs and the th DMU produces y unts of output usng x k unts of the kth nputs, the varable returns to scale (VRS) outputorented DEA model for the th DMU s expressed as follows: Max θ (3) θ, λj subject to: n j= 1 n j= 1 n j= 1 λ y θ y s = 0 j j λ x + e = x j kj k k λ = 1 j λ j 0; s 0, ek 0; k = 1,, m nputs; j = 1,, n DMUs; where θ s the proportonal ncrease n output possble for the th DMU; s s the output slack; e k s the kth nput slack; and λ j s the weght of the jth DMU. When the restrcton n λ j = 1 s removed the constant returns to scale (CRS) s j= 1 obtaned. The output-orented DEA model maxmzes the proportonal ncrease n output whle remanng wthn the producton possblty set. The proportonal ncrease n output s obtaned when output slack s zero. The th farm s effcent, whch means that the unt les on the fronter when θ = 1, λ = 1, and λ = 0 for j. The fronter level of producton for the th farm, denoted by * y, s gven by n * = λj j = θ j= 1 j (4) y y y. (5) The output-orented measure of techncal effcency of the th farm unt, denoted by TE, can be estmated by 56

5 Effcency Measurement n Greek Dary Farms: Stochastc Fronter vs. Data Envelopment Analyss y 1 TE = =. (6) * y θ Ths measure can be compared drectly wth the measure of techncal effcency obtaned under the stochastc producton fronter. Both technques consder the observed producton relatve to the correspondng potental producton, gven the quanttes of the nputs used. Hence, the techncal effcency scores from the output-orented DEA model are comparable wth those obtaned from the stochastc fronter model. The scale effcency measure for the th farm, denoted by SE, can be calculated from the relatonshp of the estmate of techncal effcency of the th farm n the VRS VRS CRS DEA ( TE ) and that n the CRS DEA ( TE ) as: CRS TE SE = (7) VRS TE where SE = 1 ndcates constant returns to scale and SE < 1 ndcates scale neffcency. The nature of scale neffcency can be of two types. Frst, a farm s too small and belongs to the secton of the fronter where ncreasng returns to scale preval; second a farm s too large and belongs to the secton of the fronter where decreasng returns to scale preval. In order to determne the type of scale neffcency the sum of the weghts s nspected. Accordng to Banker and Thrall (1992) f the sum of the weghts s greater than 1.0 we have decreasng returns to scale and f the sum of the weghts s less than 1.0 we have ncreasng returns to scale. Constant returns to scale occur when the sum of weghts equals one. (See also Banker et al., 1984; Löthgren and Tambour, 1996; Al and Seford, 1993; and Favero and Pap, 1995). Table 1. Summary statstcs for varables Varable Sample mean Standard Devaton Mnmum Maxmum Gross Output ( ) Labor (hours) Fxed Cost ( ) Varable Cost ( ) Data The farm accountng data for ths emprcal applcaton was collected from 12 prefectures n the regons of Macedona and Thessaly through a farm management survey carred out durng the perod of A sample of 165 dary farms, whch are located manly n Macedona, Greece, was surveyed for the applcaton of ths analyss. All farms have the requred characterstcs for the emprcal applcaton of both DEA and SFA. The summary statstcs of the varables gathered from the farms are 57

6 Theodords A.M. and Psychoudaks A. reported n Table 1. In the specfcaton chosen n ths study, the conventonal nputs have been aggregated nto three categores (labor, fxed captal and varable captal). The labor nput conssts of total labor, measured n hours. Fxed captal s composed of buldngs, machnery and lvestock for breedng and utlsaton, measured n Euros. The varable captal contans fertlsers, fuel, hred labour, purchased feed, rent of land and other varable nputs, all expressed n Euros. The rent of the land s ncluded n the varable captal snce the crop producton has been used as feedstuff n the farms. Gross output, measured n Euros, s selected as the dependent varable n ths study. The standard devaton of the average Gross output ndcates the large varablty of output among the farms. 4. Emprcal Results 4.1 Stochastc Fronter Results The maxmum lkelhood estmates of the Cobb-Douglas stochastc fronter are reported n Table 2. Specfcally, n ths table the coeffcents of the estmated varables, ther t- ratos and the varance of the parameters are presented. Maxmum lkelhood estmates of the parameters of the stochastc fronter model are obtaned usng the program FRONTIER 4.1 (Coell, 1996). All coeffcents are sgnfcant at the 1 percent level. As expected, the sgns of the slope coeffcents of the stochastc fronter are postve. The estmated value for the varance parameter, γ, n the stochastc producton s sgnfcant, suggestng that neffcency was present n producton and that the tradtonal average producton functon s not an adequate representaton of the data. Hence, techncal neffcency effects have sgnfcant mpact on output (Wadud and Whte, 2000; Sharma et al. 1997; Hjalmarsson et al. 1996). The estmate of γ ndcates that the porton of the one-sded error component n the total varance s as hgh as 61.6 percent. Thus, 61.6 percent of varaton n the data between farms can be attrbuted to neffcency and the remanng 38.4 percent s pure nose. The estmated parameter σ s also found to be statstcally sgnfcant at the 1 percent level. Ths result, whch s consstent wth Wadud and Whte (2000), Sharma et al. (1997) and Hjalmarsson et al. (1996), suggests that a conventonal producton functon s not an adequate representaton of the data. The mean techncal effcency estmated for the SFA approach s A more flexble translog producton functon was also appled. A Generalzed Lkelhood Rato test (LR) was performed to test whether or not Cobb-Douglas producton functon could be used as an approprate form of the producton functon estmated n ths study. The result of the LR test suggested that translog stochastc producton functon s an nadequate representaton of the data and t s rejected confdently n favor of the Cobb-Douglas. The test statstc was equal to 8.3, whch s less than 12.6, the 95 percent crtcal value for the Ch-squared dstrbuton wth sx degrees of freedom. The results presented here refer solely to the Cobb-Douglas 2 ε 58

7 Effcency Measurement n Greek Dary Farms: Stochastc Fronter vs. Data Envelopment Analyss producton functon. Another LR test was conducted to test the dstrbuton of the neffcency effects. The null hypothess, whch states that the half-normal dstrbuton s an adequate representaton for the dstrbuton of the neffcency effects could not be rejected. Table 2. Maxmum-lkelhood estmates of the Cobb-Douglas stochastc producton fronter model Name of Varables Parameters Coeffcents t-ratos Stochastc fronter Constant β (0.2885) Labor β *** (0.0603) Fxed Cost β *** (0.0459) Varable Cost β *** (0.0429) Varance Parameters Sgma-squared σε = σu + σv *** (0.0317) Gamma 2 2 γ = ( σu / σε ) *** (0.1985) Sgma-squared of u 2 σ u Sgma-squared of v 2 σ v Log-lkelhood Note: *** ndcate the varables are sgnfcant at the 1% level of sgnfcance, respectvely. Fgures n parentheses ndcate standard errors. The value of the elastcty of scale, whch s found to be statstcally sgnfcantly dfferent from unty, s 1.1, mplyng that dary farms operate under mldly ncreasng returns to scale, a fndng, whch s smlar to that of Renhard (1999). 4.2 DEA Fronter Results The constant returns to scale (CRS) and varable returns to scale (VRS) output-orented DEA models are estmated. The method has been appled to the same sample (same number of farms) and the same output and nput varables as for the stochastc fronter model. As t has been already mentoned n the prevous secton, the output orentaton 59

8 Theodords A.M. and Psychoudaks A. has been selected because the techncal effcency scores obtaned from the DEA method are comparable wth those of the stochastc fronter producton functon. Table 3. Frequency dstrbuton of techncal effcency estmates from both the stochastc fronter and techncal and scale effcency from the DEA models Data Envelopment Analyss Stochastc fronter CRS VRS SE Effcency No. of % of No. of % of No. of % of No. of % of Score farms farms farms farms farms farms farms farms < Total The mean techncal effcences estmated for the CRS and VRS DEA approaches are and 0.685; a result whch s consstent wth the theory that the VRS fronter s more flexble and envelops the data n a tghter way than the CRS fronter. The mean techncal effcences of the DEA models ndcate that there s substantal neffcency for the dary farms n the sample, whch confrms the expectatons. Seventeen farms are fully techncally effcent n terms of the VRS model and 9 farms are fully techncally effcent under the CRS model. The techncal effcency scores estmated under the CRS DEA fronter are equal to, or less than those calculated under the VRS DEA model. Ths relatonshp, as stated above, s used to obtan the measure of scale effcency SE. The scale effcency ndex for the sample ranges from to wth a sample mean and standard devaton of and respectvely. Of the 165 farms, 27 show CRS, 61 show IRS and 77 show DRS. The frequency dstrbuton of the effcency estmates obtaned from the stochastc fronter and DEA model are presented n Table 3, whle ther summary statstcs n Table 4. 60

9 Effcency Measurement n Greek Dary Farms: Stochastc Fronter vs. Data Envelopment Analyss Table 4. Summary statstcs of effcency estmates from both the stochastc fronter and DEA model Effcency score SF CRS VRS SE Mean Mnmum Maxmum Standard Devaton Skewness Kurtoss Comparson of the Effcency Results Two dfferent approaches have been appled to measure the techncal effcency of dary farms. The mean effcency for each of the methods s reported n table 4. Effcency measure obtaned from the stochastc fronter model s greater than that obtaned from the VRS and CRS DEA model. DEA effcency scores was expected to be less than those obtaned under the specfcatons of stochastc fronter because the DEA approach attrbutes any devaton of the data from the fronter to neffcency, whle stochastc fronter analyss acknowledges the fact that random shocks beyond the control of the farmers can affect output. Both the CRS and VRS DEA measures exhbt greater varablty than the stochastc fronter effcency measure. Spearman rank correlaton coeffcents between the techncal effcency rankngs obtaned from the stochastc fronter and the DEA are reported n Table 5. The general mpresson here s that all correlaton coeffcents are postve and hghly sgnfcant at the 1 percent level. The strongest correlaton s obtaned between the effcency rankngs estmated from the VRS and CRS DEA model. The weakest correlaton s acheved between the rankngs from the stochastc producton fronter and the VRS DEA model. There are very few studes whch have compared the techncal effcency estmates derved from the stochastc parametrc fronter and determnstc nonparametrc fronter. Sharma et al. (1997) reported smlar results wth ours, whle Wadud and Whte (2000) reported a greater mean techncal effcency (0.858) obtaned from the VRS DEA model than those of both CRS DEA and stochastc fronter model (0.789 and respectvely). However, Wadud and Whte (2000) dd not fnd a greater varablty of techncal effcences from the DEA models than from the stochastc fronter effcency measures. Hjalamarsson et al. (1996) reported both smlar and dssmlar results obtaned from the stochastc fronter analyss and, the DEA fronter analyss, dependng upon the ncluson of the control varables n the stochastc fronter and the sequental or ntertemporal specfcaton n the DEA fronter. Kalatzandonakes and Dunn (1995) found a sgnfcantly hgher level of mean techncal effcency under CRS DEA (0.93) than under the stochastc producton fronter model 61

10 Theodords A.M. and Psychoudaks A. (0.74), whch s opposte from what we have found n ths study. Fnally, the results from Renhard (1999), who appled the two fronter methods to a dary sample usng panel data, are very smlar to ours. Renhard (1999) found that SFA techncal effcency score (0.889) are hgher (by about 10 percent) than CRS DEA effcency score (0.783) and exhbts less varablty. Table 5. Spearman rank correlaton matrx of techncal effcency rankngs of sample dary farmers obtaned from dfferent methods. TE SF TE VRS TE CRS TESF TE VRS TE CRS Implcatons The dary sector s one of the most heavly supported and s protected by the Common Agrcultural Polcy (CAP) mechansms. The mlk quota regme (ntroduced n 1984) has put a lmt on the amount of mlk that dary farmers produce each year, n order to reduce the mbalance between supply and demand on mlk and mlk products market and the resultng structural surpluses, thereby achevng better market equlbrum. However, n Greece where the Medterranean clmatc condtons preval, the country experences a permanent defct n ts dary producton. Greece s a net mporter of mlk and mlk products. The natonal reference quantty for Greece s 820,513 tones (Greece has succeeded an ncrease n ts natonal quota by almost 100,000 tones, see EU Councl Regulaton No 1788/2003), whereas ts mlk producton s only 721,261 tones. It s of partcular nterest to examne the potental of mlk producton n Greece, f dary farms could operate effcently. Table 6 presents, accordng to farm sze, the average levels of the actual outputs and fronter outputs relatve to the stochastc and DEA fronters. The farms were dvded n ths manner n order to get a close approxmaton as possble to the structure of Greek dary sector and to nclude a satsfactory number of farms n each category. Based on the stochastc results, farms n the last category (>125 cows) could, on average, ncrease ther output by 17.8 percent, farms n the thrd category ( cows) by 16.3 percent, farms n the second category (25-75 cows) by 14.2 percent, and small farms (<25 cows) by 18.6 percent by producng ther fronter outputs. The correspondng values for the VRS DEA fronter are 9.7 percent, 18.2 percent, 28.0 percent and 36.9 percent and those for the CRS DEA fronter are 20.5 percent, 21.8 percent, 30.9 percent and 40.4 percent, respectvely. These results ndcate that dary producton could have been ncreased substantally. Ths ncreased output could restore the equlbrum between supply and demand n the nternal dary products market n Greece. Furthermore, t would ncrease 62

11 Effcency Measurement n Greek Dary Farms: Stochastc Fronter vs. Data Envelopment Analyss the proftablty and the compettveness of Greek dary sector, snce ncreased revenues would compensate for the hgh producton costs. Table 6. Average actual and fronter output for Greek dary producers by farm sze (n euros). Note: Fgures n parentheses are standard devatons. Farm sze Number of Farms < 25 cows cows cows 27 > 125 cows 17 Total farms 165 Actual output (16425) (55207) (117805) (125838) (142463) SF output (19137) (61602) (123691) (136221) (164120) DEA fronter output VRS CRS (22528) (22283) (65686) (65661) (106642) (116182) (102370) (130874) (156199) (166777) 5. Concluson In ths paper two alternatve approaches are appled for the estmaton of techncal effcency, SFA and DEA. The econometrc fronter model s estmated under the specfcaton of the Cobb-Douglas stochastc fronter producton model. A more flexble translog stochastc fronter s also appled but t s rejected n favor of the Cobb-Douglas model. In the DEA analyss, the output-orented fronters are estmated under the specfcatons of constant and varable returns to scale. Both approaches are used n order to estmate the techncal effcency of 165 Greek dary farms. The objectve of the paper s to compare the measures of techncal effcency obtaned from the two approaches and to contrbute to the exstng relevant lterature wth the use of data from Greek dary farms. The estmated mean techncal effcency n the stochastc fronter model s larger than those obtaned from the DEA analyss. Accordng to the spearman rank coeffcents the correlaton between the two approaches s postve and hghly sgnfcant. The hghest correlaton s observed between the stochastc fronter and the VRS DEA. The dary farms appear to be characterzed by mldly ncreasng returns to scale under the econometrc specfcaton, but by ncreasng and domnantly decreasng returns to scale under the DEA approach. 63

12 Theodords A.M. and Psychoudaks A. Results from both econometrc and programmng fronter ndcate that there are substantal producton neffcences among the sample dary farmers. The sample dary farmers, gven the exstng technology, could, on average, enhance ther producton by percent and mprove ther compettve poston f they could operate effcently. References Agner D.J., Lovell C.A.K. and Schmdt P. (1977): Formulaton and Estmaton of Stochastc Fronter Producton Functon Models, Journal of Econometrcs 6: Al A.L. and Seford L.M. (1993): The Mathematcal Programmng Approach to Effcency, In Fred H.O.; Knox Lovell C.A. and Schmdt S.S. (eds.): The Measurement of Productve Effcency: Technques and Applcatons. Oxford Unversty Press, New York: Banker R.D. and Thrall R.M. (1992): Estmaton Returns to Scale Usng Data Envelopment Analyss, European Journal of Operatonal Research 62: Banker R.D.; Charnes A. and Cooper W.W. (1984): Some Models for Estmatng Techncal and Scale Ineffcency, Data Envelopment Analyss, Management Scence 30: Battese G.E. and Coell T.J. (1988): Predcton of Frm-level Techncal Ineffcences wth a Generalzed Fronter Producton Functon and Panel Data, Journal of Econometrcs 38: Bjurek H.L., Hjalmarsson L. and Førsund F.R.(1990): Determnstc Parametrc and Nonparametrc Estmaton n Servce Producton, Journal of Econometrcs 46: Bravo-Ureta B.E. and Reger L. (1991): Dary Farm Effcency Measurement Usng Stochastc Fronters and Neoclasscal Dualty, Amercan Journal of Agrcultural Economcs 73 (2): Bravo-Ureta B.E and Pnhero A.E. (1993): Effcency Analyss of Developng Country Agrculture: A Revew of Fronter Functon, Agrcultural and Resource Economcs Revew 22: Charnes A.; Cooper W.W. and Rhodes E. (1978): Measurng the Effcency of Decson Makng Unts, European Journal of Operatonal Research 2 (6): Charnes A.; Cooper W.W. and Rhodes E. (1979): Short Communcaton: Measurng the Effcency of Decson Makng Unts, European Journal of Operatonal Research 3 (4): 339. Charnes A.; Cooper W.W. and Rhodes E. (1981): Evaluatng Program and Manageral Effcency: An Applcaton to Data Envelopment Analyss to Program Follow Through, Management Scence 27 (6): Coell T.J. (1995). Recent Developments n Fronter Modellng and Effcency Measurement, Australan Journal of Agrcultural Economcs 39:

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