Technical efficiency of Kansas arable crop farms: a local maximum likelihood approach

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1 Techncal effcency of Kansas arable crop farms: a local maxmum lkelhood approach Boual Guesm* a, Teresa Serra a, and Allen Merrl Featherstone b a Centre de Recerca en Economa Desenvolupament Agroalmentar (CREDA-UPC-IRTA), b Department of Agrcultural Economcs, Kansas State Unversty. *Correspondng author. Parc Medterran de la Tecnologa, Edfc ESAB, Avnguda del Canal Olímplc s/n, 886 Castelldefels, SPAIN. Tel.: ; Fax: E-mal address: boual.guesm@upc.edu Selected Paper prepared for presentaton at the Agrcultural & Appled Economcs Assocaton s 13 AAEA & CAES Jont Annu al Meetng, Washngton, DC, August 4-6, 13 Copyrght 13 by [authors]. All rghts reserved. Readers may make verbatm copes of ths document for non-commercal purposes by any means, provded ths copyrght notce appears on all such copes. 1

2 Abstract The present study uses local maxmum lkelhood (LML) methods recently proposed by Kumbhakar et al. (7) to assess the techncal effcency of arable crop Kansas farms. LML technques overcome the most relevant lmtatons assocated to manstream parametrc stochastc fronter models. Results suggest that Kansas farms reach techncal effcency levels on the order of 9%. These results are compared wth another flexble effcency assessment alternatve: the determnstc data envelopment analyss (DEA). Keywords: Techncal effcency, Nonparametrc, Local maxmum lkelhood approach JEL classfcaton: C14, Q1, D4 1. Introducton Techncal effcency s a prerequste for economc effcency, whch n turn ensures the economc vablty and sustanablty of a frm. Assessment of frms techncal effcency levels has drawn broad research nterest. Such study s mportant for producers, as t asssts ratonal nput allocaton to acheve desred output levels, whch strengthens a frms capacty to face changng market condtons, ncreasng nput costs and economc hardshps. It s also relevant for polcy makers nterested n enhancng frms economc performance and compettveness, and promotng economc development. As s well known, the analyss of techncal effcency assesses to what extent frms are able to maxmze ther output levels wth mnmum use of nputs. Two man approaches have been wdely used n the effcency lterature namely, parametrc (Stochastc Fronter Analyss - SFA) and nonparametrc approaches (Data Envelopment Analyss - DEA) (Tzouvelekas et

3 al., 1, ; Oude Lansnk et al., ; Splänen and Oude Lansnk, 5; Lohr and Park, 6). Whle both encompass several advantages, they are also characterzed by some shortcomngs. An mportant dfference between these two approaches s that the stochastc producton fronter (SPF) allows for the stochastc component of producton. Ths makes ths technque suted to assess producton processes nvolvng random varables. Most agrcultural technologes are stochastc due to unexpected stochastc changes n producton (weather nfluences, for example) and other factors that are not under the control of the farm. Further, agrcultural producton studes may be affected by measurement and varable omsson errors (Coell, 1995; Chakraborty et al., ; Oude Lansnk et al., ). Ths makes the SPF approach suted for agrcultural performance measurement. The SFA further permts the conduct of conventonal statstcal tests of hypotheses. However, ths approach presents mportant drawbacks: t reles on the assumpton of a parametrc functonal form representng the producton fronter, as well as on a dstrbutonal assumpton for the random nose and neffcency error components. Several studes show that techncal effcency results are senstve to estmaton methods and functonal form specfcatons (Ferrer and Lovell, 199; Coell and Perelman, 1999; Ruggero and Vtalano, 1999; Chakraborty et al., 1). Inadequate parametrc representatons of the fronter and the error dstrbutons can lead to based effcency estmates (Kumbhakar et al., 7; Martns-Flho and Yao 7; Serra and Goodwn, 9). Nonparametrc DEA technques overcome the most relevant lmtaton of SFA: they do not rely on specfc functonal forms. However, nonparametrc approaches do not allow for stochastc varables and measurement errors, whch precludes separatng neffcency effects from random nose or random shocks,.e., all producton shortfalls are attrbuted to the neffcency term. As a result, techncal effcency ratngs obtaned from the nonparametrc approach (DEA) are generally lower than those obtaned under the parametrc alternatve 3

4 (SFA) (Sharma et al., 1999; Pug-Junoy and Argles, ; Wadud and Whte, ). Both methods however have been found to lead to smlar rankngs of techncal performance of decson makng unts (DMUs). Recently, a new methodologcal approach based on local modelng methods has been developed (Kumbhakar et al., 7) to overcome the lmtatons of parametrc approaches, wthout foregong ther advantages. In contrast to parametrc models, ths method does not requre strong assumptons regardng the determnstc and stochastc components of the fronter: the parameters characterzng both producton and error dstrbuton are allowed to depend on the covarates through a process of localzaton. As opposed to nonparametrc approaches, local modelng methods allow for stochastc varables and varable measurement errors when estmatng techncal effcency scores. Furthermore, these technques accommodate the heterogenety n the data by dervng observaton-specfc varances of the neffcency and nose components of the error term (Serra and Goodwn, 9). The local modelng approach by Kumbhakar et al. (7) s based on local maxmum lkelhood (LML) prncples (Fan and Gjbels, 1996). In spte of the nterestng features of ths approach, the complexty of mplementng the method has lmted ts use to a few emprcal studes. The work by Serra and Goodwn (9) consttutes a notable excepton. Our work contrbutes to the scarce lterature on the use of local modelng technques to assess techncal effcency. The present study focuses on estmatng techncal effcency ratngs of a sample of cereals, olseeds and proten crops (COP) farms n Kansas usng flexble LML methods that are compared wth the results of DEA technques. Whle the exstng lterature on techncal effcency has broadly compared parametrc (SFA) and nonparametrc approaches (DEA), to date, there s no study that compares techncal effcency scores obtaned under nonparametrc (DEA) and LML modelng. In addton, ours consttutes the frst study that assesses the effcency of Kansas 4

5 arable crop farms usng local modelng approaches (Rowland et al., 1998; Cotton et al., 1999; Serra et al., 8). The relevance of Kansas as a leadng US producer of arable crops makes the analyss especally nterestng. In 1, Kansas generated almost % and 5% of total wheat and sorghum produced n the US, respectvely. Kansas s also a leadng corn and soybean producer, wth around 5% of the global US producton. The relevant role of Kansas n US arable crop producton justfes our decson to study techncal effcency of Kansas arable crop farms. The paper s organzed as follows. In the next secton we descrbe the methodology used n our emprcal analyss. The thrd secton presents the data and results from the emprcal mplementaton. We fnsh the paper wth concludng remarks.. Methodology The exstng lterature that assesses the techncal effcency under whch frms operate, has manly focused on two approaches: the stochastc parametrc approach and the determnstc nonparametrc method. Several studes have been carred out showng the drawbacks and advantages of each technque. Whle parametrc approaches requre strong assumptons regardng specfcaton of the producton fronter and the error dstrbuton, that can lead to msspecfcaton ssues and based effcency estmates, nonparametrc approaches do not rely on specfc functonal forms. However, nonparametrc technques gnore the stochastc component of producton, whch can also lead to based techncal effcency measures. Fan et al. (1996) propose a two-step pseudo-lkelhood estmator that does not requre specfcaton of the functonal form of the producton fronter, but stll requres assumng a dstrbutonal form for the stochastc components of the fronter. A new local modelng parametrc approach recently proposed by Kumbhakar et al. (7) overcomes the lmtatons 5

6 of SFA, wthout foregong ts advantages. Ths approach s bult upon the LML prncple (Fan and Gjbels, 1996) n whch the parameters of the stochastc and the determnstc components of the fronter model are localzed (flexblzed) wth respect to the covarates. Snce our analyss s based on a large number of Kansas farms over a broad geographc regon wth dfferent clmatc condtons, heterogenety s lkely to characterze the sample (dfferent farm szes, uneven sklls, etc). Implementaton of the LML approach by Kumbhakar et al. (7) s suted to deal wth heteroscedastcty, as t localzes the standard errors characterzng the dstrbuton of effcency and nose components of the error term. Based on ths approach, we seek to assess the techncal effcency wth whch COP producng Kansas farms operate and compare effcency ratngs wth scores derved by the DEA approach. The general stochastc fronter models proposed by Agner et al. (1977) and Meeusen T and Van den Broeck (1977) can be specfed as follows Y X u v, where Y denotes the observed quantty of output produced by frm 1,..., N, d X s a vector of nput quanttes requred by the producton technology, the betas are unknown parameters to be estmated, u s the neffcency term and v s a random nose term. The parametrc estmaton of stochastc fronter models s usually based on maxmum lkelhood technques. The jont pdf of Y, X s decomposed nto a margnal pdf for X, pdf x= p( x) and a k condtonal pdf for Y gven x, pdf y x g y, x, where x vector of parameters to be estmated, and g s a functon assumed to be known. s the localzed Based on the parametrc model proposed by Agner et al. (1977), the condtonal pdf for Y gven X x can be specfed as: Y r X u v, where r x s the producton fronter, and v X x N x u X x N, u x, v, and u and v are assumed to be ndependently dstrbuted, condtonal on X. Followng Kumbhakar et al. (7), the 3-6

7 dmensonal local parameter s represented as x r x, x, x u v T and s approxmated N usng local polynomals. The condtonal log-lkelhood functon L g Y X s locally approxmated by the followng mth order local polynomal ft: 1 log, m N L,,..., q Y, X x... X x K X x (1) N 1 m 1 m H 1 where x represents a fxed nteror pont n the support of, and 1 K 1 H u H K H u for j,1,..., m px, q log g,,..., T j j1 jk, where K s a multvarate kernel functon and H s assumed to be a postve defnte and symmetrc bandwdth matrx. The local polynomal estmator s gven by ˆ x ˆ x where ˆ x,..., ˆ x arg max L, 1,..., m N m (),..., m Kumbhakar et al. (7) propose to emprcally derve the LML estmator usng a local lnear ft. By assumng the random nose and neffcency components to be dstrbuted followng a local normal and a half normal dstrbuton, respectvely, the condtonal probablty densty functon of v u s specfed as: x f X x x x x (3) 7

8 where x x x, x x x and. and. u v u v represent the probablty and the cumulatve dstrbuton functons of a standard normal varable, respectvely. The local lnear parameter s gven by x r x, x, x T and the condtonal pdf of Y gven X s expressed as: y r x x g y; x y r x x x x (4) The condtonal local log-lkelhood functon s specfed as: N 1 1 Y r X X log log (5) 1 X X L X Y r X In the present study, a local lnear model for the fronter r x and a local constant model for the parameters of the error term s used that allows rewrtng expresson (5) as: N T 1 1 Y r r1 X x T N, 1 log log 1 H 1 L Y r r X x K X x (6) T T and 1 r1. The local lnear estmator of the model s gven by ˆ : where r,, ˆ x,..., ˆ 1 x arg max L N, 1 (7), 1 8

9 Followng Jondrow et al. (198), the effcency measure for a partcular pont can be obtaned from the followng expresson: uˆ X ˆ X ˆ X ˆ X ˆ X ˆ ˆ X X ˆ 1 X ˆ ˆ ˆ ˆ X X X ˆ X (8) ˆ ˆ where X Y r X. In the case of varables measured n logs, the effcency score s gven by eff ˆ exp uˆ,1. Fndng a soluton to the maxmzaton problem n (7) requres specfyng startng values. To do so, we follow Kumbhakar et al. (7) and start wth the local lnear least squares estmator of ˆr x and 1ˆr x and the global ML estmators of ˆ and. The local ntercept ˆr x s corrected for the moment condton along the lnes of the parametrc Modfed Ordnary Least Squares (MOLS) estmator. Kumbhakar et al. (7) recommend usng the followng expresson for such purpose MOLS u, where ˆ ˆ u rˆ x rˆ x ˆ MOLS are obtaned from rˆ ˆ ˆ,, ˆ ˆ 1. Hence, ntal values for solvng (7) T and r x T 1 1ˆ. d d 1 The product kernel chosen s h K h x j, where. j1 K represents the Epanechnkov Kernel and d represents the number of covarates. The bandwdth s adjusted for dfferent varable scales and sample szes and s defned as: h h s N base x 15 ; where s x represents the vector of emprcal standard devatons of the covarates and N represents the number of observatons. The choce of the optmal value for hbase s based on the cross valdaton crteron (CV) proposed by Kumbhakar et al. (7). The CV, for a gven value of h base, s computed by mnmzng the followng expresson: 9

10 ˆ N 1 CV h Y r x u N, (9) base 1 where ˆ r and u are the leave-one-out versons of the local lnear estmators defned above. As noted above, apart from Kumbakar et al. s (7) LML proposal, effcency of Kansas farms s also assessed by DEA approaches. Followng Färe et al. (1994), the DEA lnear programmng model to assess output-orented techncal effcency levels can be expressed as: max, st.. y Y x X N1 1 (1) where 1, N s the number of farms, X s a d N matrx of nputs, Y s a 1 N matrx of outputs. Techncal effcency scores are gven by 1. The constrant N1 1s ncluded to allow for varable returns to scale (VRS). As s well known, wthout such constrant constant returns to scale (CRS) are assumed (Charnes et al., 1994). To test for dvergence between the effcency dstrbutons obtaned from LML and DEA methods, the standard Kolmogorov-Smrnov (KS) two-sample (two-tal) test statstc s conducted: a b D max F ( x, N) F ( x, N) (11) 1

11 a where F ( x, N ) represents the emprcal dstrbuton functon for a sample a wth total observatons N. 3. Data and results The emprcal applcaton focuses on a sample of Kansas farms that specalze n the producton of COP crops. Farm-level data are obtaned from farm account records from the Kansas Farm Management Assocaton (KFMA) dataset and cover the perod -1. Data avalable nclude farm producton and nput use, fnancal and soco-economc characterstcs, as well as farm structural characterstcs. To ensure that COP s the man farm output, farms whose COP sales represent at least 9% of total farm ncome were selected. Ths crteron allows obtanng a relatvely homogeneous sample of farms. The dataset s an unbalanced panel that contans 1,58 observatons. We defne farm output ( y ) as an mplct quantty ndex that s computed as the rato of producton n currency unts to the output prce ndex. Snce nformaton on market prces s unavalable at the farm-level, the Paasche prce ndex s bult on the bass of state-level cash unt prces and producton data. Output y ncludes the predomnant crops n Kansas (Albrght, ): wheat, corn, soybean and sorghum sales. The nputs consdered as explanatory varables are COP land ( x 1 ) measured n acres, total labor nput ( x ), manly composed of famly labor, and expressed n annual workng unts (AWUs), as a fracton of 1-hours per day, chemcal nputs ( x 3 ), other nputs ( x 4 ) and captal ( x 5 ). Chemcal nputs are defned as a quantty ndex that ncludes the use of fertlzers and pestcdes, and s obtaned by dvdng nput expendtures by ts correspondng prce ndex. Other nputs, also defned as a quantty ndex, nclude fuel and seed expenses. Captal nput ( x 5 ) aggregates the 11

12 value of machnery, other equpment and buldngs used n the producton process, and s determned by dvdng captal value by ts correspondng prce ndex. Input prces are measured usng natonal nput prce ndces. Monetary values are measured at constant prces. Data unavalable from the Kansas database are obtaned from the Unted States Department of Agrculture (USDA) and the Natonal Agrcultural Statstcs Servce (NASS), from whch country-level nput prce ndces and state-level output prces and quanttes are determned. Table 1 provdes summary statstcs for the varables used n the analyss. Sample farms use, on average, 93 AWUs, of whch 8% represents unpad famly labor. In contrast to the European Unon (EU) arable crop farms that are manly small holdngs wth around 116 acres (Farm Accountancy Data Network, FADN 1), Kansas farms devote 1,78 acres on average to COP producton. More than 8% of the COP area s allocated to wheat, soybeans, sorghum and corn producton. The average value of farm producton (around 154 thousand dollars) almost doubles the EU value (about 84 thousand dollars). However, per acre statstcs suggest that EU farms are much more ntensve than Kansas farms: whle EU farms have an average ncome of 441 dollars per acre, Kansas ncome s 1 dollars per acre. Sample farms nvestments n machnery and buldngs are on the order of 163 thousand dollars. On per acre bass, Kansas farms are less ntensve n captal use (15 dollars per acre) relatve to the EU wth nvestment ratos on the order of 1,666 dollars per acre (FADN, 1). To ensure mmunty aganst pests and dseases and to avod productvty loss due to pest nfestatons, Kansas farmers spend around 38 thousand dollars annually on chemcal nputs. On a per acre bass, expenses n fertlzers and crop protecton products are much hgher n EU farms (178 dollars per acre versus 9 dollars per acre). Expenses n other nputs, seeds and energy, s rather low compared to chemcal nput costs and on the order of 4 thousand dollars. 1

13 Usng the aforementoned varables and followng Kumbhakar et al. (7), we specfy the parametrc model as a Cobb-Douglas functon: logy log x log x log x log x log x u v (1) It s relevant to note that rgdtes assocated to ths producton fronter are overcome by estmatng the fronter for each observaton n the sample,.e., flexblty s acheved through varyng parameter estmates. To select the bandwdth parameter requred to derve the LML estmator of (1), we use the CV procedure descrbed above and evaluated at each sample pont. It s worth notng that wth multplcatve multvarate kernels, an observaton wll only be consdered n the LML estmaton f all covarates x fall nto the nterval x h, x h ); where h h s N base x 15. If even one of the components fals to fall nto ths nterval, the observaton wll not be consdered for the estmaton. Such procedure requres relatvely large values for hbase n order to have a suffcently large subsample of observatons to locally estmate the stochastc producton fronter. Hence, the more mportant the sample heterogenety s, the bgger the requred bandwdth. We start wth a crude grd of values to then focus on a fner grd for the selecton of the optmal h base. Fnal results show that the bandwdths h 1, h, h 3, h4 and h5 take values of.38,.34, 3.37, 3.47 and.86, respectvely. Once we select the adequate bandwdth for our data, we then derve local parameter estmates. Descrptve statstcs for the varaton of the local estmates of u and v are shown n table. These statstcs confrm the presence of heteroscedastcty and ndcate an mportant degree of varaton among observatons regardng the shares of the neffcency term to the nose term ( / ). u v 13

14 Fgure 1 llustrates the varaton of the parameters of the determnstc component of the fronter. Snce we use a Cobb Douglas functonal form for our model, the coeffcents represent nput elastctes. The varaton of the localzed estmates suggests that assumng the same nput elastctes for all observatons may not be relable. Varaton s specally relevant for land, wth an elastcty that ranges from 5% to 45%, followed by chemcal nputs and captal, that have an elastcty fluctuatng from 6% to 38% and 18% to 3%, respectvely. Input elastctes ndcate that farms operate under constant returns to scale wth a mean scale elastcty equal to.997 and a standard devaton of.45 (table 3). As expected, localzed elastcty estmates are postve for a majorty of farms n that none of the nputs consdered s over-utlzed. Noteworthy s the fact that, for some observatons, the labor elastcty s negatve. Ths s not surprsng gven the share of famly labor n our sample farms. Snce ths labor type usually nvolves an opportunty cost but not a drect cost, ncentves to use t effcently may be less strong than for other nputs. Producton elastcty estmates ndcate, on average, that an ncrease n chemcal nput use has the hghest potental to ncrease output, followed by land, captal, other nputs and labor (table 3). The low contrbuton of labor to farm productvty n Kansas farms can once more be attrbuted to the hgh share of famly labor. The fact that captal, land and other nputs have lower elastctes than chemcals nputs suggests that the latter are used less ntensvely. Table 4 llustrates the dstrbuton of the localzed effcency estmates. Results show a hgh average techncal effcency score, on the order of.9, ndcatng that farmers reach 9% of ther maxmum potental output. Therefore, our sample farms could ncrease ther output by 1% by effcently usng ther nputs. Our results dffer from those n Serra et al. (8) who used the same database, but focused on the perod Through Kumbhakar s stochastc fronter model (), Serra et al. (8) obtaned mean techncal 14

15 neffcency levels of.3, versus.1 n our analyss. The use of dfferent methodologes or farmers performance mprovement over tme can explan dfferences n effcency scores across studes. However, our results are closer to other fndngs by Rowland et al. (1998) for a sample of Kansas swne operatons from 199 through 1994, or Cotton et al. (1999), for a sample of mult-output Kansas farms durng the perod 1985 to Both authors used nonparametrc DEA technques to derve effcency estmates and obtaned mean effcency scores of.89 and.91, respectvely. Hgh techncal effcency levels are assocated wth low producton costs and hgher chances of frm s economc vablty. Techncal effcences range from a mnmum of.19 to a maxmum of.99 ndcatng mportant dsperson and heterogenety wthn Kansas farms. Almost one half of the observatons dsplay hgh performance levels presentng effcency ratngs greater than.9. DEA effcency scores under CRS (.81) assumpton are, on average, lower than those derved from the LML approach. Under VRS, however, effcency ratngs are much closer to LML results (.9). 1 At the 5% level of sgnfcance, the KS test ndcates that the dfference n effcency scores derved from DEA and LML technques s statstcally sgnfcant (table 5). Gven the fact that LML s a technque that overcomes the most relevant lmtatons of DEA methods, ts relablty may be hgher. 1 DEA results suggest that Kansas farms do not operate at optmal scales. The nonparametrc L (1999) test has been also computed ndcatng that the two dstrbuton obtaned from LML and DEA methods are equal and the null hypothess cannot be rejected at the 5% level of sgnfcance wth p-value.35 and.33 for LML vs. VRS and LML vs. CRS respectvely. However, the power of ths test s very senstve to the dmensonalty and sample sze whch can conduct to msleadng mpresson of equalty of dstrbutons (Smar and Zelenyuk, 6). 15

16 4. Concludng remarks The relevance of dervng relable techncal effcency scores to assst frms management decsons as well as polcy desgn, makes t essental to use methodologes that produce farmlevel non-based effcency ratngs. The parametrc SFA and the nonparametrc DEA approach have focused the attenton of manstream effcency lterature. Both approaches have been wdely crtczed for ther shortcomngs that may lead to based effcency estmates. Recently, Kumbhakar et al. (7) proposed a new approach, namely the LML method. The method estmates the parameters of the determnstc and stochastc components of the fronter locally. LML methods overcome the shortcomngs of SFA wthout foregong ther advantages. LML technques are used n ths artcle to assess the effcency levels acheved by Kansas farms specalzed n cereals, olseeds and proten crops (COP) producton and compares them wth those obtaned from flexble DEA models. Farm-level data obtaned from farm account records from the KFMA dataset coverng the perod -1 are used. Emprcal results support the relevance of usng the LML approach through the varaton n the localzed parameter estmates, representng the varance of the composte error term and nput elastctes. Results show hgh mean effcency scores (.9) ndcatng that farmers could ncrease ther output by 1% keepng ther nput bundle constant. Techncal effcency scores derved from the LML approach are hgher (lower) than those of the DEA model under CRS (VRS). Accordng to KS test, the effcency scores obtaned from DEA and LML have dfferent dstrbutons and the dfference s statstcally sgnfcant. Snce LML allow for both stochastc error terms, as well as for flexblty n the functonal form representng the fronter functon, we suggest that effcency scores derved under LML 16

17 maybe more relable and less based than effcency ratngs under nonparametrc DEA alternatves. Our research can be extended n many dfferent ways. Dfferent methodologcal nnovatons to assess effcency have been recently ntroduced n the lterature. Noteworthy are the refnements regardng the measurement of techncal effcency n the presence of uncertanty through state-contngent technques (Chambers and Quggn, ). Falure to properly allow for rsk can lead to based effcency estmates (O Donnell et al., 1). Other nnovatons n the techncal effcency lterature nclude dynamc effcency measurement that does not rely on the assumpton of frm s ablty to adjust nstantaneously and that allows for the dynamc lnkages of producton decsons (Serra et al., 11). Extenson of LML methods to a consderaton dynamc ssues consttutes another area that merts further attenton. 17

18 References Agner, D., Lovell, C.A.K., Schmdt, P., Formulaton and estmaton of stochastc fronter producton functons models. J. Econometrcs 6, Albrght, M. L.,. Kansas Agrculture: An economc overvew for 1, Research Papers and Presentatons, Kansas State Unversty (KSU) Research and Extenson. Accessed November 11, avalable at Chakraborty, K., Bswas, B., Lews, W.C., 1. Measurment of techncal effcency n publc educaton: A stochastc and non-stochastc producton functon approach. Southern Econ. J. 67, Chakraborty, k., Msra, S., Johnson P.,. Cotton farmers techncal effcency: Stochastc and non-stochastc producton functon approaches. Agr. Resource Econ. Rev. 31, 11-. Chambers, R., Quggn, J.,. Uncertanty, producton choce and agency: The statecontngent approach. Cambrdge Unversty Press, Cambrdge, UK. Charnes, A., Cooper, W., Lewn, A., Seford, L., Data envelopment analyss, theory, methodology and applcatons. Kluwer Academc Publshers, Norwell, MA. Coell, T.J., Recent developments n fronter modelng and effcency measurement. Australan J. Agr. Resource Econ. 39, Coell, T.J., Perelman, S., A comparson of parametrc and non-parametrc dstance functons: Wth applcaton to European ralways. Eur. J. Oper. Res. 117, Cotton, M.K., Langemeer, M.R., Featherstone, A.M., Effects of weather on Mult- Output: Effcency of Kansas Farms. Journal of the ASFMRA 6, FADN, 1. FADN publc database. Accessed Aprl 1, avalable at 18

19 Fan, J., Gjbels, I., Local polynomal modelng and ts applcatons. Chapman and Hall, London, UK. Fan, Y., L, Q., Weersnk, A., Semparametrc estmaton of stochastc producton fronter models. J. Bus. Econ. Statst. 14, Färe, R., Grosskopf, S., Lovell, C.A.K., Producton fronters. Cambrdge Unversty Press, Cambrdge, UK. Ferrer, R.S., Lovell, C.A.K., 199. Measurng cost effcency n bankng: An econometrc and lnear programmng evdence. J. Econometrcs 46, Jondrow, J., Lovell, C.A.K., Materov, I.S. and Schmdt, P. (198). On the estmaton of techncal neffcency n stochastc fronter producton models. J. Econometrcs 19, Kumbhakar, S.C.,. Specfcaton and estmaton of producton rsk, rsk preferences and techncal effcency. Amer. J. Agr. Econ. 84, 8-. Kumbhakar, S.C., Byeong, U.P., Smar, L., Tsonas E.G., 7. Nonparametrc stochastc fronters: A local maxmum lkelhood approach. J. Econometrcs 137, 1-7. L, Q., Nonparametrc testng the smlarty of two unknown densty functons: Local power and bootstrap analyss. J. Nomparametr. Stat. 11, Lohr, L., Park, T.A., 6. Techncal effcency of US organc farmers: The complementary roles of sol management technques and farm experence. Agr. Resource Econ. Rev. 35, Martns-Flho, C., Yao, F., 7. Nonparametrc fronter estmaton va local lnear regresson. J. Econometrcs 141, Meeusen, W., Van Den Broek, J., Effcency estmaton from Cobb-Douglas producton functons wth composed error. Int. Econ. Rev. 18,

20 O Donnell, C.J., Chambers, R.G., Quggn, J., 1. Effcency analyss n the presence of uncertanty. J. Productv. Anal. 33, Oude Lansnk, A., Petola, K., Bäckman, S.,. Effcency and productvty of conventonal and organc farms n Fnland Europ. Rev. Agr. Econ. 9, Pug-Junoy, J., Argles, J.M.,. Measurng and explanng farm neffcency n a panel data set of mxed Farms. Pompeu Fabra Unversty, Workng Paper, Barcelona, Span, July 5. Rowland, W.W., Langemeer, M.R., Schurle, B.W., Featherstone, A.M., A nonparametrc effcency analyss for a sample of Kansas swne operatons. J. Agr. Appl. Econ. 3, Ruggero, J.,Vtalano, D., Assessng the effcency of publc schools usng data envelopment analyss and fronter regresson. Contemporary Econ. Pol. 17, Serra, T., Goodwn, B.K., 9. The effcency of Spansh arable crop organc farms, a local maxmum lkelhood approach. J. Productv. Anal. 3, Serra, T., Oude Lansnk, A., Stefanou, S., 11. Measurement of dynamc effcency: A drectonal dstance functon parametrc approach. Amer. J. Agr. Econ. 93: Serra, T., Zlberman, D., Gl J.M., 8. Farms techncal neffcences n the presence of government programs. Australan J. Agr. Resource Econ. 5, Sharma, K.R., Leung, P., Zalesk, H.M., Techncal, allocatve and economc effcences n swne producton n Hawa: A comparson of parametrc and nonparametrc approaches. Agr. Econ., Smar, L., Zelenyuk, V., 6. On testng equalty of dstrbutons of techncal effcency scores. Econometrc Rev. 5,

21 Splänen, T., Oude Lansnk A., 5. Learnng n organc farmng-an applcaton on Fnnsh dary farms. Manuscrpt presented at the XIth Congress of the EAAE. Copenhagen, Denmark, August Tzouvelekas, V., Pantzos, C.J., Fotopoulos, C., 1. Techncal effcency of alternatve farmng systems: The case of Greek organc and conventonal olve-growng farms. Food Pol. 6, Tzouvelekas, V., Pantzos, C.J., Fotopoulos, C.,. Emprcal evdence of techncal effcency levels n Greek organc and conventonal farms. Agr. Econ. Rev. 3, USDA, 11. Agrcultural prces summary, crop values annual summary and crop producton annual summary. Accessed August 11, avalable at Wadud, A., Whte, B.,. Farm household effcency n Bangladesh: A comparson of stochastc fronter and DEA methods. Appl. Econ. 3,

22 Table 1. Summary statstcs for the varables of nterest Varable Mean Standard devaton Total output (ndex) 154, ,51.51 Captal (ndex) 16, , Land (acres) 1, ,13.34 Labor (AWU) Chemcals nputs (ndex) 38, , Other nputs (ndex) 4, ,388. Statstcs on a per acre bass Total output (dollars/acre) Captal (dollars/acre) Labor (AWU/acre).4.14 Chemcals nputs (dollars/acre) Other nputs (dollars/acre)

23 Table. Summary statstcs for the local estmates of u, v and Maxmum (1%) Thrd quartle (75%) u v Medan (5%) Frst quartle (5%) 1.93E Mnmum (%) 6.93E E-4.3E- 3

24 Table 3. Dstrbuton of producton and scale elastctes for Kansas Farms Elastctes wth Standard Estmate respect to devaton Land area.5.19 Labor Captal Chemcal nputs Other nputs Returns to scale

25 Table 4. Frequency dstrbuton of techncal effcency scores TE: Range (%) Observatons (%) LML 1 VRS CRS 3 LML VRS CRS < Mean Standard devaton Mnmum Maxmum LML: local maxmum lkelhood. VRS: varable returns to scale. 3 CRS: constant return to scale. 5

26 Table 5. Kolmogorov-Smrnov test Test Value p-value LML vs. DEA VRS.57. LML vs. DEA CRS

27 Percent Percent Percent Percent Percent Percent Land (r11) Labor (r1) Chemcal nputs (r13) Other nputs (r14) Captal (r15) Returns to scale Fg. 1 Dstrbuton of localzed estmates of nput elastctes and returns to scale 7