PRODUCTIVE EFFICIENCY OF THE LITHUANIAN FAMILY FARMS ( ): A NON PARAMETRIC INFERENCE WITH POST EFFICIENCY ANALYSIS

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1 Tomas BALEŽENTIS Lhuanan Insue of Agraran Economcs, Lhuana Vlnus Unversy, Lhuana Irena RIŠČIUAITIENĖ, PhD Lhuanan Insue of Agraran Economcs, Lhuana E-mals: PRODUCTIVE EFFICIENCY OF THE LITHUANIAN FAMILY FARMS ( ): A NON PARAMETRIC INFERENCE WITH POST EFFICIENCY ANALYSIS Absrac. Ths paper analyses he producve effcency of he Lhuanan famly farms durng The producve effcency of Lhuanan famly farms was esmaed on a bass of Farm Accounancy Daa Newor sample by he means of daa envelopmen analyss, whch dd ndcae ha he average echncal effcency flucuaed around 65.8%, whereas he mean allocave effcency approached 70.5%. The mean economc effcency, herefore, was raher low, namely 46%. These fgures mply ha Lhuanan famly farms should mprove boh echnologcal and manageral pracces and hus acheve hgher producvy n order o successfully compee n he sngle mare of he EU. The second sage analyss of effcency scores whch, ndeed, had no been performed for Lhuanan agrculural secor before revealed some causes of neffcency. Specfcally, he ob model was employed o quanfy effcency effecs, whereas he log model was fed o esmae facors of ncrease n effcency. Bascally, hese analyses showed ha large lvesoc farms adoped organc farmng pracces are hose mos effcen. Moreover, hey were more lely o exhb an ncrease n he producve effcency. eywords: Effcency, Famly farms, Daa Envelopmen Analyss, Tob, Log. JEL Classfcaon: C61, D24, Q12 1. INTRODUCTION Famly farmng has been renvgorang n Lhuana snce early 1990s when he collecve farmng sysem was deconsruced. Snce hen he Lhuanan farmng sysem has undergone many economc, srucural, and nsuonal reforms. Year 2004 mars he accesson o he European Unon (EU) whch s relaed o he Common Agrculural Polcy. The Lhuanan farmng sysem, however, s no fully developed ye. In erms of he ulzed agrculural area, he average Lhuanan farm expanded from 9.2 ha up o 13.7 ha durng , whereas he oal ulzed agrculural area ncreased by some 10% and he number of agrculural holdngs decreased by 27% from 272 housand down o less han 200 housand (Sascs Lhuana, 2011). Indeed, he number of he smalles farms has decreased and hese adjusmens lead o a farm srucure whch s smlar o ha of he European counres. There s, however, a subsanal area of sae-owned or

2 Tomas Baležens, Irena rščuaenė abandoned land whch can be employed for he agrculural acves n he fuure. Therefore s mporan o analyze he farmng effcency whch denfes many facors nfluencng farmers decsons. As Hennngsen (2009) pu, he agrculural effcency s nerrelaed wh labour nensy, farm srucure, echnology and nvesmen, manageral slls, and profably. The very effcency hus can be consdered as a measure of producvy and profably. The farm srucure mpacs echnology, labour nensy, and manageral slls gven larger farms end o accumulae respecve resources o a hgher exen. The labour nensy and labour opporuny coss are recprocally relaed o he nvesmens no advanced echnologes. Managemen slls also nfluence boh labour nensy and nvesmens no echnology. The aforemenoned facors affec he profably, whereas he profably, n urn, deermnes farmers decsons on sayng n he secor or dsrbung her worng me across varous economc secors. The producve effcency, herefore, needs o be measured and analyzed n erms of mulple nerrelaed varables and dmensons. Producve effcency of agrculural secor s exensvely analyzed across he Cenral and Eas European saes where agrculure s relavely mporan economc acvy f compared o he wesern saes. Usually he wo branches of mehods are employed for effcency analyses, namely non paramerc mehods (daa envelopmen analyss, free dsposable hull) and paramerc mehods (sochasc froner analyss). These mehods can be employed for ner as well as nra sae comparsons (Hoang and Alauddn, 2012; Ferjan, 2011; Jn e al., 2010; Bojnec and Laruffe, 2011; Aldea, Cobanu, 2011; Mae, Sprcu, 2012). Lhuanan agrculural secor, hough, receved less aenon n he laer scenfc area. Moreover, hose few examples employed non-paramerc mehods, whereas paramerc mehods (e. g. sochasc froner analyss) reman underused. Alhough he Lhuanan agrculural secor was analyzed by he means of he non-paramerc mehods by, for nsance, Douarn and Laruffe (2011) and Rmuvenė e al. (2010), here are sll some ssues o be acled. Frs, all of he prevous sudes, wh excepon of Douarn and Laruffe (2011), analyzed he aggregaed FADN daa raher han mcro daa. Therefore he aforemenoned sudes provded fewer opporunes o fahom he underlyng rends n boh effcency paerns and farmers decson-mang. Second, Rmuvenė e al. (2010) analyzed he Lhuanan agrculural secor n erms of performance of he agro secors of he European Unon Member Saes. Thrd, he prevous sudes esmaed echncal and scale effcency scores, albe hey dd no analyzed cos and allocave effcency. Our sudy, herefore, ams a analyzng he mcro daa by he means of daa envelopmen analyss (DEA). As a resul echncal, scale, economc, and allocave effcency s esmaed and subsequenly employed n he second sage analyss. Ths sudy ams a analyzng he paerns of effcency across Lhuanan famly farms and hus denfyng manageral mplcaons for agrculural polcy mang. Indeed, he analyss of producve effcency can be a semnal par of susanably managemen model for he whole agrculural secor n Lhuana ensurng vably of agrculural enes.

3 Producve Effcency of he Lhuanan Famly Farms ( ): A Non paramerc Inference wh Pos effcency Analyss The paper s organzed as follows. Secon 2 presens he man measures of effcency, whereas Secon 3 dscusses he non-paramerc mplemenaon of hese measures by he means of DEA. The followng Secon 4 descrbes he daa used n he research. Secon 5 brngs he resuls of he DEA. Fnally, Secon 6 s dedcaed for he pos-effcency analyss. 2. DEFINITIONS AND MEASURES OF EFFICIENCY Insead of defnng he effcency as he rao beween oupus and npus, we can descrbe as a dsance beween he quany of npu and oupu, and he quany of npu and oupu ha defnes a froner, he bes possble froner for a frm n s cluser. The very erm of effcency was nally defned by oopmans (1951). oopmans offered he followng defnon of an effcen decson mang un (DMU): A DMU s fully effcen f and only f s no possble o mprove any npu or oupu whou worsenng some oher npu or oupu. Due o smlary o he defnon of Pareo effcency, he former s called Pareo oopmans Effcency. Such a defnon enabled o dsngush effcen and neffcen DMUs, however dd no offer a measure o quanfy he level of neffcency specfc o a ceran DMU. Thus Debreu (1951) dscussed he queson of resource ulzaon and nroduced he measure of producve effcency, namely coeffcen of resource ulzaon. Debreu s measure s a radal measure of echncal effcency. Radal measures focus on he maxmum feasble equproporonae reducon n all varable npus for an npu-conservng orenaon, or he maxmum feasble equproporonae expanson of all oupus for an oupu-augmenng orenaon. Fnally, Farrell (1957) summarzed wors of Debreu (1951) and oopmans (1951) hus offerng froner analyss of effcency and descrbng wo ypes of economc effcency, namely echncal effcency and allocave effcency (ndeed, a dfferen ermnology was used a ha me). I s worh o noe, ha he semnal paper of Farrel (1957) was dedcaed o analyss of agrculural producon n he Uned Saes. The concep of echncal effcency s defned as he capacy and wllngness o produce he maxmum possble oupu from a gven bundle of npus and echnology, whereas he allocave effcency reflecs he ably of a DMU o use he npus n opmal proporons, consderng respecve margnal coss (alrajan 2002). However, Farrell (1957) noed ha prce nformaon s raher hard o acle n a proper way, hus echncal effcency became a prmal measure of he producve effcency. Besdes, he wo oher ypes of effcency can be defned, vz. scale and srucural effcency. Scale effcency measures he exen o whch oupus ncrease due o ncrease n npu. Farrel (1957) and laer Charnes, Cooper and Rhodes (1978) employed he mos resrcve consan reurns o scale (CRS) assumpon. The laer assumpon was relaxed by Baner, Charnes and Cooper (1984), who also poned ou ha scale effcency s relaed o varable reurns o scale (VRS) effcency (pure echncal effcenc and CRS echncal effcency. The srucural effcency s an ndusry level concep descrbng he srucure and

4 Tomas Baležens, Irena rščuaenė performance of ceran secor whch s deermned by performance of s frms. Indeed, one secor can be srucurally effcen han anoher n case s frms are operang closer o he effcency froner. For nsance, one can defne hypohec average values for several secor and compue effcency scores for hem hus assessng dfferences n srucural effcency across hese secors. In order o relae he Debreu Farrel measures o he oopmans defnon, and o relae boh o he srucure of producon echnology, s useful o nroduce m some noaon and ermnology. Le producers use npus x x x,..., 1, 2 n o produce oupus y y1, y2,..., y n. Producon echnology hen can be defned n erms of he producon se: T x, y x can producey. (1) Thus, oopmans effcency holds for an npu-oupu bundle x, y T f, and only f, x ', y' T for x ', y' x, y. Technology se can also be represened by npu requremen and oupu correspondence ses, respecvely: I ( x x, y T, (2) O ( x) y x, y T. (3) The soquans or effcen boundares of he secons of T can be defned n n radal erms as follows (Farrel, 1957). Every y has an npu soquan: soi ( x x I(, x I(, 1. (4) Smlarly, every m x has an oupu soquan: soo ( x) y y O( x), x O( x), 1. (5) In addon, DMUs mgh be operang on he effcency froner defned by Eqs. 4 5, albe sll use more npus o produce he same oupu f compared o anoher effcen DMU. In hs case he former DMU experences a slac n npus. The followng subses of he boundares I( and O(x) descrbe Pareo-oopmans effcen frms: effi ( x x I(, x' I(, x' x, x' x, (6) effo ( x) y y O( x), y' O( x), y' y, y' y. (7) Noe ha effi ( soi( I( and effo ( x) soo( x) O( x). There are wo ypes of effcency measures, namely Shepard dsance funcon, and Farrel dsance funcon. These funcons yeld he dsance beween an observaon and he effcency froner. Shepard (1953) defned he followng npu dsance funcon: D I max x, y I(. (8) Here D I 1 for all x I(, and D I 1 for x soi(. The Farrel npu-orened measure of effcency can be expressed as: x m

5 Producve Effcency of he Lhuanan Famly Farms ( ): A Non paramerc Inference wh Pos effcency Analyss TE I mn x, y I(. (9) Comparng Eqs. 8 and 9 we arrve a he followng relaon: TEI 1 DI, (10) wh TE I 1 for x I(, and TE I 1 for x soi(. Smlarly, he followng equaons hold for he oupu-orened measure: D O mn x, y O( x), (11) TE O max x, y O( x), (12) TEO 1 DO, (13) where TE I 1 for x I(, and TE I 1 for x soi(. As was already sad, Farrel (1957) defned he wo ypes of effcency, whch are nown as echncal and economc effcency. The economc effcency and s measures were descrbed above. The economc effcency s dvded no cos, revenue and prof effcency. For each of he hree measures, a respecve froner s esablshed. Here we focus solely on cos effcency. However, revenue effcency s a sraghforward modfcaon of he cos effcency. m Assume ha producers face npu prces w ( w1, w2,..., w m ) and see o mnmze cos. Thus, a mnmum cos funcon cos froner s defned as: T c( y, w) mn w x D 1. (14) x Then a measure of cos effcency (CE) s defned as he rao of he mnmum cos o he acual cos: T CE y, w) c( y, w) w x. (15) A measure of npu-allocave effcency AE I s obaned by employng Eqs. 7 and 9: AEI y, w) CE( x, y, w) / TEI. (16) Thus, cos effcency can be expressed as a produc of echncal effcency E and cos allocave effcency. The effcen pon, x, mnmzes cos and hus defnes he cos froner c ( y, w) w T x E 0. The cos effcency of he pon x s hen gven by rao effcency of x x T E T rao w x w ( 0 x 0 ). 0 c T 0 T E T 0 ( y, w) w x w x w x I (cf. Eq. 15). The cos 0 x can be furher decomposed no echncal effcency T 0 0 T 0 w ( x ) w x and allocave effcency deermned by he 3. PRELIMINARIES FOR DATA ENVELOPMENT ANALYSIS The dscussed effcency froner can be esablshed by employng dfferen compuaon echnques. These can be classfed no paramerc and nonparamerc mehods.

6 Tomas Baležens, Irena rščuaenė The paramerc froner mehods rely on economerc nference and ams a esmang parameers for pre-defned exac producon funcons. These parameers may refer, for nsance, o he relave mporance of dfferen cos drvers or o parameers n he possbly random nose and effcency dsrbuons. The paramerc froner mehods can be furher classfed no deermnsc and sochasc ones. The wo deermnsc froner models, namely Ordnary Leas Squares (OLS) and Correced Ordnary Leas Squares (COLS), arbue he dsance beween an observaon and he effcency froner o sascal nose or neffcency, respecvely. The sochasc paramerc mehod Sochasc Froner Analyss (SFA) explans he gap beween an observaon and he effcency froner n erms of boh neffcency and random errors. On he oher sde, non-paramerc froner mehods do no allow sascal nose and hus he whole dsance beween he observaon and producon froner s explaned by neffcency. In addon, he producon froner (surface) s defned by envelopng lnearly ndependen pons (observaons) and does no requre subjecve specfcaon. Therefore non-paramerc models are easer o be mplemened. Daa Envelopmen Analyss (DEA) and Free Dsposable Hull (FDH) are he wo wdely renowned non-paramerc models. Indeed, SFA and DEA are he wo semnal mehods for, respecvely, paramerc and non-paramerc analyss. These mehods are o be dscussed hroughou he remanng par of he sudy. DEA specfes he effcency froner wh respec o he wo assumpons, namely free dsposably and convexy. The assumpon of he free dsposably means ha we can dspose of unwaned npus and oupus. Frs, f we can produce a ceran quany of oupus wh a gven quany of npu, hen we can also produce he same quany of oupus wh more npus. Second, f a gven quany of npus can produce a gven quany of oupus, hen he same npu can also be used o produce less oupu. By combnng hese wo assumpons we arrve a he free dsposably of npus and oupus. The echnology relaed o free dsposably assumpon s called he free dsposable hull. Assume here are 1,2,..., frms each possessng a ceran npu-oupu bundle ( x, y ), hen he free dsposable hull s defned as m n T 1,2,..., : x x, y y. (17) The convexy assumpon mples ha any lnear combnaon of he feasble producon plans ( x, y ) s also feasble. The convex echnology se s defned n he followng way: T x 1 x, y 1 y, 1 1, 0, 1,2,...,. (18) By combnng assumpons of he free dsposably and convexy (cf. Eqs. 17 and 18) he followng echnology se s obaned:

7 Producve Effcency of he Lhuanan Famly Farms ( ): A Non paramerc Inference wh Pos effcency Analyss T x 1 x, y 1 y, 1 1, 0, 1,2,...,. (19) The laer echnology se ncludes all pons ha can be consdered as feasble ones under assumpon of eher convexy or free dsposably. DEA mehod analyses effcency n erms of suchle echnology se. DEA s a nonparamerc mehod of measurng he effcency of a decson mang un (DMU) such as a frm or a publc secor agency. The modern verson of DEA orgnaed n sudes of A. Charnes, W. W. Cooper and E. Rhodes (Charnes e al., 1978, 1981). Hence, hese DEA models are called CCR models. Inally, he fraconal form of DEA was offered. However, hs model was ransformed no npu and oupu orened mulpler models, whch could be solved by means of he lnear programmng (LP). In addon, he dual CCR model (. e. envelopmen program) can be descrbed for each of he prmal programs (Hajagha e al., 2013). Unle many radonal analyss ools, DEA does no requre o gaher nformaon abou prces of maerals or produced goods, hus mang suable for evaluang boh prvae and publc secor effcency. Suppose ha here are 1,2,...,,..., DMUs, each producng j 1,2,..., n oupus from 1,2,..., m npus. Hence, he h DMU exhbs npu orened echncal effcency, whereas oupu orened echncal effcency s a recprocal number and The npu orened echncal effcency followng mulpler DEA program: / 1. may be obaned by solvng he mn, s x y 0, j x, 1,2,..., m; y, j 1,2,..., n; j 1,2,..., ; (20) In Eq. 20, coeffcens unresrced. are weghs of peer DMUs. Noeworhy, hs model presumes exsng consan reurns o scale (CRS), whch s raher arbrary condon. CRS ndcaes ha he manufacurer s able o scale he npus and oupus lnearly whou ncreasng or decreasng effcency.

8 Tomas Baležens, Irena rščuaenė Whereas he CRS consran was consdered over resrcve, he BCC (Baner, Charnes, and Cooper) model was nroduced (Baner e al. 1984). The CRS presumpon was overrdden by nroducng a convexy consran 1 1, whch enabled o acle he varable reurns o scale (VRS). The BBC model, hence, can be wren by supplemenng Eq. 20 wh a convexy consran 1 1. The bes achevable npu can herefore be calculaed by mulplyng acual npu by echncal effcency of ceran DMU. On he oher hand, he bes achevable oupu s obaned by dvdng he acual oupu by he same echncal effcency 1 /, where s obaned from Eq. 20. In addon, s possble o asceran wheher a DMU operaes under ncreasng reurns o scale (IRS), CRS, or decreasng reurns o scale (DRS). CCR measures gross echncal effcency (TE) and hence resembles boh TE and scale effcency (SE); whereas BCC represens pure TE. As a resul, pure SE can be obaned by dvdng CCR TE by BCC TE. Noeworhy, echncal effcency descrbes he effcency n converng npus o oupus, whle scale effcency recognzes ha economy of scale canno be aaned a all scales of producon. The cos effcency s obaned by he vrue of he followng lnear cos mnmzaon model: mn c( y, w) m, x 1 w x s x y j x, y j, j 1,2,..., m 1,2,..., n, (21) w where are he npu prces for he h DMU. Indeed, hs model yelds he mnmum cos whch s he npu for Eq DATA USED The echncal and scale effcency was assessed n erms of he npu and oupu ndcaors commonly employed for agrculural producvy analyses (Bojnec, Laruffe 2008, 2011; Douarn, Laruffe 2011). More specfcally, he ulzed agrculural area (UAA) n hecares was chosen as land npu varable, annual wor uns (AWU) as labour npu varable, nermedae consumpon n Las, and

9 Producve Effcency of he Lhuanan Famly Farms ( ): A Non paramerc Inference wh Pos effcency Analyss oal asses n Las as a capal facor. On he oher hand, he hree oupu ndcaors represen crop, lvesoc, and oher oupus n Las, respecvely. Indeed, he hree oupu ndcaors enable o acle he heerogeney of producon echnology across dfferen farms. The cos effcency was esmaed by defnng respecve prces for each of he four npus descrbed earler. The land prce was obaned from he Eurosa and assumed o be unform for all farms durng he same perod. The labour prce s average salary n agrculural secor from Sascs Lhuana. The prce of capal s deprecaon plus neress per one Las of asses. Meanwhle, he nermedae consumpon s drecly consdered as a par of oal coss. The daa for 200 farms seleced from he FADN sample cover he perod of Thus a balanced panel of 1200 observaons s employed for analyss. The analyzed sample covers relavely large farms (mean UAA 244 ha). As for labour force, he average was 3.6 AWU. In order o quanfy he facors nfluencng he agrculural producvy, we employed he followng ndcaors for he second sage analyss. Toal oupu was used o denfy relaonshp beween farm sze and effcency. Sol ndex was used o chec wheher sgnfcanly nfluences producvy. Farmer s age was used o es he lnage beween demographc processes and effcency. The dummy varable for organc farmng was nroduced o explore he performance of he organc farms. The share of crop oupu n he oal oupu was used o asceran wheher eher he crop or lvesoc farmng s more effcen n Lhuana. The rao of producon subsdes o he oal oupu was employed o esmae he effec of suppor paymens, whereas he rao of subsdes for equpmen o he oal oupu was defned o denfy he mpac of capal nvesmens. 5. ESTIMATES OF THE PRODUCTIVE EFFICIENCY The npu orened VRS DEA model (Eq. 20) was employed o analyze he FADN daa whch were arranged no he cross secon able. The cos effcency esmaes were obaned by employng Eq. 21. Fnally, he allocave effcency scores were compued resdually. The summary of effcency scores s presened n Table 1. The laer able descrbes he mean values for he whole perod of Consderng he VRS echnology, he mean echncal effcency flucuaed around 65.8%, whch vrually means ha average farm should reduce s npus by some 35% and susan he same oupu level o acheve he effcency froner (hese numbers do also nclude he scale effec). The mean value of allocave effcency was equal o 70.5% and ndcaed ha he cos producvy can be ncreased by 29.5% due o changes n npu mx. Consderng hese ypes of effcency, he mean economc effcency or, alernavely, cos effcency of 46% was observed for he Lhuanan famly farms. Therefore, hese farms should be able o produce he same amoun of oupu gven he npu vecor s scaled down by some 54%. Suchle shfs, however, mgh no be feasble for every farm gven hey are specfc wh ceran heerogeney across farmng ypes. Table 1 also

10 Tomas Baležens, Irena rščuaenė suggess ha he hghes varaon was observed for he economc effcency esmaes where coeffcen of varaon was 7.2% for VRS echnology. The nensy varables (peer weghs) nvolved n Eq. 20 defnes he shape of he producon froner. These varables, herefore, enable o assess wheher he DMU s operang n he range of ncreasng, consan, or decreasng reurns o scale. In case he DMU s operang n he range of DRS (IRS) reurns o scale, s sad o be operang a he supra-opmal (sub-opmal) scale. Table 1. Descrpve sascs of npu orened echncal (TE), scale (SE), allocave (AE), and cos (CE) effcency scores under CRS and VRS assumpons TE AE CE SE VRS CRS VRS CRS VRS CRS Arhmec Mean Medan Sandard Devaon Sample Varance Coeffcen of varaon Mnmum Grossopf (1986) offered a mehodology o deermne he range of scale reurns he DMU operaes n. for hs purpose one needs o esmae effcency scores under non-ncreasng reurns o scale (NIRS). The sad esmaes can be obaned by supplemenng Eq. 20 wh he followng convexy consran: CRS VRS 1 1. For he npu-orened DEA, he followng rules hold: If, hen he DMU operaes under CRS (. e. a he opmal scale). If CRS VRS NI R S CRS VRS NI S, he DMU operaes under DRS. If R, he DMU operaes under IRS. Fg. 1 presens he dynamcs of farm srucure n erms of reurns o scale. As one can noe he share of farms experencng ncreasng reurns o scale flucuaed n beween he mnmum value of 81% n 2008 and he maxmum value of 95% n Hence, he larges share of he observed farms was operang a a sub opmal scale and could ncrease s effcency by ncreasng he operaon scale. Meanwhle he share of farms operang a he opmal scale was close o nl and oscllaed n beween 0.5% and 8%.

11 Producve Effcency of he Lhuanan Famly Farms ( ): A Non paramerc Inference wh Pos effcency Analyss 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% IRS CRS DRS Fgure 1. The share of farms experencng decreasng (DRS), consan (CRS), and ncreasng (IRS) reurns o scale, The dynamcs of dfferen ypes of effcency hroughou s presened n Table 2. As one can noe, here were wo major shocs n producve effcency: he frs one occurred n 2006, whereas he second one n Obvously he former s relaed o worsened clmac condons, for he mean gran yeld dropped from 28.9 /ha n 2005 down o 18.8 /ha n 2006 (Sascs Lhuana, 2011). The second shoc s relaed o some urmol n he agrculural mares. Consderng he varaon of dfferen ypes of effcency one can conclude ha he cos effcency (CE) was he mos me varan, whereas he allocave effcency (AE) he mos me nvaran. Indeed, he coeffcens of varaon presened n Table 1 are 4% for AE and 7.2% for CE under VRS. Therefore, he shfs n economc effcency can be arbued o shfs n echncal and scale effcency o a hgher exen. Ths fndng ndcaes ha farmers end o adjus he npu mx for her farms a a reasonable rae gven he changes n prces of he producon facors.

12 Tomas Baležens, Irena rščuaenė Table 2. Dynamcs of he Lhuanan famly farm effcency, TE AE CE SE VRS CRS VRS CRS VRS CRS Crop farmng Average Lvesoc farmng Average Mxed farmng Average Noe: he repored esmaes are he npu orened echncal (TE), scale (SE), allocave (AE), and cos (CE) effcency scores under CRS and VRS assumpons Alhough he dscussed descrpves of he effcency scores provde some nsghs, he furher analyss s needed o fahom he processes affecng producve effcency. The underlyng causes and sources of neffcency hus are furher analyzed by he means of ob and log models. 6. EXPLAINING INEFFICIENCY: TOBIT AND LOGIT MODELS Ths secon explores he man deermnans of neffcency and quanfes her mpac on effcency scores or dynamcs hereof. We have defned he wo man

13 Producve Effcency of he Lhuanan Famly Farms ( ): A Non paramerc Inference wh Pos effcency Analyss foc for our pos effcency analyss, namely () ob regresson for parcular facors of effcency and () log regresson for facors nfluencng longudnal changes n effcency. The followng facors were chosen as regressors. The logged oupu (lnoupu) denfed he scale of operaon and was consdered a proxy for farm sze. Indeed, he queson of he opmal farm sze has always been a salen ssue for polcy maers and scenss. The sol qualy ndex (Sol) was ncluded n he models o es he relaonshp beween he envronmenal condons and effcency. The rao of crop oupu o he oal oupu (CropShare) capures he possble dfference n farmng effcency across crop and lvesoc farms. Smlarly, he dummy varable for organc farms (Organc) was used o quanfy he dfference beween organc and convenonal farmng. I s due o Offermann (2003) ha Lhuanan organc farms exhb 60 80% lower crop yelds dependng on crop speces f compared o same values for convenonal farmng. The demographc varable, namely age of farmer (Age) was nroduced o asceran wheher young farmers orened measures can nfluence he srucural effcency. Fnally, he effec of producon and equpmen subsdes on effcency was esmaed by consderng raos of producon subsdes o oupu (SubsShare) and equpmen subsdes o oupu (ESubsShare), respecvely Tob model Gven he effcency scores are bounded o he nerval [0, 1], one needs o use he ob model for he second sage analyss (Samarajeewa e al., 2012). An mplc assumpon of he ob approach s ha an unobservable laen varable E* underles he observed sample (Hoff, Vesergaard, 2003). A lnear model descrbes he relaonshp beween E* and explanaory varables x : E * x u x u, where u s he error erm. Due o censorng of he dependen varable (vz. effcency score) one observes he bounded varable E whch ges he followng values: a, x u a E x u, a x u b, (22) b, b x u where a and b are he lower and upper bounds of he censored varable, respecvely. Maxmum lelhood funcon s herefore defned o f he model for he sample daa; see Hoff and Vesergaard (2003) for furher deals. As for DEA effcency scores, we can always bound hem o he nerval [0, 1]. Indeed usually neher of he DMUs exhb zero valued effcency. The lower bound a hus can be dropped from Eq. 22. Gven he abovemenoned peculares of he ob model, he margnal effec of a sngle explanaory varable x s a funcon of he whole vecor of coeffcens β, explanaory varables hemselves, varance of he error erm σ, and bounds a and b:

14 Tomas Baležens, Irena rščuaenė EV ( E x) b x a x, (23) x where Φ s he sandard normal densy funcon. The hree ob models were specfed for cos (economc), allocave, and echncal effcency wh prevously defned facors as regressors. Tables 3 and 4 presen he fed ob model. As one can noe, he auoregressve erms were ncluded n he hree ob models (Table 3) o ncrease her robusness. The bacward procedure was carred ou n erms of heeroscedascy and auocorrelaon conssen (HAC) z values. Therefore, Tables 3 and 4 presen he sgnfcan facors of effcency. Furhermore, Eq. 23 was employed o esmae margnal effecs (he resuls are avalable upon reques). Table 3. Coeffcens of he ob regresson descrbng he mpac of effcency facors CE AE TE Esmae z value Esmae z value Esmae z value (Inercep) *** *** CE *** CE ** AE *** AE *** TE *** TE ** lnoupu *** *** lnoupu *** *** Sol * * * Age ** ** Organc * CropShare ** SubsShare ** SubsShare ** Log(scale) *** *** *** Noes: () CE, AE, and TE sand for cos, allocave, and echncal effcency, respecvely; () z values are heeroscedascy and auocorrelaon conssen (HAC) ones; () sgnfcance codes for respecve p values: '***' 0.001; '**' 0.01; '*' 0.05; '.' 0.1. The ob regresson (cf. Table 3) suggess ha boh cos and allocave effcency s posvely mpaced by he scale of operaon (. e. he amoun of oupu), whereas echncal effcency has no sgnfcan relaon o he laer

15 Producve Effcency of he Lhuanan Famly Farms ( ): A Non paramerc Inference wh Pos effcency Analyss varable. Therefore can be concluded ha he larger farms are more lely o mae more effcen decsons regardng npu mx. Indeed bgger quanes nvolved n supply and producon chan managemen n larger farms provde more flexbly for large farms. Ths s especally he case n raher small mare of Lhuana. Alhough some oher sudes repored effcency o follow U-shaped curve across farm sze groups (Laruffe e al. 2004), our fndngs mgh dverge from he forms, gven we analyze sample parcularly coverng large farms. Thus only he rgh al of he effcency curve s wha we focus a. The sol ndex had a negave mpac on he hree ypes of effcency, namely cos, allocave, and echncal effcency. Furhermore, hese effecs are for he whole range of he values of he laer ndcaor. Sol qualy, hence, affecs boh echnology and npu managemen. Ths fndng s lely o be an oucome of poor esmaon mehodology for hs varable and farmng pracces relaed o areas specfc wh hgher sol qualy. Indeed, farms locaed n ferle areas end o explo exensve agrculure raher han nensve one and hus op for less nnovave echnologes. Furher research, however should be conduced o denfy he exac facors of he negave ln beween sol qualy ndex and effcency. Farmer s age had a posve effec on allocave and economc effcency, albe hs effec was negave for he younges farmers. Thus farmer s age maers o a hgher exen for younger farmers, whereas s mpac decreases laer on. Furhermore, farmer s age s lely o be relaed o economc raher han echncal sde of farmng. Organc farmng appeared o be more effcen f compared o convenonal farmng. To be specfc, an average organc farm exhbed cos effcency score whch was greaer by a margn of 4.7%, whereas echncal effcency ncreased by some 8.2%. Therefore he resuls suppor Tzouveleas e al. (2001) who argued ha organc farmng regulaons may encourage a more reasonable applcaon of ferlzers ec., whch, n urn, deermnes respecve echnologcal mprovemens. In addon, organc farms produce more expensve producon. Due o he negave coeffcen for crop oupu share n he oal oupu, crop farmng can be consdered less effcen f compared o anmal farmng. Indeed, ncrease n crop share of 1 pp causes declne n effcency of 4.8% (Table 3), whereas he margnal effec a he maxmum crop share dmnshes o 2.5%. Ths fndng s conssen wh sudy by Laruffe e al. (2004) who dscovered smlar paern for Polsh farms. The ob model suggess ha producon subsdes had a negave smulaneous effec on echncal effcency,. e. ncrease of subsdes o oupu rao by 1 pp. lead o an average decrease n effcency equal o 10%. Meanwhle, he lagged effec of producon subsdes on cos effcency was also observed. Thus producon subsdes affeced echncal effcency raher han allocave effcency. As for equpmen subsdes, hey apparenly had no sgnfcan effec on level of producve effcency. The dscussed facors deermned he level of cos, allocave, and echncal effcency. The followng sub secon dscusses he mpac of hose facors on changes n effcency.

16 Tomas Baležens, Irena rščuaenė Log model The log model s employed o esmae he followng regresson: * x u, (24) y 0 * where y s a laen varable (Maddala 2001). The observed dummy varable, y, ges he bnary values: y * 1, y 0 0, oherwse. (25) By nong P Prob( y 1) and assumng ha u s symmercally dsrbued, we have P F x, (26) 0 where F s ceran funcon chosen wh respec o assumed dsrbuon of he error erm. In case of he logsc cumulave dsrbuon we have exp( Z ) FZ ( ) 1 exp( Z ), (27) and hus FZ ( ) ln Z. (28) 1 FZ ( ) As for he log model, he followng equaon holds: P ln 0 x, (29) 1 P where lef-hand sde of he equaon s called he log-odds rao and means he rao beween probables o observe y 1 and y 0. The changes n effcency scores were explored by he means of log regresson. Therefore we defned y 1 n case a ceran farm experenced ncrease n effcency and y 0 oherwse. The same facors as for ob regresson were employed. The bacward procedure was carred ou wh respec o HAC z values. Table 4 presens he fnal resuls.

17 Producve Effcency of he Lhuanan Famly Farms ( ): A Non paramerc Inference wh Pos effcency Analyss Table 4. Coeffcens of he log regresson descrbng shfs n effcency scores wh respec o ceran deermnans of effcency. Esmae z value Sg. CE (Inercep) lnoupu *** Sol *** CropShare Organc *** SubsShare ** ESubsShare *** AE (Inercep) *** lnoupu *** Sol ** CropShare * Organc SubsShare ESubsShare TE (Inercep) *** lnoupu *** Sol *** CropShare Organc *** SubsShare * ESubsShare ** Noes: () CE, AE, and TE sand for cos, allocave, and echncal effcency, respecvely; () z values are heeroscedascy and auocorrelaon conssen (HAC) ones; () sgnfcance codes for respecve p values: '***' 0.001; '**' 0.01; '*' 0.05; '.' 0.1.

18 Tomas Baležens, Irena rščuaenė As Table 4 suggess, larger farms were more lely o experence ncrease n effcency. Specfcally, he ncrease n he oal oupu of 1% caused ncrease of he odd rao rangng beween 1.4 for cos effcency and 1.6 for echncal effcency. These numbers subsequenly are ranslaed no rao beween probables of evens 1 y (. e. ncrease n effcenc and y 0, respecvely. The sol qualy ndex exhbed a negave relaon o ncrease n economc, allocave, and echncal effcency. These relaonshps can be explaned by nsuffcen pressure for farmers who have her farms locaed n ferle areas o adop nnovave manageral pracces. Crop farmng s more lely o acheve posve shf n allocave effcency (effec on odd rao accouns 1.6 mes), hough s no he case for cos and echncal effcency. Indeed, crop mare s raher dynamc and herefore farmers can adjus her decsons relaed o npu mx n a more dynamc way. The fed log model mposes ha farms adoped organc farmng ncrease her odd rao for achevng hgher cos effcency a a margn of 8.2, whereas gans n echncal effcency are also o be posvely affeced by he same decson. Boh producon and equpmen subsdes are lely o cause decrease n cos and echncal effcency, albe hey do no sgnfcanly affec allocave effcency. These phenomena mgh be lned o excessve purchases of long-erm asses. On he oher hand, equpmen subsdes end o dsor he npu mare and hus nflae prces of he raded npus, vz. machnery, buldngs. Furhermore, farms recevng hgher producon subsdes mgh be locaed n less favoured areas, where hey are subjec o lower producvy due o agro-clmac condons. As one can noe, farmer s age had no sgnfcan mpac on probably o experence effcency ncrease. To conclude, large lvesoc farms adoped organc farmng pracces are hose mos lely o exhb an ncrease n producve effcency. 7. CONCLUSIONS The producve effcency of Lhuanan famly farms was esmaed on a bass of FADN daa sample by he means of DEA, whch dd ndcae ha he mean echncal effcency flucuaed around 65.8%, whereas he mean allocave effcency approached 70.5%. The mean economc effcency, herefore, was raher low, namely 46%. These fgures mply ha Lhuanan famly farms should mprove boh echnologcal and manageral pracces and hus acheve hgher producvy n order o successfully compee n he sngle mare of he EU. The second sage analyss of effcency scores whch, ndeed, had no been performed for Lhuanan agrculural secor before revealed some causes of neffcency. Specfcally, he ob model was employed o quanfy effcency effecs, whereas he log model was fed o esmae facors of ncrease n effcency. Bascally, hese analyses showed ha large lvesoc farms adoped organc farmng pracces are hose mos effcen. Moreover, hey were o exhb an ncrease n producve effcency.

19 Producve Effcency of he Lhuanan Famly Farms ( ): A Non paramerc Inference wh Pos effcency Analyss Indeed, crop farmng provdes nermedae goods for anmal farmng and hus he laer acvy generaes hgher value added and, hus, s specfc wh hgher effcency. The new Rural Developmen Programme for Lhuana should herefore pay more aenon o mea breedng whch can furher mprove aracably of anmal farmng as well as effcency of suchle acves. Furhermore, effcency ndcaors should be ncluded n progress repors and consue a par of monorng sysem. I should be noed ha hs analyss was based on daa from large farms (mean UAA was over 240 ha). Hence, here s a need for furher sudes on a wder range of famly farms. Furhermore, farmng effcency s o be esmaed by he means of paramerc mehods, namely sochasc froner analyss, whch allow more flexbly n aclng heerogeney relaed o dfferen farmng ypes. ACNOWLEDGEMENTS Ths research was funded by he European Socal Fund under he Global Gran measure. The auhors would le o han Dr Algrdas Barus from Vlnus Unversy for hs valuable suggesons. The usual dsclamer apples. REFERENCES [1] Aldea, A., Cobanu, A. (2011), Analyss of Renewable Energy Developmen Usng Boosrap Effcency Esmaes. Economc Compuaon and Economc Cybernecs Sudes and Research, 45(1), 77 90, ASE Publshng; [2] Baner, R. D., Charnes, A., Cooper, W. W. (1984), Some Models for Esmang Techncal and Scale Ineffcences n Daa Envelopmen Analyss ; Managemen Scence, 30(9), ; [3] Bojnec, Š., Laruffe, L. (2008), Measures of Farm Busness Effcency; Indusral Managemen & Daa Sysems, 108(2), ; [4] Bojnec, S., Laruffe, L. (2011), Farm Sze and Effcency durng Transon: Insghs from Slovenan Farms; Transformaons n Busness and Economcs, Vol. 10, No. 3, pp ; [5] Charnes, A., Cooper, W. W., Rhodes, E. (1978), Measurng he Effcency of Decson Mang Uns; European Journal of Operaonal Research, 2(6), ; [6] Charnes, A., Cooper, W. W., Rhodes, E. (1981), Evaluang Program and Manageral Effcency: An Applcaon of Daa Envelopmen Analyss o Program Follow Through ; Managemen Scence, 27(6), ; [7] Debreu, G. (1951), The Coeffcen of Resource Ulzaon; Economerca, 19(3), ; [8] Douarn, E., Laruffe, L. (2011), Poenal Impac of he EU Sngle Area Paymen on Farm Resrucurng and effcency n Lhuana; Pos-Communs Sudes, 23(1), ; [9] Farrell, M. J. (1957), The Measuremen of Techncal Effcency; Journal of he Royal Sascal Socey, Seres A, General, 120, Par 3, ;

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