MODELLING FARMS PRODUCTION DECISIONS UNDER EXPENDITURE CONSTRAINTS RAUSHAN BOKUSHEVA AND SUBAL KUMBHAKAR

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1 MODELLING FARMS PRODUCTION DECISIONS UNDER EXPENDITURE CONSTRAINTS RAUSHAN BOKUSHEVA AND SUBAL KUMBHAKAR ETH Zurch (Swss Federal Insttute of Technology) State Unversty of New York n Bnghamton kkar@bnghamton.edu Paper prepared for presentaton at the 07 th EAAE Semnar "Modelng of Agrcultural and Rural Development Polces". Sevlla, Span, anuary 29 th -February st, 2008 Copyrght 2007 by [Raushan Bokusheva and Subal Kumbhakar]. All rghts reserved. Readers may make verbatm copes of ths document for non-commercal purposes by any means, provded that ths copyrght notce appears on all such copes.

2 Abstract Lmted budget for the purchase of varable nputs mght adversely affect producer s nput use decsons and mght result n a non-optmal nput usage. If expendture constrans are present and bndng, unconstraned proft-maxmzaton s not vald for modellng producers nput use decsons. In ths paper we apply the ndrect producton functon approach whch descrbes output maxmzaton subect to a gven technology, a set of quas-fxed nputs and a gven budget for the purchase of varable nputs. By employng the ndrect producton functon n the stochastc fronter framework we can estmate producer s output loss due to both expendture constrants and techncal neffcency. Our estmaton results show that most of the study farms were expendture constraned durng the consdered perod. Expendture constrants have caused on average a potental output loss of percent. Output loss due to techncal neffcency s qute moderate and averages 8 percent. Key words: Indrect producton functon, SFA, expendture constrants, techncal effcency, Russan agrculture. 2

3 Introducton The nput use decsons and producton effcency of Russan farms have been subect of many nvestgatons n the past decade (Sotnkov, 998; Osborne and Trueblood, 2002; Bokusheva and Hockmann, 2006). These studes were prmarly sought to evaluate the effect of economc transformaton on the allocaton of productve resources. Under the central plan economy, farm producton nputs were delvered accordng to the governmental plans and thus were not necessarly the subect of farmers decson makng. However, producers nput allocaton decsons, partcularly nput adustments have ganed mportance n the transtonal context, prmarly due to need to ncrease effcency n nput use. At the same tme, low lqudty of farms and an only lmted access to external fnance due to fnancal market mperfectons serously lmted producers space for nput decsons durng transton. Hence, lmted budget for the purchase of varable nputs mght have nduced a nonoptmal nput usage, whch n turn resulted n productvty and effcency losses. If expendture constrans are present and bndng, then the assumpton of a proft-maxmzng frms s hghly questonable, because t presupposes that farms face no constrants n ther nput-allocaton decsons. On the other hand, n the cost-mnmzng formulaton, farmers are assumed to mnmze the cost of a pre-determned level of output. Although ths formulaton ncorporates some constrants on producers behavour, the exact nature of the constrant seems to be msspecfed. That s the constrant s not n terms of output. Indeed, n the transtonal context farms are constraned by the avalablty of funds requred for purchase of varable nputs. Ths type of constrant can not be suffcently represented n the cost-mnmzng formulaton. In partcular, f the farm has lmted budget for purchase of varable nputs, then proft maxmzaton s equvalent to revenue/output maxmzaton, gven the avalablty of funds. Ths s especally true when the markets (nputs and output) are compettve. Lee and Chambers (986) develop the theory of expendture-constraned proft maxmzaton. They derve the expendture-constraned supply by dfferentatng expendtureconstraned proft functon and show that proft-maxmzng output supply under expendture constrants equals to revenue-maxmzng supply evaluated at the optmal nput level. In ths paper we apply the ndrect producton functon approach whch descrbes output maxmzaton subect to a gven technology, a set of quas-fxed nputs and a gven budget for the purchase of varable nputs. Apart from beng a more approprate characterzaton of producers behavour, the ndrect producton functon approach has the advantage that t allows for the drect computaton of the output or the budget effect (the producton analogue of the ncome effect) resultng from a change n nput prce. In addton to facng a budget constrant, a farm may be techncally neffcent. That s, t mght not be able to operate on the producton functon (we defne t as the fronter) gven the nput quanttes. We use the stochastc fronter approach to model techncal neffcency. The presence of techncal neffcency mght also affect allocaton of nputs, and gven the presence of budget constrant the mpact on output loss wll be more. Here output loss s defned n potental sense by comparng proft maxmzng output levels wth and wthout budget constrants and techncal neffcency. 3

4 Emprcally the analyss uses survey data for 90 farms from three dfferent regons n Central, South and Volga Russa for the perod from 999 to The data contans results of structured ntervews wth farm managers conducted n 2004, as well as farm accountng data from 999 to In ths paper, we utlse the farm bookkeepng data and the data whch s related to basc characterstcs of the farm, enterprse organsaton, manageral characterstcs, producton-related characterstcs, farm busness envronment. The paper s organzed as follows. The next secton presents the general concept the ndrect producton functon wthout and wth techncal neffcency. In secton 3, we derve the econometrc specfcaton of the ndrect producton functon n the stochastc fronter framework. In secton 4 we specfy the emprcal model and descrbe estmaton procedure. The data employed n ths study s presented n Secton 5. We proceed wth the dscusson of model estmaton results n Secton 6. We fnsh by drawng conclusons. 2 Model 2. The ndrect producton functon The concept of the ndrect producton functon (IPF) s relevant n the context of maxmzaton of output subect to a gven technology, a set of quas-fxed nputs and a gven budget for the purchase of varable nputs. Underlyng ths functon, there s the famlar formulaton of producton functon that relates nputs and output: y = f ( x ; z ) () where y s the output of producer ( I ), x denotes a vector of N varable nputs used by producer, z denotes the quas-fxed nput vector of order M. The budget constrant faced by the producer can be wrtten as: C = w ' x (2) where w denotes the vector of varable nput prces faced by producer and C represents the budget avalable to producer for the purchase of varable nputs. If the producers maxmze output, gven by (), subect to the constrant n (2), the Lagrangean for the problem s: L = f ( ) + λ ( C w' x) (3) where λ denotes the Lagrange multpler assocated wth the constrant n (2), and the choce varables are the nputs, x. The exogenous varables are the elements n vectors z, w and the total budget of the producer, C, whle the nput vector x and λ are determned endogenously. Solvng the frst-order condtons ( f = λw and C wx= ' 0), we get the soluton of the endogenous varables n terms of the exogenous varables, vz., * x = g ( w; C; z) =,..., N (4a) * λ = h( w; C; z) (4b) 4

5 Substtutng the optmal values of x * from (4a) n () we get the optmal value of the obectve functon: y = ψ ( w ; C ; z ) (5) Equaton (5) represents the ndrect producton functon (IPF), whch expresses the maxmum attanable output for producer n a specfed perod as a functon of the avalablty of funds, the prce of varable nputs, the quantty of fxed nputs. y y=π+ wx y=f(x) B A C* C=wx <C* x Source: Authors own representaton. Fgure : Output and proft wth and wthout expendture constrants Unfortunately, from the precedng analyss, we cannot determne whch farms are expendture constraned and what s the potental output loss due to the presence of budget constrant. To do so, we assume that the desred budget for farm (s consstent wth maxmum proft, for * example) s C, whch by defnton can not be lower than the actual expendture (C ). That s, C * C where the strct nequalty means that the farm n queston s expendture constraned. The presence of constrants means that the farm n queston can only spend C and not because C * * C and C output wll be lower and so s proft. That s, output (proft) assocated wth * C (say y * ( ; * = ψ w C; z ) ) wll be hgher than y whch s assocated wth the budget C (gven n (5)). Ths can be shown graphcally, where the expresson for proft s rewrtten as y = π + wx wth output prce used as a numerare (Fgure ). Thus the vertcal ntercept of the lne y = π + wx measures proft. Proft wthout constrant s measured by the ntercept of the 5

6 sold lne and proft assocated wth expendture constrant s measured by the ntercept of the dotted lne that s assocated wth lower expendture. The optmzaton problem wth budget constrant can be expressed as maxmzaton of () * * η subect to C C C e = C = wx ', η 0. The Lagrangean of the problem s * η L= f() + λ( C e wx ' ) = f() + λ( C wx ' ) (6) whch s not dfferent from the one we dscussed before (3). Thus, the IPF s exactly the same. Snce we do not observe C * the correspondng output level y * cannot be observed. In other words, one can not drectly observe whch producer s expendture constraned and the extent of such constrants from the IPF. However, there s a way to get the necessary nformaton. It s through the Lagrange multpler λ. Snce at the optmum λ = L/ C = y/ C, one can get an estmate of λ by dfferentatng the estmated IPF wth respect to the observed expendture C. If a farm s not constraned ts output wll be the same as the proft maxmzng level and the value of λ wll be unty, f the output s measured n value terms. That s, at the optmum the return from spendng an addtonal euro has to be matched by a return of one euro n addtonal output. If not, ts proft can be ncreased by spendng more (less) and the farm s not operatng at the optmum. If the farm faces an expendture constrant (.e., C * C) the value of λ wll exceed unty. It follows from the fact that the producton functon s concave n x. Snce we can estmate λ for each farm (once the IPF s estmated), we can easly fnd out whch farms are expendture constraned. Snce the value of λ for an unconstraned proft maxmzng farm s unty, we can obtan C * as a soluton of C from the equaton: y/ C =. C * can then be plugged nto the IPF to get the optmum (unconstraned) output level, y *. The devaton of actual (predcted) output from the optmal output can then be vewed as output loss due to expendture constrant. 2.2 The IPF wth techncal neffcency So far we assumed that all farms are techncally effcent. That s, gven the nputs the produced output s the maxmum from the technologcal pont of vew. If farms fal to produce the techncally maxmum level of output, the producton functon can be expressed as u y = f( x ; z ) e, u 0 (7) u where u s a measure of techncal neffcency. Alternatvely, e s defned as techncal effcency. We can nterpret 00.u as the percentage loss of output for beng techncally neffcent. 6

7 Snce techncal neffcency n (7) s neutral, t does not affect margnal rate of techncal substtuton (the rato of margnal product of nputs) between two nputs. Thus, nput allocaton s not affected by the presence of techncal neffcency. In other words, the soluton of x n (4a) s not affected by the presence of techncal neffcency. However, the soluton of λ and y wll be affected n the followng fashon, * u λ = e h( w; C; z ) (8) u y = e ψ ( w ; C; z ) (9) u Snce e, margnal return to the euro ( y/ C) s lower. More specfcally, the return s only 90% f techncal effcency s 0.9. To fnd out whch farms are expendture constraned and by how much (or the affect of t on output) as well as the mpact of neffcency on output, we need to estmate * u u λ = e h( w; C; z ) n whch the e term shows the effect on output due to neffcency. The effect of credt constrant on output can be examned as before (the case wthout neffcency). 3. Stochastc ndrect producton fronter model Econometrcally, the IPF s specfed as follows: y = ϕ ( w ; C ; z )exp( v u ), (0) where φ( ) represents the ndrect producton fronter, v s a producer specfc random nose component and u 0 represents techncal neffcency. Accordngly, the producton fronter s defned as a maxmum feasble output for producer consderng hs fxed nputs endowment, varable nput prces and budget for the purchase of varable nputs. Thus, IPF allows explanng dfferences n the producers nput use by both factors - budget constrants as well as techncal neffcences. To mpose mnmum a pror restrctons on the underlyng producton technology we use a parametrc flexble functonal form to approxmate the IPF n (5). The translog functonal form s chosen because t mposes no a pror restrctons on any of the elastctes. After ntroducng the frm, fxed and varable nput subscrpts, ( I ), m (m M) and ( ), respectvely, the IPF specfcaton of the stochastc fronter gets the followng form: Here we mplctly assume that farms are allocatvely effcent. We capture allocatve neffcency n a somewhat ad hoc fashon n the error terms n the share equatons. 7

8 ln y + M + 2 = α + M M 2 β k ln w ln wk + βcc (lnct ) + k= = n= m= m= = γ 0 m = ln w α ln w ln z m + + M m= = φ ln z γ m C m ln w + α lnc C lnc + F m= θ μ ln z mc mn ln z m m ln z n lnc + v u () In addton to the usual symmetry restrctons on the coeffcents, β k,, μ ml, γ m, economc theory tells that the IPF s homogeneous of degree zero n nput prces and C. Ths gves rse to the followng set of restrctons on the parameters of the model: = = = = α + α = 0 ; (2) C β + γ = 0, =,..., ; (3) k C γ + θ = 0, m =,..., M ; (4) m mc γ + β = 0. (5) C CC These homogenety condtons can be easly mposed by scalng (dvdng) nput prces and expendture by one of the nput prce. That s, all prces and C are to be normalzed n terms of one nput prce. The constant-cost demand functon for the th varable nput can be derved from the IPF by usng Roy s dentty: y y x = / (6) w C Usng ths equaton the share of the th nput n total varable cost can be determned as followng: ln y ln y ey S = / =. (7) ln w ln C e yc where e yc denotes the output elastcty wth respect to a change n the producer s budget and e y denotes the output elastcty wth respect to a change n the prce of nput. 8

9 4 Emprcal specfcaton and estmaton procedure 4. The econometrc model The econometrc model conssts of the ndrect producton functon and (-) cost share equatons. To accommodate panel data we amend equaton () by ntroducng tme varable t and change the subscrpt wth subscrpts and t. Ths results n the followng IPF system: ln y + τ + S where e e Ct M t m= = = α + m = lnctt + 2 t yct yt γ 0 yct ln w α ln w M M 2 β k ln wt ln wkt + βcc (lnct ) + k = = n= m= t ln z mt t + + M m m= = φ ln Z γ C ln w mt t + α lnc lnc C t + M t + t + t θ mc m= 2 ln z + mt = ml lnc τ ln w t t μ ln z + v mt t t t + ln z u t lt M mt m= τ ln z eyt = + ξ t, =,...,, (9) e N = M = α + τ t + β ln C + γ ln w + θ ln z (20) C Ct CC t N k= C t M f = f = = α + τ t + γ ln C + β ln w + γ ln z (2) t C t k kt Snce the nput share equatons are not ndependent (ther sum beng unty), one nput share equaton has to be dropped to avod the problem of sngularty of the dsturbance covarance matrx. Ths s automatcally done when one nput prce s used as the numerare. The econometrc model conssts of (8) and (9) whch gve a system of equatons. Note that we have added stochastc terms ξ t n the share equatons. These nose terms can be vewed as allocatve/optmzaton errors whch can have zero or non-zero means. Non-zero means can be nterpreted as systematc over- (under-) utlzaton of nputs. f fc ft ft mt t (8) 4.2 Sngle-step vs. two-step method of estmaton Our nterest s not only to estmate the parameters n the IPF but also neffcency, whch s treated as a random varable. Ths can be done n a sngle-step usng the stochastc fronter modelng approach (see Kumbhakar and Lovell, 2000) that reles on the maxmum lkelhood method. To mplement the ML method we need to make dstrbutonal assumptons on all the stochastc components n the model. If these dstrbutonal assumptons are rght, the ML estmates are consstent and effcent. However, one can never be sure about the dstrbutonal assumptons. To guard aganst possble msspecfcaton so far as dstrbutonal assumptons are concerned, t s often better to use a two-step procedure n whch the estmators n the frst-step are free from dstrbutonal assumptons. However, to estmate neffcency, we need to make dstrbutonal assumptons. These dstrbutonal assumptons do not affect the parameter estmates n the frst-step. Furthermore, the estmaton procedure s much smpler when one uses the two-step procedure whch s what we do here. 9

10 Frst-step: In conductng the fst-step procedure we rewrte the composed error term n the IPF as * εt vt ut = vt ( ut Eu ( t )) Eu ( t ) = εt Eu ( t ) so that the mean of ε * t s zero. The Eu ( t ) term s subsumed n the ntercept f ts mean s a constant. By dong so we get a seemngly unrelated regresson (SUR) equaton system that can be easly estmated wthout makng any specfc * dstrbutonal assumptons on ε t and ξ t, except that ther means are zero. The SUR procedure gves consstent estmate of all the parameters, except for the ntercept n the IPF whch s based because t ncludes the Eu ( t ) term. The bas can be corrected usng the correcton factor that can be obtaned from the second-step. Second-step: In the second-step our prmary obectve s to obtan estmates of neffcency. Snce neffcency appears only n the IPF, we use the resduals from the IPF to recover parameters assocated wth u and also obtan-observaton-specfc estmates of u. To do so we make some dstrbutonal assumptons whch are standard n the stochastc fronter lterature (see Kumbhakar and 2 2 Lovell, 2000). These are: () u s d N(0, σ u ) truncated at zero from below; () v s d N(0, σ v ) ; and () u and v are dstrbuted ndependent of each other. Based on these assumptons the probablty densty functon of (v-u) can be easly obtaned usng the convoluton formula. The model n the second stage s: τ t = α0 + vt ut (22) where τ s the resdual from the IPF (calculated wthout usng the estmated ntercept). The ML 2 2 method can be used on the above model n (8) to obtan estmates of α,, 0 σu σ v. These are used to estmate u for each observaton (see Kumbhakar and Lovell, 2000, for detals). The techncal neffcency model can be extended n several drectons. One s to allow neffcency to be explaned n terms of some covarates. Ths can be done by allowng the mean and/or varance of techncal neffcency to be a functon of some covarates, whch are labelled as determnants of techncal neffcency. The other extenson s allow heterogenety/heteroskedastcty by makng the varance of the nose term a functon of covarates. Fnally, t s also possble to allow systematc over- (under-) use of nputs due to allocatve neffcency (optmzaton error) by makng the mean of the share equatons functons of covarates. 5 Data To test the IPF formulaton of stochastc fronter model we employ the data obtaned n the framework of a farm survey of 90 agrcultural enterprses n Orel, Samara and Stavropol regons. The data contans farm accountng data for the perod from 999 to 2003 as well as results of structured ntervews wth farm managers. Havng calbrated the data and excluded farms wth hgh level of specalsaton on a partcular producton lne, we formed an unbalanced panel data set contanng 347 observatons from totally 73 farms. In addton, the study utlzes data on the prce ndces for 0

11 agrcultural output and nputs as provded by the Russan State Statstcal Agency - Rosstat (Rosstat 2005). For the IPF emprcal specfcaton we defne farms producton output as annual farm revenue from agrcultural producton (Y). Land (L) and fxed captal (K) are regarded as quas-fxed nputs, whle farm permanent and hred labor (A), fertlzer (Fert), fuel and other materals (Fuel) are defned as varable nputs. The quantty of land s measured by the area of sown land adusted by the farm s average sol fertlty ndex. The value of farm s fxed assets n agrcultural producton s used as proxy for captal 2. Varable nputs are defned by means of farms nput prces and shares of respectve nputs n the farm total varable cost n agrcultural producton. We use farm average annual labor wages (w A ) measured n 000 Rub per one farm s average agrcultural worker, aggregated fertlzer prces 3 (w Fert ) measured n 000 Rub per one tonne of fertlzer actve substance, and fuel prces (w Fuel ) measured n 000 Rub per one tonne of fuel, as varable nput prces. Addtonally, to take account of all remanng varable nputs (plant protecton, seed, electrcty etc.), whch we don t have any prces for, we assume that ther prces can be approxmated by the farms fuel prces. Respectvely, we aggregate ther cost share wth the fuel cost share. Moreover, we use fuel prces to normalze the prces of 2 other varable nputs consdered n the study,.e. of labour and fertlzer. Snce no data were avalable for the farm predetermned expendture, we follow Lee and Chambers (986) and defne the expendture varable as the farm observed expendture on varable nputs n ndvdual years 4. The set of exogenous varables used to explan the heteroskedastcty n techncal effcency contans followng ndvdual characterstcs of the study farms: farm age (q age ), ownershp structure (q own ), sze (q sze ), ntal technology level (q tech99 ), manageral competence (q manag ), dversfcaton level (q dv ), and severty of producton rsk (q rsk ) 5. These varables were constructed by means of factor analyss and were found to explan a substantal part the varance n the orgnal data set contanng 3 farm characterstcs related to basc characterstcs of the farms, enterprse organzaton, manageral characterstcs, producton-related characterstcs and farm busness envronment. 2 All monetary varables are measured n,000 Rub. Farm agrcultural revenue and the captal stock value were adusted to the prce level n 2003 by employng annual prce ndces for agrcultural output and machnes n agrculture, respectvely. 3 We construct an aggregated fertlzer prce by dvdng the farm total fertlzer cost by the fertlzer physcal amount calculated as a sum of actve substances n dfferent types of fertlzers appled n the producton. 4 Descrptve statstcs for the varables employed to specfy the IPF can be found n Table A. 5 Descrpton of these varables can be found n Table A2.

12 6. Estmaton results Table reports the estmates of IPF for the farms consdered n ths analyss. To take account for possble regonal dfferences we ntroduced nto the model dummy varables for 3 selected regons. 6 Though only one dummy varable has a sgnfcant estmate (n case of Stavropol farms), LR test ndcate that the IPF specfcaton wth regonal dummes appears to be more approprate than the specfcaton whch does not account for regonal dfferences at the 5% level sgnfcance. One thrd of the parameters have sgnfcant estmates. The nsgnfcant parameters are prmarly assocated wth the square-term and cross-product varables. However, a smple model such as the Cobb-Douglas s reected aganst the translog model at the % level of sgnfcance usng the standard LR test. Table IPF parameter estmates varable coeffcent estmate t-value varable coeffcent estmate t-value constant wfert*wfert dummy Samara wlabor*wlabour dummy Stavropol wfert*wlabour wfert C*C wlabour Land*Land C (expendture) Captal*Captal Land Land*Captal Captal wfert*land t wfert*captal t*t wlabour*land wfert*t wlabour*captal wlabour*t wfert*c C*t wlabour*c Land*t Land*C Captal*t Captal*C Source: Authors own estmaton. The partal elastctes for the quas-fxed nputs,.e., land and captal, are postve (0.6 and 0.05 at the mean values of the data, respectvely). The output supply elastcty wth respect to the farms budget for varable nputs s equal 0.92 on average, ndcatng that output s expected to rse by 0.92 per cent by a one per cent rse n budget. The output supply elastctes wth respect to fertlzers and labor are 0.9 and 0.3 on average, respectvely. Consequently, the output supply elastcty of further 6 The IPF constant term coeffcent s the ntercept estmate for farms n Oroel regon. The coeffcent estmates for the dummy varables present dfferences of the ntercept estmates for the farms from Samara and Stavropol, respectvely, compared to the farms from Oroel. 2

13 varable nputs ncludng fuel equals to These results show that Russan farms output s much more senstve to changes n the avalablty of varable than quas-fxed nputs and, thus, underlne the mportance of farm budget constrants. Addtonally, the senstvty of the farms to the avalablty of addtonal funds for purchase of varable nputs seems not to decrease durng the consdered perod the coeffcent at the tme-expendture product term C*t s not sgnfcantly dfferent from zero. Besdes, our results suggest the land-usng and captal-savng mpact of technologcal change. In Table 2 we present the results of our assessment regardng the expendture constrants and related output losses n the study farms. We calculate the level of expendture constrant for the ndvdual farms as a dfference between the desred budget and the farm s observed expendtures. 8 The results show that 33 from totally 347 farms face expendture constrants: the level of farm actual expendtures has been on average by 3 per cent lower than the desred level; wth the half of the farms beng expendture constraned at the level more than 0.2. In addton, accordng to our calculatons, the expendture constrants have caused an output loss of per cent, on average. Table 2 Expendture constrants, output loss and techncal effcency estmates Lambda Expendture constrants (C*-C)/C Output loss (Y * -Y IPF )/Y IPF a) Techncal effcency TE Mean S.D Quantles 99% % % % % % % % Notes: a) Y IPF s constraned output level (determnstc part of the IPF); Y* s unconstraned output level (calculated by replacng the observed farm s expendture C by the desred budget level C*). Source: Authors own estmatons. Techncal neffcency presents another source of farms output loss. We estmated the basc model wthout heteroskedastcty n the nose terms and determnants of neffcency. Ths model 7 Output supply elastcty for the varable nput used for the nput prce normalzaton (n our case fuel and further varable nputs) can be calculated as the dfference between the output supply elastcty wth respect to the farms budget and the output supply elastctes of all remanng varable nputs employed n the IPF. Ths 8 We determne the desred budget level as descrbed n secton 2.. 3

14 specfcaton s reected aganst the more general models wth heteroskedastcty and determnants of neffcency. Frst we report results from the model n whch determnants of neffcency s ntroduced va the varance of u. That s, the model s heteroskedastc n terms of both v and u. The heteroskedastcty n v s explaned by such ndvdual farm characterstcs lke farm age, ownershp and management competence. The parameter estmates are reported n Table 3. The management varable has negatve coeffcent whch means that better management reduces mean neffcency. Note that Eu ( ) = 2/ πσu( z). Thus f z affects σ u negatvely, the mean neffcency s reduced when z s ncreased. In the present case, management reduced mean neffcency by 3.6%. Smlarly, age of the farmers and the ownershp are found to reduce varablty n output, ceters parbus. On the other hand, management ncreases varablty n output. The average techncal neffcency of farms n the sample s 0.8. That means, output s reduced, on average, by 8% due to techncal neffcency. In Fgure 2 we report the frequency dstrbuton of the estmates of techncal neffcency. It can be seen from the fgure that techncal neffcency estmates for most of the farms are wthn the 0%- 25% range. Output loss due to neffcency can be obtaned from the last column of Table 2, vz., from -TE. Table 3 Parameter estmates of the fronter model (second stage) varable Fronter coeffcent estmate t-value const σ u functon const q manag σ v functon const q age q own q manag Source: Authors own estmatons. We also estmated a model n whch systematc allocatve optmzaton errors are allowed. Ownershp, management and rsk varables are used to explan such systematc errors (means of the error terms n the share equatons). The mean output loss due to expendture constrants s found to be qute smlar. For brevty, here we report only effcency results whch are also qute smlar (the mean value) from the prevous model. The entre dstrbuton s plotted n Fgure 3. 4

15 0 Source: Authors own estmatons. Fgure 2: Dstrbuton of techncal neffcency 0 8 Densty E(u e) Densty E(u e) Source: Authors own estmatons. Fgure 3: Dstrbuton of techncal neffcency wth systematc optmzaton errors. 5

16 7. Conclusons The study appled the ndrect producton functon approach to descrbe producers output maxmzaton problem under expendture constrants. The ndrect producton functon descrbes the maxmum attanable output as a functon of the avalablty of funds, gven the prce of varable nputs and the quantty of fxed nputs. By dervng condtons for the optmal nput use, we determne the effect of expendture constrants on the producer output. Ths allows us dentfyng the potental output loss due to the presence of budget constrant. An addtonal source of potental output loss regarded n our analyss s techncal neffcency. To estmate techncal effcency of producers under expendture constrants, we defne IPF as the producton fronter. Accordngly, the producton fronter s defned as a maxmum feasble output subect to a gven technology, a set of quas-fxed nputs and a gven budget for the purchase of varable nputs. Thus, IPF allows explanng dfferences n the producers nput use by both factors - budget constrants as well as techncal neffcences. The emprcal analyss s based on the survey data for 90 farms from three dfferent regons n Central, South and Volga Russa for the perod from 999 to Our results show that most of the study farms were expendture constraned durng the consdered perod farm actual expendtures have been on average by 3 per cent lower than ther desred level. The expendture constrants have caused on average a potental output loss of per cent. Addtonally, we have found the average techncal neffcency of farms to be 8%. Ths ndcates that even n the presence of mperfectons n fnancal markets, Russan farms have potental for ncreasng ther output, ceters parbus. Fnally, from a set of varous farm characterstcs only manageral competence has been found to determne sgnfcantly the farms techncal effcency. Ths s n lne wth the tradtonal hypothess done n the stochastc fronter analyses and shows that management s decsve for reducng techncal neffcences. 6

17 References: Battese, G. E. and Coell, T.. (995). A model for techncal neffcency effects n a stochastc fronter producton functon for panel data. Emprcal Economcs 20: Bhattacharyya, A. and Kumbhakar, S. (997). Market mperfectons and output loss n the presence of expendture constrant: A generalzed shadow prce approach, Amercan ournal of Agrcultural Economcs 79: Bokusheva, R and Hockmann, H. (2006). Producton rsk and techncal neffcency n Russan agrculture. European Revew of Agrcultural Economcs 33: Kumbhakar, S. C. and Lovell, C. A. K. (2000). Stochastc Fronter Analyss. Cambrdge: Cambrdge Unversty Press. Lee, H. and Chambers R.G. (986). Expendture Constrants and proft maxmzaton n U.S. agrculture. Amercan ournal of Agrcultural Economcs 68: Osborne, S. and Trueblood, M.A., (2002a). An examnaton of economc effcency of Russan crop output n the reform perod. In Schulze, E., Knappe, E., Serova, E. and Wehrhem, P. (eds), Studes on the Agrcultural and Food Sector n Central and Eastern Europe 2. Success and Falures of Transton - The Russan Agrculture between Fall and Resurrecton: Halle/Saale: Agrmeda. Rosstat (2005). Russan statstcal yearbook. Moscow, Russa: Russan State Statstcal Agency. Sotnkov, S. (998). Evaluatng the effects of prce and trade lberalsaton on the techncal effcency of agrcultural producton n a transton economy: The case of Russa. European Revew of Agrcultural Economcs 25:

18 APPENDIX Table A Descrptve statstcs of the IPF varables ( ) Output 000 RUB Land (hectures of sown area adusted for sol fertlty) Captal 000 RUB of 2003 Observed expendture 000 RUB Labor wages 000 RUB per annum Aggregated fertlzer prce 000 RUB per tonne Fuel prce 000 RUB per tonne Labor cost share Fertlzer cost share Mean S.D Mn Max Source: Authors own calculatons. Table A2 Descrpton of farms ndvdual characterstcs Varable Farm age (q age ) Farm sze (q sze ) Farm ownershp structure (q own ) Farm manageral competence (q manag ) Level of ntal technology (q tech99 ) Producton rsk magntude (q rsk ) Farm dversfcaton (q dv ) Descrpton assessed by consderng the perod snce farm establshment, farmhead s years wth the farm, average farm managers years wth the farm; assessed by consderng farm agrcultural area, number of employees, fxed assets and lvestock; assessed by consderng ownershp status of the farm-head and share of the farm co-owners n the total number of farm managers. assessed by consderng share of managers wth hgh educaton and personnel loyalty; evaluated by the farm head wth the scores - technology s dated to 5 - one of the most modern technologes for 999; evaluated by the farm head wth the scores - low to 5 - hgh ; assessed by consderng dversfcaton wthn agrculture, use of onfarm processng and membershp n a vertcally-ntegrated holdng. Note: Most of farm characterstcs are based on the farmers evaluaton of several related characterstcs/ndcators by usng a Lkert-scale; Source: Authors own assessment. 8