DUAL TECHNOLOGICAL DEVELOPMENT IN BOTSWANA AGRICULTURE: A STOCHASTIC INPUT DISTANCE FUNCTION APPROACH

Transcription

1 DUAL TECHNOLOGICAL DEVELOPMENT IN BOTSWANA AGRICULTURE: A STOCHASTIC INPUT DISTANCE FUNCTION APPROACH Xaver Irz and Davd Hadley 2 Deparmen of Agrculural and Food Economcs. Unversy of Readng, Readng RG6 6AR, UK. E-mal: X.T.Irz@readng.ac.uk 2 School of Geography and envronmenal Scences, Unversy of Brmngham, Egbason, Brmngham B5 2TT, UK. ABSTRACT To mprove he welfare of he rural poor and keep hem n he counrysde, he governmen has been spendng 40% of he value of agrculural GDP on agrculural suppor servces. Bu can nvesmen make smallholder agrculure prosperous n such adverse condons? Ths paper derves an answer by applyng a wo-oupu sx-npu sochasc ranslog dsance funcon, wh neffcency effecs and based echncal change o panel daa for he 8 dsrcs and he commercal secor, from 979 o 996. Ths model demonsraes ha herds are he mos mporan npu, followed by draf power, land and seeds. Mullaeral ndces for echncal change, echncal effcency and oal facor producvy (TFP) show ha he echnology level of he commercal secor s more han sx mes ha of radonal agrculure and ha he gap has been ncreasng, due o echnologcal regresson n radonal agrculure and modes progress n he commercal secor. Snce he levels of effcency are smlar, he same paern s repeaed by he TFP ndces. Ths resul hghlghs he polcy dlemma of he rade-off beween effcency and equy objecves. JEL classfcaon: O4, Q Keywords: smallholder, commercal, agrculural effcency, Boswana INTRODUCTION Boswana s a landlocked souhern Afrcan counry, bordered o he souh and eas by Souh Afrca and Zmbabwe and o he wes and norh by Namba. Wh an area of 566,000 square klomeres and a populaon of only abou.5 mllon, he populaon densy s unusually low a 2.6 persons per square km (World Bank, 2002). However he carryng capacy s also low, snce he sols are mosly poor and he clmae sem-ard, wh frequen droughs, so he vas majory of he land s beer sued o cale ranchng han arable agrculure. Indeed, n he pas, beef expors (manly o he European Unon) were he major source of foregn exchange, bu damonds (Boswana s he world s leadng exporer n value erms) and oursm are now more mporan. Alhough he dscovery of damonds has rescued Boswana from s former poson as one of he poores counres on earh, mnng provdes lle employmen, so he wealh s no shared and he real mporance of agrculure s ha s sll he man source of ncome for approxmaely half he populaon. Snce accouns for less han fve percen of GDP (World Bank, 2002), s clear ha he agrculural populaon s relavely poor and he dsrbuon whn he secor s also exremely unequal. Abou half he farm famles own no cale a all, whle he polcally well conneced have accumulaed large herds. However, he damond revenue allows he governmen o spend as much as fory per cen of agrculural GDP on suppor schemes ha are nended o mprove he welfare of he agrculural populaon and keep hem n he rural areas, despe he very harsh condons (Thrle e al., 2000). 2 Ths paper nvesgaes he effecveness of hs expensve suppor program, a queson ackled by Seleka (999) who nvesgaed he performance of radonal arable agrculure n Boswana for he perod. Hs concluson was ha governmen suppor o he secor had a posve effec on he welfare of rural households bu was unsusanable, and ha agrculural producvy acually declned over he sudy perod. Proceedngs of he 25 h Inernaonal Conference of Agrculural Economss (IAAE) 6 22 Augus 2003 ISBN Number: Durban, Souh Afrca Proceedngs produced by: Documen Transformaon Technologes Conference Organsed by: Even Dynamcs

2 The frs conrbuon of our paper s o fll a gap n he exsng leraure by evaluang he producvy performance of he whole of Boswana agrculure. Arable agrculure (he sub-secor suded by Seleka (999)) accouns for only around 0% of agrculural GDP, so hs sudy also covers anmal producon and he growng commercal secor. The second conrbuon s o demonsrae he advanages of he paramerc dsance funcon approach o characersng he agrculural echnology and decomposng producvy growh n he conex of a lowncome counry. The only pror example of use of dsance funcons for hs purpose s Brümmer e al. (2002) who nvesgaed farm-level producvy growh n dary producon n hree European counres. The emprcal model s a wo-oupu sochasc npu dsance funcon ha s used o analyse agrculure effcency and producvy n he egheen dsrcs of Boswana and he commercal secor, for he perod from 979 o 996. The approach s approprae, frs because requres only daa on oupus and npus, whch are well recorded, whereas markes for he major npus, such as land and labour, are no suffcenly developed for here o be meanngful prces. 3 Second, accouns for nose, whch s an advanage over nonparamerc mehods such as DEA. Thrd, ess show ha he crop and anmal secors canno be aggregaed, whch rules ou he use of sochasc producon funcons o esmae he echnology and effcency levels. By conras, dsance funcons can accommodae mulple npus and oupus. The mehod produces oupu and npu elasces and leads o he esmaon of ndces for echncal change, echncal effcency and oal facor producvy. Ths allows he commercal secor o be compared wh radonal agrculure. The remander of he paper s organzed as follows. Secon wo dscusses he heory and secon hree very brefly descrbes he daa. The resuls are repored n secon four, begnnng wh ess o deermne he approprae model. Secon fve presens he effcency and producvy ndces and he fnal secon concludes by summarsng he resuls and suggesng furher developmens. THE INPUT DISTANCE FUNCTION: DEFINITION, PROPERTIES AND INTERPRETATION The npu dsance funcon frs nroduced by Shepard (970) s defned on he npu requremen se L ( as: D (x,=max{ρ: x/ρ L (} () I measures he larges facor of proporonaly by whch he npu vecor x can be scaled down n order o produce a gven oupu vecor y wh he echnology exsng a a parcular me. For any npu-oupu combnaon (x, belongng o he echnology se, he dsance funcon akes a value no smaller han uny, whle a value of uny smply ndcaes echncal effcency. More generally, he dsance funcon provdes a measure of echncal effcency snce s recprocal s he well-known Farrell (957) npu-based ndex of echncal effcency. The npu dsance funcon s always homogenous of degree one n npus and nhers properes from he paren echnology as dealed n Färe and Prmon (995). 4 Mos useful for he nerpreaon of he emprcal esmaes s he dualy beween he cos and npu dsance funcons, whch s easly expressed as: C ( w, = Mn{ wx : D ( x, } x From hs mnmsaon problem, where w denoes a vecor of npu prces, s sraghforward o relae he dervaves of he npu dsance funcon o he cos funcon. Frs, wh respec o npu levels x k, one obans: * D ( x ( w,, wk * = = rk ( x, (3) xk C ( w, Hence, he dervave of he npu dsance funcon wh respec o a parcular npu k s equal o he cosdeflaed shadow prce of ha npu r k *, whch s herefore expeced o ake a posve value. 5 The prevous equaly s more convenenly expressed n erms of he log dervave of he dsance funcon: D, x k ln D = ln x k * wk xk ( w, = = S C ( w, ε (4) k (2)

3 Equaon (4) saes ha he log dervave of he npu dsance funcon wh respec o npu k s equal o s cos share S k. I herefore capures he relave mporance of ha npu n he producon process, a propery ha we use o nerpre our esmaon resuls. Wh respec o he oupu vecor y, applcaon of he envelope heorem o mnmsaon problem (2) leads o he followng equaly: * ln D ( x ( w,, ln C ( w, ε = = (5) D, ym ln y m ln y m The elascy of he npu dsance funcon wh respec o any oupu s herefore equal o he negave of he cos elascy of ha oupu. I s expeced o be negave for all desrable oupus and, n absolue value, reflecs he relave mporance of each oupu. Fnally, and mos mporanly for our purpose, he dsance funcon can easly nform he researcher on he evoluon of he echnology over me. For analycal racably, hs paper follows Chambers (988) n assumng ha a sable relaonshp exss beween oupus, npus and me, or: D ( x, = D ( x, y, ) (6) Once agan, sraghforward applcaon of he envelope heorem o mnmsaon problem (2) leads o: D, ln = D * ( x ( w, y, ), y, ) lnc( w, y, ) = ε (7) Hence, he elascy of he npu dsance funcon wh respec o me s equal o he elascy of cos reducon and provdes a dual measure of he speed of echncal change. A negave value for hs elascy ndcaes echnologcal regresson and a posve value echnologcal progress. Ths analyss can be pursued furher, by consderng a Hcksan-syle defnon of echncal change bas based on he relave facor shares expressed n equaon (4): 2 S k ln D Bk = = ln xk A posve (negave) value of B k ndcaes ha echncal change s based n favour of (agans) npu k. Fnally, noe ha he dsance funcon can be used o derve vrually all he classcal properes of he underlyng echnology, such as reurns o scale and measures of npu and oupu subsuably (Färe and Prmon (995), Grosskopf e al. (995), Morrson Paul e al. (2000), Km (2000)). Consan reurns o scale are defned n erms of he dsance funcon by: λ > λ = λ (9) 0, D( x, y, ) D( x, y, ) The oher properes of he dsance funcon are no developed, snce hey are no used n hs applcaon. An Esmable Model The value of he dsance funcon s no observed so ha mposon of a funconal form for D (x,y,) does no perm s drec esmaon. A convenen way of crcumvenng hs problem was suggesed by Lovell e al. (994) who explo he propery of lnear homogeney of he npu dsance funcon, expressed mahemacally as: D (λx,y,) = λd (x,y,) λ>0 (0) Assumng ha x s a vecor of dmenson K and seng λ=/x, where x denoes s (arbrarly chosen) frs componen, he prevous equaon s expressed n logarhmc form as: 6 ln D ( x, y, ) = ln x ln D ( x / x, y, ) () + Smlar reasonng s used o esablsh ha mposng CRS mples he followng relaonshp: ln D ( x, y, ) = ln x ln y ln D ( x / x, y / y, ) (2) + (8)

4 The nex sage of he analyss reles on he dea ha he logarhm of he dsance funcon n () measures he devaon of an observaon (x,y,) from he deermnsc border of he npu requremen se L(y,) whch, followng he sochasc froner leraure, s self explaned by wo componens. The frs one corresponds o random shocks and measuremen errors ha can ake eher posve or negave values and are descrbed by a symmerc error erm -v. The second one corresponds o echncal neffcences ha are also assumed o be sochasc and are capured by a non-negave random varable u. A a concepual level, he presence of neffcences can n urn be jusfed by a non-unform dsrbuon of manageral sklls across he populaon of frms usng he same echnology. Mahemacally, he prevous assumpons are summarzed by: lnd (x,y,)=u - v (3) Equaons () and (3) are now combned o gve: -ln(x ) = lnd (x/x,y,) - u+ v (4) If CRS s mposed, we oban a slghly dfferen expresson: -ln(x )+ln(y ) = lnd (x/x,y/y,) - u+ v (5) Gven a parameersaon of he dsance funcon and dsrbuonal assumpons on he random erms, he prevous equaons (4) or (5) can be esmaed by he maxmum lkelhood mehods ha have now become commonplace n he sochasc froner leraure (summarsed n Coell, Rao and Baese, 998). All models consder ha he random error erms v are d and follow a normal dsrbuon N(0,σ 2 v) bu dffer wh respec o he dsrbuon of neffcences u. Exendng he semnal model of Agner, Lovell and Schmd (977), Baese and Coell (995) relax he assumpon of dencally dsrbued neffcency erms n order o denfy he deermnans of echncal neffcences and s hs model ha we use n he emprcal applcaon. Accordngly, s assumed ha he sochasc erms u are obaned by runcaon a zero of a normal varable N(µ ; σ 2 u ) where: 7 µ = z δ (6) The erm z denoes a vecor of observable explanaory varables whle δ s a vecor of parameers o be esmaed. In hs conex, he lkelhood funcon can be expressed algebracally and maxmsed numercally o produce esmaes of boh he npu dsance funcon and he vecor of parameers δ. Furher, whle he ndvdual neffcency levels are no drecly observable, he mehod allows for calculaon of her predcors expressed as (Coell and Perelman, 996): TE P P = / D = / E[exp( u ) v u ] (7) Funconal Form The ranslog s used because mposng lnear homogeney n npus s no possble for he oher flexble funconal forms and he Cobb-Douglas volaes he convexy condon, as well as beng oo resrcve. The model wh K npus and M oupus herefore akes he followng form: K M K K ln Dxy (,, ) = α + α ln x + β ln y + ε + α ln xln x k k m m kk' k k' k= m= 2 k= k' = M M K M K M 2 βmm ' ln ym ln ym ' + ε + γ km ln xk ln ym + γ kln xk + γ mln ym m= m' = k= m= k= m= (8) The condons for lnear homogeney n x are: K K K K α = ; k, α = 0; m, γ = 0; γ = 0 (9) k kk' km k k= k' = k= k= The emprcal applcaon models regonal, raher han farm level, producon and s herefore preferable o mpose consan reurns o scale (CRS) on he echnology. The mpled resrcons for he ranslog are: M M M M M β = ; m, m', β = β = 0; k, γ = 0; γ = 0 (20) m mm' mm' km m m= m= m' = m= m=

5 Usng he wo ses of resrcons (9) and (20) produces an esmable equaon, whch s he specal case of equaon (5) for he ranslog: ln + ln = + ln + ln + + ln ln K M K K * * * * x y α0 αk x k βm y m ε αkk' x k x k ' k= 2 m= 2 2 k= 2 k' = 2 M M K M K M * * 2 * * * * βmm ' ln m ln m' ε γ km ln k ln m γ k ln k γ m ln m m= 2 m' = 2 k= 2 m= 2 k= 2 m= 2 + y y + + x y + x + y u+ v 2 2 (2) where x k * denoes he normalsed npu quany x k /x and y m *=y m /y denoes he normalsed oupu quany y m /y. We furher mpose symmery of he dsance funcon by seng: k, k', α β = β (22) kk ' = α k ' k ; m, m', Gven he dual naure of Boswana agrculure, a dummy varable D s added o allow he echnologes o dffer n level n he wo secors and a cross-erm beween he dummy varable and he me rend allows dfferen pahs of echnologcal change n he wo secors. Ths gves he full model as: mm' x + y = TL x y αβεγ + φd+ φ D u+ v (23) m' m * * ln ln (,,,,,, ) D D The lmed daa avalable resrced he choce of neffcency effecs and n he end hree varables were seleced: a me rend, a cross-erm beween he commercal dummy and he me rend and fnally he oupu mx p: µ = δ 0 + δ + δ D + δ p (24) Ths specfcaon allows neffcences o vary over me, bu n a possbly dfferen manner n he wo subsecors. DATA The deal of how he daa se was bul s gven n Annex. All seres are for 979 o 996, gvng a panel of 342 observaons. Noe ha wha s referred o as year corresponds n fac o he agrculural season beween year and year + and ha s also how he resuls are repored n he emprcal secon of he paper. The oupus are crops and lvesock and he componens were aggregaed usng consan (995) prce weghs, so hese seres are equvalen o physcal quanes of oupu. The npu seres nclude sx dfferen facors of producon, whch are eher measured n physcal uns (land, labour and draf power) or are consan (995) prce aggregaes (seeds, ferlsers and herds). The oupu mx varable p was smply defned as he revenue share of lvesock n oal oupu. RESULTS Tess of hypoheses for model selecon Alernave specfcaons of he model were evaluaed usng generalsed lkelhood rao ess, whch compare he lkelhood funcons under he null and alernave hypohess, represened by he model descrbed n he las secon. 8 Table frs repors he es ha compares he froner wh he mean npu dsance funcon, esmaed by consderng ha he neffcency erm u s non-sochasc and equal o zero. In hs conex, any devaon from he froner of he npu requremen se s solely explaned by random shocks and he dsance funcon can be convenenly esmaed by ordnary leas squares. The sgnfcan drop n he lkelhood funcon assocaed wh hs model, from 5.34 o 43.35, mples a clear rejecon of he null hypohess. Ths s confrmed by he sgnfcanly large value of parameer γ n Table 3 (0.95) ha ndcaes ha mos of he devaon from he deermnsc border of he npu requremen se s due o echncal neffcences raher han random shocks. Hence, sgnfcan echncal neffcences exs n Boswana agrculure. d p

6 Table. Tess of Hypohess. The second es deermnes wheher he varables nroduced as neffcency effecs mprove he explanaory power of he model. The null hypohess s rejeced a he % level, mplyng ha he dsrbuons of neffcences are no dencal across ndvdual observaons bu depend on he varables ncluded n vecor z. Ths resul gves srong suppor o he neffcency model of Baese and Coell (995) as opposed o he smpler models of he older leraure. The hrd es s on he separably of he npus and oupus n he npu dsance funcon. Ths hypohess s defned mahemacally by equang all cross-erms beween npus and oupus (γ km) o zero. These resrcons are srongly rejeced, whch mples ha s no possble o aggregae conssenly he wo oupus no a sngle ndex. Ths s why he dsance funcon s used raher han a sochasc froner producon funcon, whch requres oupu aggregaon pror o esmaon. Then, he ranslog funconal form s esed agans he null hypohess ha he Cobb-Douglas represens an accepable approxmaon of he rue npu dsance funcon and agan he null s rejeced, mplyng ha he resrcons mposed by he Cobb-Douglas are napproprae. The ffh es focuses on he dual naure of Boswana agrculure by consderng he null hypohess ha all hree parameers assocaed wh he commercal secor dummy varable are smulaneously equal o zero. Ths s rejeced, mplyng ha he wo sub-secors have dfferen echnologcal characerscs ha wll be nvesgaed furher n he nex secon. Fnally, he las es relaes o he hypohess ha echnologcal progress s cos-neural, meanng ha does no affec facor shares. Ths proposon s rejeced a he fve percen level of sgnfcance. Alogeher, he resuls of hese specfcaon ess pon o he complexy of echnologcal relaonshps n Boswana agrculure: echncal neffcences are sgnfcan, npus and oupus are no separable, he Cobb- Douglas whch s resrcve n erms of subsuon possbles s no approprae, echnologcal change s based and here s evdence of mporan dfferences beween radonal and commercal agrculure. We now urn o he esmaon resuls n order o characerse he echnology and s evoluon over me. Dsance funcon resuls The resuls are repored only for he model seleced on he bass of he ess. The mporan parameer esmaes are repored n Tables 2 and 3, whle he remanng parameers are relegaed o Annex 2, Table A. Togeher he ables show ha ou of he 44 esmaes, 22 are sascally sgnfcan a he 5% level. 9 The several sgnfcan cross produc and squared erms n Table A show why he es rejeced he Cobb Douglas as nadequae. Table 2. Elasces of npu dsance funcon a sample mean.

7 Nex, he parameer esmaes can be nerpreed n lgh of he heory developed n he frs secon. All he varables were mean dfferenced pror o esmaon so ha he elasces of he dsance funcon wh respec o npu quanes, oupu quanes and me esmaed a he sample mean correspond smply o he frs order coeffcens. Equaon (5) esablshed ha he elascy of he dsance funcon wh respec o each oupu corresponds o he negave of he cos elascy of ha parcular oupu. Table 2 repors ha, as expeced, hese wo elasces are negave and hghly sgnfcan. Hence, ncreasng producon of eher of he wo oupus resuls n a subsanal ncrease n cos. The esmaes also ndcae ha he cos elascy of lvesock oupu (0.90) s much larger han he correspondng elascy for crops (0.0). Ths resul means ha a 0% ncrease n lvesock oupu resuls n a 9% ncrease n oal cos, whle he correspondng fgure for crops s only %. Hence, he esmaes clearly reflec he domnance of lvesock producon n Boswana agrculure. The elasces of he dsance funcon wh respec o npu quanes are equal o he cos shares and herefore reflec he relave mporance of he npus n he producon process. Table 2 reveals ha four of he sx elasces are posve, as expeced, wh reasonable levels of sascal sgnfcance. The elascy wh respec o herd sze s larges wh a value of 0.75 ha means ha he cos of ha npu represens 75% of oal cos a he sample mean. Ths s no an unexpeced resul gven he mporance of lvesock producon n Boswana agrculure. Draf power comes nex n erms of cos share wh a value of 0.2, a resul ha suggess ha sol preparaon s crucal for crop producon n Boswana. Land s obvously an mporan facor of producon n agrculure and s refleced by an elascy of 0., whch s sascally sgnfcan a he 0% level. Fnally, he seed npu has a posve elascy equal o Conrary o heorecal expecaons, he model also produces wo small negave elasces, for ferlser and labour npu. The ferlser resul can be explaned by he fac ha Boswana agrculure s domnaed by exensve ranchng, wh very lle use of chemcal ferlser, relave o he (unrecorded) exensve use of anmal manure. The nsgnfcan elascy of labour mus reflec he low opporuny cos and producvy of smallholder labour, bu s also parly caused by collneary wh herd sze and land area. DUAL AGRICULTURAL DEVELOPMENT: EFFICIENCY OF TRADITIONAL AND COMMERCIAL AGRICULTURE Insghs from he regresson resuls The specfcaon ess esablshed ha here are subsanal echnologcal dfferences beween he commercal and radonal secors. Table 3 shows ha he parameer of he commercal dummy varable n he dsance funcon has a posve value of.93 and s hghly sgnfcan. The exponen of hs parameer, whch s 6.9, can be nerpreed as he rao of he commercal and radonal dsance funcons, meanng ha compared o he radonal echnology, he commercal echnology can produce he same oupu wh less han one sxh he npus. 0 Ths s an mporan resul ha suggess ha here s a huge echnologcal gap beween commercal and radonal agrculure. Ths large gap s conssen wh he lmed evdence avalable for arable agrculure. Seleka (999) repors ha average yelds for sx dfferen crops n he commercal secor over he perod were beween wo and a half and eleven mes hose for radonal farmng. Table 3. Technology n radonal and commercal agrculure. Nex, we analyse how he echnologes evolved over me n he wo sub-secors. The heory secon shows ha he dervave of he npu dsance funcon wh respec o me s equal o he elascy of cos reducon and herefore provdes a convenen dual measure of he rae of echnologcal progress.

8 Table 3 repors a value of 0.03 for he parameer ε,, whch mples ha he radonal secor of Boswana agrculure has undergone echnologcal regresson from 979 o 996, a he rae of 3.% per annum. The elascy of cos reducon n he commercal secor evaluaed a he sample mean s equal o ε +φ D, where he second em s he coeffcen of he cross-erm beween he commercal dummy and he me rend n he dsance funcon. The esmae of for φ D n Table 3 means ha he commercal secor has undergone echnologcal progress a a rae of 4.8% (7.9%-3.%) per annum over he perod. Thus, he echnologcal gap beween radonal and commercal agrculure n Boswana s no only large bu also ncreasng quckly, as he dfference n raes of echnologcal change n he wo sub-secors s almos 8% over he perod. Table 3 hen repors ha he overall mean level of echncal effcency n he sample s 85%, whch s concdenally also he mean effcency level n he wo sub-secors. Once he dfference n echnologcal levels s aken no accoun, he wo secors are herefore largely smlar n erms of echncal effcency. More neresng s he evoluon of he effcency ndces over me. Frs, he coeffcen of he me rend, nroduced as an neffcency effec (δ n equaon (24)) akes a negave and hghly sgnfcan value. Consequenly, as me goes by, he mean of he normal dsrbuon ha s runcaed a zero o represen neffcences n he radonal secor becomes more negave, whch sgnals an mprovemen n echncal effcency. Hence, hs resul suggess ha he radonal secor operaes progressvely closer o s echnologcal froner, whch s no surprsng snce we have jus esablshed ha hs froner s self regressng. In he commercal secor, he evoluon of neffcences over me follows a dfferen paern snce he coeffcen of he cross erm beween he dummy varable and he me rend n he neffcency componen s sascally sgnfcan a he % level. For hs secor, he effec of he me rend s refleced by he sum δ + δ D, whch akes a posve value, ndcang a progressve decrease n effcency. Fnally, he las column of Table 3 demonsraes ha farms wh a relavely large oupu share of lvesock end o be more effcen han farms specalsng more heavly n crop producon. In summary of hs secon, he resuls show echnologcal dualsm beween he commercal and radonal secors. A a sac level, here exss a major echnologcal gap beween he wo sub-secors, wh he commercal secor performng much beer han s radonal counerpar. There s also no sgn ha hs suaon s mprovng snce, o he conrary, he radonal secor appears o have experenced a slow echnologcal regresson over he sudy perod, whle smulaneously he commercal secor was experencng echnologcal progress. Ths paern of echnologcal change explans he evoluon of echncal effcences. The radonal secor ends o operae progressvely closer o s regressng froner, whle n he commercal secor here s evdence ha neffcency has ncreased. Techncal Change, Techncal Effcency and TFP Indces The resuls repored above are averages over he full perod a he sample mean and do no ake accoun of some mporan aspecs of he model, such as he bases of echnologcal change. 2 The magnude of he effcency changes over he whole perod and her mpac on producvy also reman o be quanfed. Thus, we now presen ndces of echncal change, echncal effcency and oal facor producvy (TFP), whch provde a full accoun of he way n whch agrculure has developed n Boswana. The echnology ndex s obaned by channg he ndces of annual echnologcal change calculaed from equaon (7) 3 whle he effcency scores are he predcors descrbed n equaon (7). The chaned TFP ndex s hen smply he produc of he wo oher ndces. Table 4 begns by reporng mullaeral echncal change ndces. The commercal secor s gven he convenonal arbrary sarng value of 00. The frs resul of he las secon was ha he commercal secor was, on average, 6.9 mes more effcen han radonal agrculure. Thus, he average of he echnology ndex for he radonal secor s se a 4.5 (penulmae row), whch gves a sarng value of 9.8. Wh he bases of echnologcal change aken no accoun, here s echnologcal regresson n radonal agrculure of 2.88% per annum, whle he commercal secor echnology mproves a.42% per annum (las row). Ths s conssen wh he resuls of he prevous secon bu he dfferences n facor proporons n he wo sub-secors end o reduce he rae of echnologcal dvergence beween he wo secors.

9 Table 4. Technology, effcency and producvy ndces. The annual resuls n Table 4 show ha for he commercal secor here was sagnaon n he frs par of he perod, followed by growh, as he governmen began major echnologcal suppor projecs. Ths paern s more easly dscerned n Fgure, whch plos he seres. The commercal secor growh rae from 987 s an mpressve 2.7% per annum, bu he able and fgure show ha he very expensve effors o ad smallholders, such as he Acceleraed Ranfed Arable Programme, consdered by Seleka (999), dd nohng more han sop he regresson of echnology n he smallholder secor, where here s sll no growh. Snce he commercal secor s 97% ranchng, hese programmes have concenraed on nfrasrucure mprovemens, such as drllng boreholes, alhough here have been effors o mprove sock and veernary servces. 4 Fgure. Producvy growh and s componens.

10 The echncal effcency ndces dffer far less, wh radonal agrculure only abou 0% worse han he commercal secor a he sar of he perod. Then, confrmng he resuls of he las secon, effcency mproves n radonal agrculure, whch can be explaned n par by he regressng froner. However, he annual fgures n Table 4, ploed n Fgure, sugges ha weaher condons (droughs) also nfluence echncal effcency n radonal agrculure and are responsble for relavely large and sudden decreases n years such as 987 and 99. Many of he smallholder programmes are a maer of drough relef, such as dsrbung free anmal feed o preven slaugher n bad years. The payoff, n erms of mananng he lvelhoods of he poor may be subsanal, bu he cos of hese modes effcency gans, of 0.60% per year, s consderable. The echncal effcency seres for he commercal secor shows he droughs even more clearly and heses accoun for much of he effcency losses, bu here s also some ncrease n neffcency over me, a 0.26% per annum, whch suggess ha some producers are no assmlang he new echnologes and are fallng behnd he advancng froner. Las, he TFP ndces are he produc of he echncal change and echncal effcency ndces and, as he fgure shows, hey follow smlar pahs o he effcency ndces, because echncal change s smooher and more gradual. Ths combnaon of echncal and effcency changes resuls n a TFP for radonal agrculure ha falls from a value of 6, o 0.8, whch s a declne of 2.3% per annum. Thus, despe all he programmes, he smallholder s producvy has declned over he full perod, alhough he resuls for he las fve years sugges ha hs rend has now come o a hal. The commercal secor has sagnang TFP n he early perod, bu does seem o have made rapd progress n he second half of he sudy perod. The annual growh rae for he full perod s only.6%, bu from 989, s 2.94% per annum, drven by rapd echnologcal progress. If hs rae of growh can be mananed, he prospecs for commercal agrculure n Boswana are good, bu here s a clear case of dualsc developmen. Despe massve suppor programmes, whch may well be excellen n equy erms, he effcency of radonal agrculure has no mproved a all. Seldom has he rade-off beween equy and effcency objecves resuled n such a clear polcy dlemma. CONCLUSIONS Boswana has used damond revenues o suppor agrculure, whch accouns for only 4% of GDP, bu suppors abou half he populaon. Ths paper sudes he effcency effecs of hese programmes, usng a wo-oupu dsance funcon froner model, wh dummes for he commercal secor and neffcency effecs, whch was seleced on he bass of exensve ess. The daa are a panel of 342 observaons, for 8 regons and he commercal secor, over he perod from , whch are suffcen o suppor hs reasonably sophscaed model. The resuls show ha here s a huge echnology gap beween radonal agrculure and he commercal secor, whch s more han sx mes as echnologcally advanced. Despe he effors of he governmen o mprove he lvelhoods of he poor smallholders, her level of producvy has fallen, whle he commercal secor, whch specalses heavly n cale ranchng, has progressed. Hence, almos 40 years afer he ndependence, and despe major nvesmens o suppor smallholders, agrculure n Boswana has become ncreasngly dualsc. The resuls show ha pas agrculural polces have no been successful n effcency erms and have made lle conrbuon o he process of economc developmen. Naurally, hese polces can be jusfed on equy grounds bu he resuls seem raher unsasfacory n vew of he hgh level of governmen suppor o agrculure, whch would be clearly unsusanable whou damond revenue. The polces amoun o provdng a safey ne for smallholders and amelorang many of he effecs of he harsh and varable clmae. Ths s laudable, bu he lack of echnologcal progress n he radonal secor suggess ha here s lle scope for mprovng he echnologes of he resource poor. Those wh no cale are unlkely o prosper wh a few smallsock and low yeldng gran crops.

11 The Mnsry of Agrculure connues o nroduce new polces ha dffer from hose of he pas. The NAMPAADD 5 programme launched n Ocober 2002 focuses on he arable and dary secors and has he explc am of ryng o enable radonal farmers o ransform o commercal farmng and o arge ncenves o benefcares and areas where hey guaranee a posve change o farm producvy (Mnsry of Agrculure, 2003). Whls s hard o argue agans commercalsaon as he way o mprove he ncomes of subssence producers, he scope for hs n arable and dary farmng s lmed o a few areas. The majory of he counry s suable for lle bu ranchng and no oher agrculural acvy seems parcularly vable. For commercalsaon o be based around cale ranchng, he governmen needs o desgn schemes o spread ownershp o more of he rural populaon, or ensure ha he benefs from larger herds spll over o he locals who do no have cale. ACKNOWLEDGEMENTS The auhors are graeful o he Deparmen for Inernaonal Developmen for fundng hs sudy and Oxford Polcy Managemen for organzng. The saff of he Deparmen of Agrculural Plannng and Sascs, Mnsry of Agrculure, Boswana conrbued o he daa collecon and provded local experse. We parcularly hank Howard Sgwele, Mrs K Molefh and Sephen Ackroyd. REFERENCES Agner D., K. Lovell and P. Schmd. (977), Formulaon and Esmaon of Sochasc Froner Models, Journal of Economercs, 6, 2-37 Baese, G. and T. Coell (995). A Model for Techncal Effcency Effecs n a Sochasc Froner Producon Funcon for Panel Daa, Emprcal Economcs, 20, Brümmer, B., T. Glauben and G. Thjssen (2002). Decomposon of Producvy Growh Usng Dsance Funcons: The Case of Dary Farms n Three European Counres, Amercan Journal of Agrculural Economcs, 84(3): Chambers, R.G. (988). Appled Producon Analyss A Dual Approach, Cambrdge Unversy Press Coell, T. and S. Perelman (996). Effcency Measuremen, Mulple-oupu Technologes and Dsance Funcons: Wh Applcaons o European Ralways, Unversy of Lege, CREPP workng paper No 96/05 Coell, T.J., D.S.P. Rao and G.E. Baese. (998). An Inroducon o Effcency and Producvy Analyss. Boson: Kluwer Academc Publshers Färe, R. and D. Prmon (995). Mul-oupu Producon and Dualy: Theory and Applcaons, Kluwer Academc Publshers Farrell, M.J. (957). The Measuremen of Techncal Effcency, Journal of he Royal Sascal Socey, 20: Grosskopf, S., D. Margars and V. Valdmans (995). Esmang oupu subsuably of hospal servces: A dsance funcon approach, European Journal of Operaonal Research 80: Halu, A. and T.S. Veeman (2000). Envronmenally Sensve Producvy Analyss of he Canadan Pulp and Paper Indusry, : An Inpu Dsance Funcon Approach, Journal of Envronmenal Economcs and Managemen, 40: Km, H.Y. (2000). The Anonell Versus Hcks Elascy of Complemenary and Inverse Inpu Demand Sysems, Ausralan Economcs Papers, 39(2): Kodde, D. A. and F.C. Palme (986). Wald crera for jonly esng equaly and nequaly resrcons, Economerca, 54(5), Lovell, C.A.K., S. Rchardson, P. Travers and L.L. Wood (994). Resources and Funconngs: A New Vew of Inequaly n Ausrala, W. Echlorn (ed.), Models and Measuremen of Welfare and Inequaly, Berln, Sprnger-Verlag Mnsry of Agrculure (2003). Homepage of Mnsry of Agrculure of Boswana a hp:// Morrson Paul, C.J., W.E. Johnson and G.A.G. Frengley (2000). Effcency n New Zealand Sheep and Beef Farmng: The Impacs of Regulaory Reform. The Revew of Economcs and Sascs, 82(2): Seleka, T.B. (999). The performance of Boswana's radonal arable agrculure: growh raes and he mpac of he acceleraed ranfed arable programme (ARAP), Agrculural Economcs, 20:2-33 Shephard, R. W. (970). Theory of Cos and Producon Funcons. Prnceon: Prnceon Unversy Press

12 Thrle, C., A. Lusg, K. Molefh, J. Pesse and K. Suharyano (2000). Sudy o Assess he Soco-economc Impac of Agrculural Research and Developmen Programmes n Boswana, , fnal repor of projec commssoned by he Deparmen of Agrculural Plannng and Sascs, Mnsry of Agrculure, Boswana and funded by DFID (UK) World Bank (2002). Afrcan Developmen Indcaors, World Bank

13 ANNEX : DATA The oupu and npu daa seres requred for he esmaon were manly obaned from he key sources lsed below. Some seres were recovered from he compuerzed daabase of he Cenral Sascal Offce (CSO) and ohers were provded by he Boswana Agrculural Markeng Board (BAMB). All seres are for 979 o 996, unless oherwse saed, and as menoned earler, wha s referred o as year corresponds n fac o he agrculural season beween year and year +. Lvesock Producon: Sales and home slaugher: Number of Cale, Sheep and Goas for he 8 dsrcs and 6 regons, from he Boswana Agrculural Census Repors and Boswana Agrculural Sascs, CSO, ( ). Labour: Lvesock labour use per average herd of Cale, Sheep & Goas from Farm Managemen Surveys (Deparmen of Agrculural Plannng and Sascs (DAPS), varous years). Herds: Number of Cale, Sheep and Goas by dsrc and regon from Boswana Agrculural Census Repors and Boswana Agrculural Sascs (CSO, ). Crops Producon: Toal producon n onnes of Sorghum, Maze, Mlle, Beans/pulses by dsrc and regon from he Boswana Agrculural Census Repors and Boswana Agrculural Sascs (CSO, ). Labour: Toal labour used for ploughng and planng by dsrc and regon from Boswana Agrculural Sascs (CSO, ). Seed: Seed Planed: Kg/Ha of sorghum, maze, mlle, beans/pulses planed by dsrc and regon from Boswana Agrculural Sascs (CSO, ). Ferlzer: Toal ferlzer used by dsrc and regon (CSO Inernal Daa, ) Area: Area planed by dsrc and regon of sorghum, maze, mlle, beans/pulses by dsrc and regon from Boswana Agrculural Census Repors (979-93) and Boswana Agrculural Sascs (CSO, ) Draf Power: Toal number of oxen and donkeys from Boswana Agrculural Census Repors (varous years) and Boswana Agrculural Sascs (CSO, ). Daa References Cenral Sascal Offce, (979-96). Boswana Agrculural Sascs, Dvson of Agrculural Plannng and Sascs, Mnsry of Agrculure, Gabarone Cenral Sascs Offce, (varous years), Boswana Agrculural Census, Dvson of Agrculural Plannng and Sascs, Mnsry of Agrculure, Gabarone Deparmen of Agrculural Plannng and Sascs, (varous years). Farm Managemen Survey Resuls, Governmen of Boswana, Gabarone

14 ANNEX 2: Table A: Oher parameer esmaes Parameer Esmae -rao α α ss α aa α hh α ff α dd β ll ε α sa α sh α sf α sd γ sl γ s α ah α af α ad γ al γ a α hf α hd γ hl γ h α fd γ fl γ f γ dl γ d γ l δ Noes: LLF σ FAOSTAT repors an agrculural labour force of 300,000 n 2000 from a oal labour force of 673,000. For he same year, he agrculural populaon was 686,000 and he non-agrculural populaon 855, Ths level of expendure would be mpossble whou he damond revenue. Four per cen would be a more usual level, so supporng a secor o hs exen s mos unusual; bu hen Boswana s an unusual counry. 3 Ths prevens he esmaon of dual cos and prof funcons, whch have he addonal drawback of mposng resrcve behavoural assumpons. 4 In parcular, as descrbed n Halu and Veeman (2000), he npu dsance funcon s non-decreasng and concave n npus and non-ncreasng and quas-concave n oupus. 5 x * (.) denoes he vecor of cos-mnmsng npu quanes. 6 The noaon x/x s used o denoe he K- vecor of raos x k /x, for k. 7 The ndvdual and me subscrps and were gnored up o hs pon for clary. 8 Tha s, we compue he sasc λ = 2[lnLH( H o ) ln LH( H)], where LH(.) denoes he lkelhood funcon, H 0 he null hypohess and H he alernave hypohess. Under he null, hs sasc follows a ch-squared dsrbuon wh a number of degrees of freedom equal o he number of resrcons. The esmaon resuls are usually repored n erms

15 of parameers σ 2 =σ u 2 +σ v 2 and γ=σ u 2 /σ 2 raher han n erms of he orgnal varances. If he null hypohess nvolves parameer γ, whch as a rao of wo varances s necessarly posve, he es sasc follows a mxed ch-squared dsrbuon and he crcal values can be found n Kodde and Palme (986). 9 The subscrps used o repor he coeffcen esmaes are l for lvesock, c for crops, s for seeds, a for land, h for herds, f for feeds, d for draf anmals and L for labour. Noe ha Table 2 does no repor -raos for he elasces of he dsance funcon wh respec o crops and labour. Ths s so because he values of hese parameers are nferred from he resrcons expressed n (9) and (20). 0 I s sraghforward o esablsh ha he values of he dsance funcon n he wo secors D c and D r are relaed by he followng expresson for any npu-oupu combnaon: D c (x,y,0)/d r (x,y,0)=exp( D ). Ths rao measures he dfference n echnologcal levels beween he wo secors. In parcular, suppose ha he npu-oupu combnaon (x, s echncally effcen for he radonal secor,.e. D r (x,y,0)=. The npu dsance funcon for he commercal secor akes a value of exp( D ) whch s srcly greaer han uny snce D s srcly posve. Hence, n order o produce he oupu vecor y, he npu vecor x could be scaled down by usng he commercal echnology. Hence, for maze, average yelds n he commercal and radonal secors were equal o 723 and 66 kg/ha respecvely. 2 For nsance, f a parcular regon makes relavely more use of a facor agans whch echnologcal change s based, ha regon wll experence relavely slow echncal change. 3 The exac mehod of calculaon s smlar o ha used by Coell e al. (998), page 234, for a sochasc producon froner. 4 There have also been programmes o develop rrgaed arable agrculure, such as frus and vegeables, n he commercal secor, bu hese are no ncluded n he naonal sascs and requre separae evaluaon. 5 Naonal Maser Plan for Arable Agrculure and Dary Developmen.