Key words: Smallholder dairy, technical efficiency, stochastic production frontier

Transcription

1 JAGST Vol. 14(2) 2012 Smallholder daryng n Kenya SMALLHOLDER DAIRYING IN KENYA: THE ASSESSMENT OF THE TECHNICAL EFFICIENCY USING THE STOCHASTIC PRODUCTION FRONTIER MODEL E. B. Majwa 1, M. M. Kavo 1 and H. Murage 1 1 Jomo Kenyatta Unversty of Agrculture and Technology Emal: eucamajwa@gmal.com Abstract Daryng n Kenya remans a mult-purpose cattle system provdng mlk, manure and captal assets to the farmer. Dary actvtes n Kenya are predomnantly run by smallholders and are concentrated n the hgh and medum potental areas. Smallholders operatng 1-3 dary cows on small farms are predomnant n Kenya. They produce 56% of the total mlk n the country and supply 80% of Kenya s marketed mlk. Estmated growth n the consumpton of mlk and dary products n developng countres s 3.3%, whch s n lne wth Kenya s 3% per year. Natonal statstcs show that mlk producton contnues to declne. For example, snce 2000 mlk annual growth rate has been 1.4% compared to 9.2% experenced between 1980 and The man challenge of Kenya s dary ndustry s how to confront growng mlk demand and a hghly compettve export envronment when yelds are as low as 195 ltres per lactaton. One of the key optons s to develop a vbrant compettve dary sector n Kenya by ncreasng the effcency of producton. Thus, ths study examned the techncal effcency of smallholder dary farms of rural Kenya. Data from a 2005 survey of smallholder farms n fve provnces was utlzed to examne the techncal effcency of smallholder farms. The Cobb-Douglas stochastc producton fronter model was used to dentfy the determnants of techncal neffcency. The fndngs revealed that the mean effcency was 79 percent, whch suggested that 21 percent of producton was lost due to techncal neffcency. The techncal effcency also vared across regons rangng from a mean of 83.9% n Central regon and 72.5% n Nyanza regon. Land sze, access to extenson servce, nfrastructure and the level of schoolng were found to reduce neffcency. Key words: Smallholder dary, techncal effcency, stochastc producton fronter Jomo Kenyatta Unversty of Agrculture and Technology 3

2 Smallholder daryng n Kenya JAGST Vol. 14(2) Introducton Kenya s a developng country and the agrcultural sector s partcularly mportant for ts large contrbuton to natonal ncome and employment. Kenya s economy s stll heavly dependent on agrculture. The Natonal statstcs show that the agrcultural sector currently contrbutes about 26% of Kenya's gross domestc product (GDP) and s a major source of lvelhood for the majorty of households, especally n the rural areas. The dary ndustry s the sngle largest agrcultural subsector contrbutng about 14% of agrcultural GDP and 3.5% of total GDP respectvely. Omore (1999) has shown that, mlk producton sustans about 800,000 small-scale farmers who account for 80 per cent of the country's total mlk producton and offers employment of about 350,000 jobs along the mlk marketng chan. Mlk sales are benefcal to farmers. Annual net earnngs from mlk cash ncome averages $370 (Ngg et. al, 2003). The stated Government polcy n the Natonal Food Polcy and the Kenya Dary Development Polcy s to mantan a poston of broad self-suffcency n food crops, mlk and meat producton. The polcy also seeks to establsh reserve stocks that wll ensure both the securty of food supply and an equtable dstrbuton of foodstuffs to each secton of the communty. Currently, the demand for mlk s growng because mlk s an mportant part of the det of both rural and urban Kenyans, wth per capta mlk consumpton of ltres per year. It has been estmated that annual consumpton of mlk and dary products n developng countres wll more than double (.e. from approxmately 168 to 391 mllon tonnes) between 1993 and 2020 (Thorpe et al., 2000). Populaton growth, urbanzaton and ncreased purchasng power are expected to drve ths ncrease n consumpton. Estmated growth n the consumpton of mlk and dary products n developng countres s 3.3%. Ths projecton s closely n lne wth Kenya s annual populaton growth rate of 3%. However, Food and Agrculture Organzaton (FAO) statstcs (2005a) show that the annual mlk growth rate n Kenya contnues to lag behnd the projected consumpton and populaton growth rates. For example snce the year 2000 mlk annual growth rate has been 1.4% as compared to 9.2% experenced between 1980 and The productvty per anmal remans as low as 195 ltres per lactaton despte the avalablty of advanced dary producton technologes when compared wth other developng countres lke Inda whose productvty per cow s more than 2000 ltres per lactaton (Karanja, 2003). Kenya was a net exporter of dary products but snce 1997, mports have grown and exports declned. The Common Market for Eastern and Southern Afrca (COMESA) statstcs ndcate that currently the mlk producton n ths regon s estmated to be 12 mllon tonnes per year aganst a demand of 14 mllon tonnes. The demand for mlk and mlk products n ths regon s expected to rse to about 400 mllon metrc tonnes of mlk n the year Thus, gven the massve 4 Jomo Kenyatta Unversty of Agrculture and Technology

3 JAGST Vol. 14(2) 2012 Smallholder daryng n Kenya ncreases n the demand for food of anmal orgn that has been predcted for developng countres n the comng years, wll the expected large ncrease n populaton and demand for mlk be met by the current level producton? To answer the above queston, there was need to know the current effcency of producton of the smallholder dary farms n rural Kenya snce they are the majorty of the producers of mlk n East Afrca as well as n the Sub Saharan regon. The man purpose of ths paper was, therefore, to nvestgate the techncal effcency of smallholder dary farms n rural Kenya. It also determned the soco economc factors nfluencng mlk yelds for small holders. 2.0 Methodology 2.1 Data sources and varables Cross sectonal data was used n ths study. The data came from the REPEAT Research on Poverty and Envronment and Agrcultural Technology survey carred out n 2005 by Temegeo Insttute of Agrcultural Polcy and Development, Kenya and the Foundaton of Advanced Studes n Internatonal Development (FASID), Japan. Stratfed random samplng was used to select 900 agrcultural households coverng fve (5) man agrcultural provnces of Kenya.e. Central, Rft Valley, Western, Nyanza and Eastern Provnces. The sample was a natonal representaton of all crop and dary keepng farmers n the man agrcultural provnces. Then a survey of all the respondents was undertaken for the study. A structured questonnare nstrument was used to collect data on physcal quanttes of nputs, ther costs and producton of crops and lvestock for the perod. Household socoeconomc varables were also collected durng the survey, e.g. assets owned, educaton level, type of household head.e. whether female headed or male headed and dstance to the nearest urban centre. In the analyss of techncal effcency the regons were classfed nto the hgh potental areas (.e. Central Provnce) and the medum potental areas (.e. Rft Valley, Nyanza, Western and Eastern Provnce). Afterwards the dary keepng households were selected from the sample. Then data cleanng ensued, removal of outlers was done and observatons wth mssng values were dscarded. Ultmately, 474 household cases were used for the stochastc fronter analyss. Techncal effcency (TE) was estmated smultaneously along wth ts determnants. The level of effcency was measured usng Cobb Douglas producton functon; the output and nput varables ncluded n the producton fronter are descrbed below and summarzed n Table 1. Output refers to the total quantty of mlk produced measured n ltres. The nputs ncluded labor (sum of famly and hred labor), number of mlkng cows, total costs for commercal feeds and veternary servces and the breed type of the cows. The varables for neffcency model were manly farm specfc factors, farmers specfc factors and Jomo Kenyatta Unversty of Agrculture and Technology 5

4 Smallholder daryng n Kenya JAGST Vol. 14(2) 2012 organzatonal factors. These varables ncluded land sze; educaton level of household male and female; off farm ncome; use of extenson servces and nfrastructure. Land sze was measured n acres, educaton level was measured by the number of years of schoolng, off farm ncome was measured by the total revenue earned outsde the farm n Kenyan shllngs, nfrastructure was captured by the amount of tme n hours t took to get to the nearest urban Centre, a dummy varable was used to capture water nfrastructure (.e. 1 f there s water on the farm, 0 otherwse); a dummy varable was used to captures extenson servce provson usng Artfcal Insemnaton servce (.e. 1 f the farmer s served wth A.I, 0 otherwse). Fnally, a dummy varable was used to dfferentate the potental n provnces (.e. 1 for central provnce as a hgh potental area, 0 otherwse). The descrptve statstcs are as presented n Table 1. Table 1: Descrptve statstcs for the varables Varable Unts Mean Std. Dev Mn Max Mlk Yeld Yeld n ltres Labor Man hours Mlkng cows Number Cost of feeds Kenya Shlngs Breed Type (Improved or local) Health costs Kenya Shlngs Land sze Hectares Offncome Kenya Shlngs Travel tme Hours Educ Male Number of years of schoolng Educ Female Number of years of schoolng Water Dummy for yes=1, No = A.I Servce Dummy for yes=1, No= Source: Tegemeo Insttute, Kenya, REPEAT Survey, 2007 The average yeld of mlk per cow per lactaton of the sampled farms was ltres whle the mnmum was 195 ltres per lactaton. Ths yeld was relatvely low compared to other mlk producers who realze a mnmum of 6000 ltres of per cow per lactaton such as Israel and South Afrca. Ths yeld was obtaned by mlkng 4 cows on average whch used: 4.29 Man-hours, expendtures of Kshs on purchased feeds and Kshs veternary servces and 4.57 Hectares. In addton, farmers spent 30 (0.52*60) mnutes of travellng to the nearest shoppng centre. Dary farmers engaged n off-farm actvtes realzed Kshs About 47% of the farmers had mproved breeds whle about 42% had local breeds. Only 33% of the sampled farms had water on farm. About 42% of the farmers used Artfcal Insemnaton servce whle 56% used bulls. 6 Jomo Kenyatta Unversty of Agrculture and Technology

5 JAGST Vol. 14(2) 2012 Smallholder daryng n Kenya 2.2 Techncal neffcency effects model The techncal effcency of an ndvdual s defned n terms of the rato of the observed output of the correspondng fronter output condtoned on the level of nputs used by the farm. Techncal neffcency s therefore defned as the rato of the amount by whch the level of producton for the farm s less to the fronter output. The use of stochastc fronter producton approach s the most popular approach to measure techncal effcency. The stochastc producton Fronter functon that was frst proposed by Agner, and hs colleagues (1977) and Meeuseen and Van den Broecl (1977) s defned as follows: Y f ( x ; ) e (1) where = 1, 2, N, e v u, Where Y represents the output level of the th sample farm; f(x; β) s a sutable functon such as Cobb Douglas or translog producton functons of vector X of nputs for the th farm and vector β of unknown parameters; e s an error term made up of two components, v whch s a random error havng zero mean N(0; 2 ) assocated wth for example measurement errors n producton and weather condtons whch farmers do not have control over and µ whch s a non negatve 2 truncated half normal N(0; ) random varable assocated wth farm specfc factors whch leads to the th farm not attanng maxmum effcency of producton. It s assocated wth techncal effcency and ranges between zero and one. Thus, ^ TE Y.. (2) * / Y * Y where, = f ( x ; ), hghest predcted output for the th farm TE u Y ( ) * Exp ( Actualoutput / Fronteroutput) (3) Y Techncal Ineffcency = 1 ^ TE. (4) 2.3 Emprcal model specfcaton The Cobb Douglas producton Fronter was used to specfy the stochastc producton fronter hence formng the bass for dervng the techncal effcency and ts related effcency measures. The stochastc Cobb Douglas producton functon was chosen because ths functonal form has been wdely used n farm effcency analyses for both developng and developed countres. The frst Jomo Kenyatta Unversty of Agrculture and Technology 7

6 Smallholder daryng n Kenya JAGST Vol. 14(2) 2012 applcaton of the stochastc fronter model to farm-level agrcultural data was presented by Battese and Corra (1977). Data from the 1973/74 Australan Grazng Industry Survey were used to estmate determnstc and stochastc Cobb-Douglas producton fronters for the three states ncluded n the Pastoral Zone of Eastern Australa. The varance of the farm effects were found to be a hghly sgnfcant proporton of the total varablty of the logarthm of the value of sheep producton n all states. The parameter estmates exceeded 0.95 n all cases, hence the stochastc fronter producton functons were sgnfcantly dfferent from ther correspondng determnstc fronters. Kalrajan (1981) estmated a stochastc fronter Cobb-Douglas producton functon usng data from 70 rce farmers for the rab season n a dstrct n Inda. The varance of farm effects was found to be a hghly sgnfcant component n descrbng the varablty of rce yelds. Bag (1982a) used the stochastc fronter Cobb-Douglas producton functon model to determne whether there were any sgnfcant dfferences n the techncal effcences of small and large crop and mxed-enterprse farms n West Tennessee. The varablty of farm effects were found to be hghly sgnfcant and the mean techncal effcency of mxed-enterprse farms was smaller than that for crop farms (about 0.76 versus 0.85, respectvely). However, there dd not appear to be sgnfcant dfferences n mean techncal effcency for small and large farms, rrespectve of whether the farms were classfed accordng to acreage or value of farm sales. Dawson and Lngard (1989) used a Cobb-Douglas stochastc fronter producton functon to estmate techncal effcences of Phlppne rce farmers usng four years of data. The ndvdual techncal effcences ranged between 0.10 and 0.99, wth the means between 0.60 and 0.70 for the four years nvolved. In developng countres, studes on techncal effcency nclude that of Nega et al. (2006) who analyzed the neffcency of smallholder dary producers n the central Ethopan hghlands usng the stochastc producton fronter technque and confrmed the exstence of systematc neffcency n mlk producton. The average effcency level of the farmers was only 79% mplyng that mlk output would be attaned on average by 21% wth the exstng technology by tranng dary farmers on better producton technques. The study recommended tranng of farmers on proper feedng, calvng, mlkng, cleanng of cows, storng mlk, marketng as well as other management sklls to mprove effcency n mlk producton. Kbaara (2005) analyzed the techncal effcency n Kenya s maze producton usng a translog producton functon. The results ndcated that maze farmers were 49% effcent wth a range of 8 to 98%. The number of years of formal schoolng, age of household head, health of the household head, gender of the household head, use or non use of tractors and off-farm ncome were found to have an mpact on techncal effcency. In ths study, the Fronter (4.1) software program was used to estmate the Stochastc Fronter Model. Ths program used the maxmum lkelhood technque 8 Jomo Kenyatta Unversty of Agrculture and Technology

7 JAGST Vol. 14(2) 2012 Smallholder daryng n Kenya for estmaton (Coell 1996). The general non-log form model s specfed as follows: y f x 1, x ).. (5) y ( 2 The general log form model s specfed as follows: 5 0 k ln xk v u (6) k 1 Where, ln denotes natural logarthms, y and x varables are defned n Table 1, α s are parameters to be estmated. The neffcency model s estmated from the equaton gven below. 8 u 0 mz... (7) m 1 The varables z are the varables n the neffcency model. Equaton 7 above shows a jont estmaton of the stochastc fronter producton functon n Fronter 4.1. lny β β lnlabour β lnlabour ^2 β lncows β lnfeeds β lnothercosts β Breed δ δ land δ offncome δ traveltme δ schyrsmale δ schyrsfemale δ watersource δ AIservce δ regonaldummy u Where : Y= mlk yeld n ltres; Feeds = cost of feeds; Other costs = Veternary costs; Cows = number of cows; Breed = Type of breed (mproved or local) Labor = labor n man hrs; Land sze= number of acres of land; Offnc = dummy for off farm ncome Yes =1 No = 0; Travel tme= tme n hrs to the nearest urban centre; Educmale = number of years of schoolng for males; Educfemale = number of years of schoolng for females; Water= dummy for source of water, has water on the farm: Yes = 1 No =0; AI = dummy for AI servces, Uses AI: Yes = 1 No =0; Regonal dummy = dummy for hgh potental regon; v = error terms, and the former refers to normal statstcal error whle the u latter concerns techncal effcency of farms. Jomo Kenyatta Unversty of Agrculture and Technology 9

8 Smallholder daryng n Kenya JAGST Vol. 14(2) Model estmaton results The estmated coeffcents of the producton fronter for smallholder dary farms are presented n Table 2. Most of the estmates were found to be sgnfcant at the fve percent sgnfcance level. The summary statstcs on the techncal effcency of ndvdual farms for the 474 smallholder farms are presented n Table 3, whch presents the range of techncal effcency scores of the farms and the number of farms wthn each range. The mean effcency of the small dary farms was 79%, wth the hghest effcency value of 94% and the lowest farm effcency value of 46%. These results clearly rejected the null hypothess that there was no gap between potental and actual mlk producton of smallholders dary farmng n rural Kenya meanng that most farmers had not yet attaned full effcency and there was stll potental to ncrease mlk producton by 21% on average. Table 2: Results of the maxmum lkelhood estmates of stochastc producton functon Parameter Coeffcent Standard Error t-rato Beta *** Labor *** labour^ *** Mlkng cows *** Cost of feeds *** Breed *** Health costs Delta Land sze Off farm ncome Travel tme ** Educ Male ** Educ Female Water ** AI servce *** Regonal *** sgma^ *** gamma *** Log lkelhood functon= e+03 Source: Authors Analytcal Estmates, Astersk ndcates: *sgnfcant at 10%, ** sgnfcant at 5% and ***sgnfcant at 1%. 10 Jomo Kenyatta Unversty of Agrculture and Technology

9 JAGST Vol. 14(2) 2012 Smallholder daryng n Kenya Table 3: Results of summary statstcs on techncal effcency of ndvdual farms Techncal Effcency Frequency Percentage < Total Source: Authors Analytcal Estmates, The summary statstcs of techncal effcency for the smallholder farms n the fve regons presented n Table 4 ndcated the dversty of scores of effcency among regons, whch suggests that the dversty n soco economc factors can have dfferent mpacts on effcency n mlk producton n dfferent regons. Table 4: Results of scores of techncal effcency among regons Regon Observaton Mean Std. Dev Mn Max Nyanza Western Rft Valley Central Eastern Source: Authors Analytcal Estmates, Techncal neffcency and soco-economc characterstcs Consderng the detaled results, the coeffcent of labor was sgnfcant at 1% though t had a negatve sgn, whle when labor was squared; the coeffcent became postve and statstcally sgnfcant at 1%. Ths shows that when labor ncreased from the present level, mlk producton declned, but after some tme mlk producton ncreases. The plausble explanaton for ths observaton beng that daryng requres some experence especally on management practces lke feedng and not all the laborers may possess ths experence. In the absence of such experence n the majorty of employed labor, the coeffcent tends to be negatve. Wth an ncrease n experenced labor force, mlk producton tends to ncrease as shown by the squared labor term. Another possble explanaton s that n most cases, famly labor may be used whch may not be restrcted to only daryng and hence t may be dffcult to correctly quantfy the amount of tme strctly spent on daryng actvtes. The coeffcent of feeds was postve and statstcally sgnfcant at 1% as was expected meanng that feeds are crtcal n mlk producton and thus an ncrease n feedng ncreased mlk producton. The coeffcent of cows was sgnfcant at 1% and had a postve sgn as was expected, meanng that mlk producton ncreased Jomo Kenyatta Unversty of Agrculture and Technology 11

10 Smallholder daryng n Kenya JAGST Vol. 14(2) 2012 wth the ncrease n the number of mlkng cows. The number of cows was a good proxy for farm sze. Thus, the hgher the number of cows a farmer owns, the hgher the mlk producton. The coeffcent of breed was sgnfcant at 1% and had a postve sgn as was expected, meanng that mlk producton ncreased wth the type of breed, mproved cows would gve more mlk than the local breeds. The coeffcent of health costs was negatve though t was not sgnfcant. Normally a hgh expendture n health s a proxy for unhealthy anmals or poor management and ths reduces mlk producton. Consderng the estmates of the determnants of techncal effcency, the coeffcent of land was negatve, meanng that land sze may reduce neffcency due to economes of scale, though the coeffcent was not statstcally sgnfcant. The explanaton s that n smallholder dary farms, there s a tendency of ntegratng dary and the growng of food or cash crops on the same pece of land; hence, economes of scale may not be realzed. Furthermore, ntensfcaton of dary, such as zero grazng, s enablng farmers to keep cows wthout necessarly havng land as long as they have a source of feeds. Thus, land may not have an mpact on effcency. The coeffcent of off farm ncome was postve, meanng that an ncrease n off farm ncome may ncrease neffcency, but ths coeffcent was not statstcally sgnfcant. Ths may ndcate that the surveyed farmers may solely be dependng on farmng and therefore the off farm actvtes do not affect ther farm actvtes. The coeffcent of years of schoolng for males was postve and statstcally sgnfcant at 5%, whch clearly ndcates that more years of schoolng for males ncreases ther neffcency n mlk producton, whle the coeffcent of that of females was negatve but was not statstcally sgnfcant. The major argument s that wth more years of schoolng, males tend to get off farm employment and ncome actvtes, whch may result n daryng neffcency. The coeffcent of travel tme to the nearest urban centre whch was a proxy for nfrastructure was postve and statstcally sgnfcant at 1%, meanng that neffcency ncreased when more tme was taken n travelng to the nearest urban centre. Bad roads are evdent n most rural areas of Kenya and thus t takes a lot of tme to get mlk to the market and to get the nputs to the farms especally the feeds. Bad roads also deter extenson servces from beng effectve, thus ncreasng neffcency. Mlk producton requres speedy transportaton to the market and requres easy access to commercal feeds and artfcal nsemnaton servces whch are obtanable from the nearest urban centres. 12 Jomo Kenyatta Unversty of Agrculture and Technology

11 JAGST Vol. 14(2) 2012 Smallholder daryng n Kenya The dummy for source of water at the farm was negatve and statstcally sgnfcant at 1%, meanng that havng water on the farm reduced neffcency. Daryng requres water throughout and access to water on the farm cannot be overemphaszed. The dummy for artfcal nsemnaton was negatve and statstcally sgnfcant at 1%, meanng that t reduced neffcency to use artfcal nsemnaton. Artfcal nsemnaton was a good proxy for extenson servce. Artfcal nsemnaton allows farmers to upgrade ther anmals and reduces fertlty dseases such as brucelloss, whch reduce mlk producton. Thus, Artfcal Insemnaton helps n reducng neffcency. The government provded ths servce to the farmers up to 1992 when the dary ndustry was lberalzed and the prvate agents started to offer ths servce. The regonal dummy that represented the hgh potental areas (.e. Central Provnce) was negatve and statstcally sgnfcant at 1%. Ths means that beng n a hgh potental regon reduces techncal neffcency. Ths regon s notceable for ts good nfrastructure, hgh qualty breeds and ts close proxmty to the captal cty of Narob, where most of the mlk s sold and nputs especally the commercal feeds are processed. 5.0 Polcy mplcatons and recommendatons One of the mportant polcy mplcatons concerns technology. Feeds were found to reduce neffcency. Technologes that wll enable the farmers to produce feeds cheaply should be ntroduced as several farmers depend on manufactured feeds besdes grazng land to feed mlkng cows, t s thus mperatve to facltate easy access to manufactured feeds at affordable prces. The government needs to encourage producton of manufactured feeds by promotng ndustral actvtes. Another polcy mplcaton s to make the artfcal nsemnaton servces affordable to farmers snce t reduces neffcency. Ths wll help the farmers to upgrade ther dary cows wthout usng the tradtonal bulls that may have low qualty genetc potental and are capable of transmttng breedng dseases. Importantly, the government needs to mprove nfrastructure especally rural roads, whch n most cases are n a deplorable condton. Ths wll enable the farmers to access the nputs and to market ther produce wth ease. Ths s not only benefcal to the mlk producers but also to the other agrcultural actvtes. Water s an mportant nput n dary producton and ts supply on farms cannot be overemphaszed. The supply can be pped water or borehole water and ths wll greatly reduce the nconvenence and the tme that the farmers have to take to fetch water for ther anmals. Ths wll also save useful labor tme that can be used n other farmng actvtes. Jomo Kenyatta Unversty of Agrculture and Technology 13

12 Smallholder daryng n Kenya JAGST Vol. 14(2) 2012 Acknowledgements We acknowledge the Japan Internatonal Cooperaton Agency (JICA) for the fnancal assstance to undertake a Masters Degree Program and a Thess n Natonal Graduate Insttute of Polcy Studes, Japan from whch ths research artcle was extracted. We are also grateful to Tegemeo Insttute of Agrcultural Polcy and Development for provdng household survey data used n ths study. Fnally, specal thanks go to Prof. Kalappa Kalrajan for hs nput n ths paper. References Ahmad M. and Bravo-Ureta B. (1995). Techncal effcency measures for US dary farms usng panel data: A comparson of alternatve model specfcatons. Amercan Journal of Agrcultural Economcs, 77, pp Agner D. K., Lovell C. K. and Schmdt P. (1977). Formulaton and Estmaton of Stochastc: Fronter Producton Functon Models. Journal of Econometrcs, 6, pp Al M. and Flnn J. (1989). Proft effcency among Basmat rce producers n Pakstan Amercan Journal of Agrcultural Economcs, 71, pp Alvarez A. and Aras, C. (2004). Techncal effcency and farm sze: A condtonal analyss of Spansh dary farms. Amercan Journal of Agrcultural Economcs, 30 (3), pp Bag F. S. (1982a). Relatonshp Between Farm Sze and Techncal Effcency n West Tennessee Agrculture. Southern Journal of Agrcultural Economcs, 14, pp Battese G.E. and Corra G.S. (1977). Estmaton of a Producton Fronter Model: Wth Applcaton to the Pastoral Zone of Eastern Australa. Australan Journal of Agrcultural Economcs, 21, pp Central Bureau of Statstcs (2002). Economc Survey, 2002, Mnstry of Fnance and Plannng, Narob, Kenya. Coell T. J Recent development n fronter estmaton and effcency measurement, Australa Journal of Agrcultural Economcs, 39, pp Dawson P. J. and J. Lngard (1989). Measurng Farm Effcency Over Tme on Phlppne Rce Farms, Journal of Agrcultural Economcs, 40, pp Food and Agrcultural Organzaton. (2005). FAOSTAT Data, Food and Agrculture Organzaton, Rome. Farell M., (1957). The measurement of productve effcency. Journal of Royal Statstcal Socety, Seres A (General), 120 (3), pp Huang Y. and Kalrajan K. P. (1997). Potental of Chna s gran producton evdence from the household data. Agrcultural Economcs Elsever, 17(2), pp Jomo Kenyatta Unversty of Agrculture and Technology

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