Evaluating the Performance of Maize Farmers in Nigeria using Stochastic Distance and Stochastic Production Frontiers

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1 Kamla-Ra 2012 J Hum Ecol, 40(2): (2012) Evaluatng the Performance of Maze Farmers n Ngera usng Stochastc Dstance and Stochastc Producton Fronters G. C. Aye * and E. D. Mungatana Department of Agrcultural Economcs, Extenson and Rural Development, Unversty of Pretora, 0002 Pretora South Afrca * E-mal: aye_goody@yahoo.co.uk KEYWORDS Effcency. Stochastc Fronter. Farmers. Polcy. Technology ABSTRACT Ths study estmates the techncal, allocatve and cost effcency of farm households usng stochastc dstance and stochastc producton fronters. Further, the study examnes determnants of effcency. Data was collected from a random sample of 240 maze farmers n Benue State Ngera usng structured questonnares. Results from both dstance and producton fronters show that farmers n the area are neffcent. Although the effcency measures from the two fronters are quanttatvely dfferent from each another, the overall consstency check shows that the farm households were ranked smlarly by both approaches. Ths s partcularly robust to allocatve and cost effcency. Improved maze seed, norganc fertlzers, conservaton practces, sze of farm holdngs, educaton, and access to extenson servces, credt and market were found to have sgnfcant mpact on effcency. Thus, nvestment n agrcultural research coupled wth complementary polces s an effectve nstrument for revampng agrculture and poverty reducton n Ngera. 1. INTRODUCTION Increasng agrcultural productvty s consdered as one of the maor solutons to effectvely addressng the current global food crss. Maze s one of the maor staples n Ngera. The report of a food consumpton survey shows that maze was the most often consumed staple, wth 20% of the populaton eatng t at least once a week (Internatonal Insttute of Tropcal Agrculture 2004). Current producton s about 8 mllon tonnes and average yeld s 1.5 tonnes per hectare. The average yeld s low when compared to the world average of 4.3 tonnes/ha. It s even lower when compared to average yeld from other Afrcan countres lke South Afrca, Maurtus and Egypt wth average of 2.5 tonnes/ha, 5.8 tonnes/ha and 7.1 tonnes/ha respectvely (Food and Agrculture Organzaton 2009). Thus, there has been a growng gap between the demand for maze and ts supply. Ths necesstated the Federal government n 2006 to ntate a programme of doublng maze producton n Ngera through the promoton of mproved producton technologes such as fertlzer, hybrd seeds, pestcdes, herbcdes and better management practces. Subsequently, other programmes amed at ncreasng maze and agrcultural productvty has been ntated. Despte the efforts by the Ngeran government, maze productvty stll remans below expectaton consderng the demonstrated and potental yelds of 4.5t/ha and above 5.0t/ha respectvely (Remson 2005). The falure to realze ncreased productvty n the Ngeran maze sector rases questons about the effcency wth whch maze farmers use producton resources and f neffcency s observed, could ths be attrbuted to technologcal nnovaton and other polcy factors? The answer to these polcy questons wll serve as ustfcaton for further nvestment n maze producton and agrcultural technology development. There are three man effcency measures namely techncal, allocatve and cost effcency. In mcroeconomc theory, the prmal producton fronter descrbes the maxmum output that may be obtaned from gven nputs. Any devaton from the maxmal output s typcally consdered techncal neffcency. A frm that operates at the producton fronter has a techncal effcency of 100%. Even though farmers may be techncally effcent, they may not be cost effcent because they are allocatvely neffcent. That s, they do not utlse the nputs n optmal proportons, gven the observed nput prces, and hence do not produce at mnmum possble cost. Therefore, the modellng and estmaton of both techncal and allocatve effcency of agrcultural producton s often motvated by the need for a more complete representaton of economc or cost effcency of farmers mpled by the economc theory of producton. Wthn the parametrc fronter lteratures, the tradtonal approach to answer the sort of emprcal questons posed n ths study would be to

2 178 G. C. AYE AND E. D. MUNGATANA estmate a producton or cost fronter (see Ngeran studes for example, Ogunynka and Abefun 2004; Umeh and Asogwa 2005; Ogundar et al. 2006; Amaza and Ogundar 2008; Abefun 2008; Oyekale and Idesa 2009). The problem wth the drect estmaton of cost fronters s that t wll not be practcal when nput prces do not dffer among frms and also not approprate when there s systematc devaton from cost-mnmsng behavour. In ths stuaton, the dualty between the cost and producton functons breaks down, and the resultng bas n the cost fronter estmates wll bas the estmates of cost effcency (Bauer 1990). The Bravo-Ureta and Regger (1991) producton fronter approach has also been crtqued for smultaneous equaton bas (Coell et al. 2003; Alene and Hassan 2005). These problems wth both the producton and cost fronters have motvated recent nterest n the use of dstance functons n effcency analyss (Coell and Perelman 2000; Halu and Veeman 2000; Morrson-Paul et al. 2000; Coell et al. 2003; Irz and Thrtle 2004; Alene and Manfred 2005; Herrero 2005; Alene et al. 2006; Sols et al. 2009; Aye and Mungatana 2011) though maorty of the studes are lmted to techncal effcency. The dstance functon approach does not requre behavoural assumptons to provde a vald representaton of the underlyng producton technology, does not suffer from smultaneous equatons bas when frms are cost mnmsers or shadow cost mnmsers, and does not necessarly requre varaton n nput prces across frms to provde vald estmates of allocatve and cost effcency. Although, dstance functons easly accommodates multple outputs; they are also sutable for sngle output analyss. Polcy conclusons may vary dependng on the methodology used. However, consstency of results from dfferent approaches valdates polcy conclusons. Aganst ths background, ths study employs dualty theory n obtanng the parameters of the cost fronter from parametrc stochastc nput dstance functon (SIDF) and parametrc stochastc fronter producton functon (SFPF). Subsequently, t analyses smallholder maze farm households techncal, allocatve and cost effcency from these two approaches. The present study s by no means the frst to nvestgate the senstvty of effcency estmates to alternatve approaches. However, the senstvty of results to analytcal approaches has not been fully explored and results from dfferent studes have been mxed. For nstance, Coell and Perelman (2000) compared results from three specfcatons of dstance functons and two specfcatons of producton fronters. The study focused on the use of techncal effcency as a measure of performance of the European ralways. The results obtaned ndcate substantal dfferences n parameter estmates and techncal effcency rankngs. Wadud and Whte (2000) compared data envelopment analyss (DEA) and stochastc fronters producton functon (SFPF) measures of the effcency of 150 rce farmers n two vllages n Bangladesh. For the stochastc fronter model both the one-stage and two-stage procedures were mplemented. The techncal effcency estmates from SFPF was lower than that from constant returns to scale DEA but greater than that of the varable returns to scale DEA. However, the correlaton between dfferent effcency scores from dfferent methods were postve and sgnfcant. Results from both approaches ndcate that techncal effcency s sgnfcantly nfluenced by factors measurng envronmental degradaton and rrgaton nfrastructure. Estache et al. (2004) appled DEA and econometrc methods for performance assessment and rankng of South Amercan electrcty unts. Specfcally they estmated two parametrc dstance models (an nput dstance functon and an nput requrement functon) and four determnstc nonparametrc DEA models (two nput dstance functons, one wth varable returns to scale and another wth constant returns to scale, and two nput requrement functons, one wth varable returns to scale and another wth constant returns to scale). Testng the nternal consstency of results obtaned from all approaches, frst they found that techncal effcency levels from dfferent approaches were sgnfcantly dfferent. Secondly, they found hgh correlaton between dfferent econometrcs as well as DEA models. However, there was low correlaton between DEA and econometrcs models. Jaforullah and Premanchandra (2004) estmated techncal effcency for the New Zealand dary ndustry usng three dfferent estmaton technques under both constant returns to scale and varable returns to scale n producton. The approaches used were the SFPF, corrected ordnary least squares (COLS) and DEA. Mean techncal effcency of the ndustry was found to be senstve to the choce of estmaton technque. In general, the SFPF and DEA

3 DISTANCE FUNCTION AND PRODUCTION FRONTIERS 179 fronters resulted n hgher mean techncal effcency estmates than the COLS producton fronter. Alene and Manfred (2005) compared the performances of the parametrc determnstc dstance functons (PDF) and DEA wth applcatons to adopters of mproved cereal technology n Eastern Ethopa. Although they found postve and sgnfcant correlatons between the two approaches, the result from PDF was more robust when analyss was subected to senstvty to possble outlers. Herrero (2005) compared four dfferent approaches data envelopment analyss, stochastc producton fronter, panel data, and dstance functon to estmaton of techncal effcency of the Spansh Trawl Fshery that was operated n Moroccan water. Ther fndngs show that the effcency estmates were smlar and hghly correlated. Thus, they conclude that none of the methodologes can be sad to be better than the rest; rather, the most approprate methodology depends on the characterstcs of the producton process, the degree of stochastcty, number of outputs and possblty of aggregaton. López et al. (2006) used stochastc producton fronters and stochastc dstance fronters to measure techncal effcency for a sample of dary farms n Abasto Sur, Argentna. Four alternatve models were evaluated. Average techncal effcency across the four models ranges from 67.2% to 88.4% whle the correlaton for techncal effcency scores ranges from to A key concluson of ther paper s that stochastc producton fronters and stochastc dstance fronters models exhbt smlar patterns wth respect to the estmated producton functon parameters; however, the techncal effcency measures were relatvely lower for the SDF than SFPF models (67.2% and 88.4%, respectvely). Cuesta et al. (2009) compared the performance of parametrc stochastc hyperbolc dstance functons wth DEA n the analyss of envronmental effcency of U.S. electrcty generatng unts and found that although the means and dstrbutons of the models were sgnfcantly dfferent, the rankng of the unts by each model s smlar. As s clear from the studes revewed above, the few effcency studes comparng results from dstance and producton fronters have been lmted to techncal effcency only. Therefore, ths study extends the prevous comparatve studes by consderng techncal, allocatve and cost effcency results from stochastc dstance and stochastc producton fronters. To the best of our knowledge, no study has estmated allocatve and cost effcency relatve to a stochastc dstance and producton fronters usng the same data set. 2. OBJECTIVES OF THE STUDY The man obectve of ths paper s to evaluate the performance of maze farmers n Ngera usng parametrc stochastc nput dstance functon (SIDF) and parametrc stochastc fronter producton functon (SFPF). The specfc obectves are to: () estmate techncal, allocatve and cost effcency of maze farmers n Ngera; () compare effcency estmates from stochastc dstance and stochastc producton fronters; and () examne the mpact of polcy, technology and socoeconomc varables on techncal, allocatve and cost effcency of maze farmers n Ngera. 3.1 Data and Varables 3. METHODOLOGY A multstage stratfed samplng procedure was employed n selectng the respondents for ths study. A total of 240 farmers were ntervewed from four local government areas of Benue State. Data on output and nput quanttes and prces were collected. The output varable, PROD s the quantty of maze produced durng 2008/2009 agrcultural season by a farm household and s measured n klograms. LAND s measured as the area of land n hectares cultvated wth maze by a farm household n the relevant perod. LA- BOUR s measured as the amount of both famly and hred labour n man-days used by the farm household. FERT s the amount of norganc fertlzer n klograms used by the farm household. OTHER s the Fsher quantty ndex of seed, herbcdes and pestcdes used by the farm household. Observed average prce per unt of nputs used were used n the analyss. W LAND s rental prce of a hectare of farm land. W LABOUR s prce of labour per day. W FERT s prce of norganc fertlzer per klogram. W OTHER s an mplct prce ndex of seed, herbcdes and pestcdes derved by dvdng the cost of other nputs by OTHER. All prces were n local currency, Nara. AGE s the age of the household head n years. GEN- DER s 1 f the household head s a male; 0 oth-

4 180 G. C. AYE AND E. D. MUNGATANA erwse. EDU s the number of years of formal educaton completed by the household head. HHS s the number of persons n the household. OFFWORK s 1 for engagement n off-farm work; 0 otherwse. MFG s 1 f the household head s a member of any farmer organzaton. EXT s the number of extenson vsts durng the croppng perod. CREDIT s 1 f farmer had access to credt. MARKET s the dstance to the nearest market n km. HYV s the area of maze farm (ha) cultvated wth hybrd maze varety. AFERT s the area of maze farm (ha) appled wth norganc fertlzer. HERB s the area of maze farm (ha) subected to herbcde applcaton. PRACTICES s the number of conservaton practces adopted by a farmer on hs or her maze farm. 3.2 Emprcal Models Stochastc Input Dstance Functon and Cost Effcency Decomposton In order to estmate the nput dstance functon n a parametrc settng the Cobb-Douglas (CD) functonal form s assumed n ths study. The specfcaton s admttedly restrctve. However, a lkelhood rato test could not be reected CD aganst the alternatve of a translog (TL) form at 5% level of sgnfcance. Moreover, the man advantage of TL s ts flexblty, but at the same tme ts man dsadvantage s that t does not easly permt the decomposton of and dentfcaton of allocatve effcency as the CD does. For the case of sngle output, K nputs, N farms, the emprcal model s specfed as: 4 ln D ln Y ln X, 1,...240, 1 where Y s the observed maze output for the th farmer and X s the th nput quantty for the th farmer, namely land, labour, norganc fertlzer and Fsher ndex of other nputs (seed, pestcde and herbcdes). ln represents the natural logarthm of the assocated varables, and, and are unknown parameters to be estmated. Imposng the restrcton for homogenety of degree +1 n nputs and representng the resultng unobserved term ln D as the composed error term, equaton (3) becomes: 4 1 lnx k lny ln X / Xk v u, (2) 1 The statstcal nose ( v ) s assumed to be 2 d N(0, v ) and ndependent of the techncal neffcency, u. A lkelhood rato test was (1) conducted to test the hypothess that u s halfnormally dstrbuted aganst the alternatve that t has a truncated normal dstrbuton. The hypothess of half-normal dstrbuton could not be reected at 5% level of sgnfcance. The techncal effcency scores are predcted usng the condtonal expectaton predctor. The techncally effcency nput quanttes are obtaned as a product of the observed nput vector and predcted techncal effcency. From the parameters of the Cobb-Douglas nput dstance functon and, usng the frst order condton for cost mnmsaton, the correspondng parameters of the dual cost functon are analytcally derved and defned as: 4 ln C b0 b lnw ln Y (3) 1 4 where b ˆ, ˆ, b ˆ ˆ and. C ln( ˆ 0 ) 1 s the cost of producton of maze for the th farmer, W s the th nput prce vector whch ncludes the prce of land, prce of labour, prce of norganc fertlzer and mplct prce ndex for other nputs. Y s the maze output of the th farmer. b 0, b and are unknown parameters whch are derved from the prmal functon. The cost effcent nput quanttes are obtaned usng Shepard s Lemma. Usng the observed and mnmum cost of producton, cost effcency and allocatve effcency are derved for each farmer Stochastc Fronter Producton Functon and Cost Effcency Decomposton The Cobb-Douglas stochastc fronter producton functon s assumed for ths study and specfed as: lny 4 1 ln X, v u All varables are as defned for the SIDF model. and ' s are parameters to be estmated. The parameters of the SFPF were estmated usng the maxmum lkelhood method. The observed output of the th farm, Y, s adusted for statstcal nose by subtractng v from both sdes of the equaton (4): Y * Y v f ( X ; ) u * where Y s the adusted output. The techncally effcent nput vector, for a gven level of s derved by solvng smultaneously equaton (5) and the nput ratos,, where s the rato of the observed nputs. Gven the vector of nput prces for the th farm household (4) (5)

5 DISTANCE FUNCTION AND PRODUCTION FRONTIERS 181 (W ), parameter est mates of the SFPF ( ) n equaton (4), and the nput orented adusted output level n equaton (5), the correspondng Cobb-Douglas dual cost fronter s derved and wrtten as The cost effcent nput vector s derved by usng Shephard s Lemma and then substtutng the frm s nput prces and adusted output quantty nto the system of demand equatons. Usng the techncally effcent, cost effcent and actual costs of producton, techncal allocatve and cost effcency are calculated for each farmer (Bravo-Ureta and Reger 1991) Technology and Polcy Impacts on Effcency (6) To analyse the mpact of technologcal nnovaton and other polcy varables on techncal, allocatve and cost effcency a second stage procedure s used whereby the effcency scores obtaned from the frst stage are regressed on the selected explanatory varables usng a double-bounded Tobt model. The one stage procedure would have been preferable n the case of techncal effcency snce the stochastc fronter s estmated under the assumpton that the techncal neffcency effects are dentcally dstrbuted (Battese and Coell 1995). However, allocatve and cost effcency are derved, not estmated, hence, a one stage procedure cannot be mplemented for them. Therefore, the two stage procedure s followed n ths study to ensure unformty and consstency n the nterpretaton of results from all the three measures of effcency. The ncluson of technology nnovaton varables n an effcency model presents the problem of potental endogenety and self selectvty. The exogenety of these varables were tested usng the nstrumental varable approach as proposed by Smth and Blundell (1986). To correct for endogenety, ths study follows a two step approach, n whch each endogenous technology varable s estmated n a frst stage and ther predcted values are ncluded n a second step as addtonal explanatory varables whch yelds unbased estmates of the mpact of technologcal nnovaton on effcency. 4. RESULTS AND DISCUSSION 4.1 ML and OLS Estmates of the SIDF and SFPF Models Table 1 presents both the maxmum lkelhood (ML) and the ordnary least square (OLS) estmates of the SIDF and SFPF. Results show that all varables are sgnfcant at 1 per cent and have expected sgns n both SIDF and SFPF. The estmated coeffcent of output n the SIDF s less than one n absolute terms, ndcatng ncreasng returns to scale. It should be stressed here that the homogenety restrcton on the nput coeffcents of the SIDF does not translate to constant returns to scale, as s the case wth the conventonal producton fronter. The returns to scale for SIDF was computed as the nverse of the negatve of the output coeffcent (Coell et al. 2005). Smlarly, the SFPF ndcated ncreasng returns to scale, but ths was computed as the sum of the nput coeffcents. The partal output elastcty of land s 0.67 and 0.82 n the SIDF and SFPF respectvely and s the largest among the nputs thereby depctng the mportance of land n the household producton. It mples that a 10% ncrease n land sze would ncrease output by 6.7 and 8.2% respectvely n the SIDF and SFPF models. Ths fndng confrms the observaton of ths study, that the share of expendture on land n the cost of producton of sampled farmers s hghest among other nputs. Land s the scarcest nput and the hgh margnal returns to land are a reflecton of the very small sze of plot many farmers are constraned to cultvate. The least contrbutor to household producton s other nputs. The estmate of the varance parameter,, n the SIDF and SFPF models s 0.83 and 0.84 respectvely. These are sgnfcant at 1% mplyng that 83-84% of the total varaton n output s due to neffcency, that s, the techncal neffcency effects are sgnfcant n both models. Ths result s confrmed by conductng a lkelhood rato test, to test the hypothess of OLS versus SIDF and OLS versus SFPF. In each case, the adequacy of the OLS model n representng the data was reected. Based on the estmated parameters of the SIDF, the parameters of the correspondng dual cost functon as specfed n equaton (3) were derved and ths formed the bass of computng the cost and allocatve effcency. The dual cost fronter s gven as: (7)

6 182 G. C. AYE AND E. D. MUNGATANA Table 1: The MLE and OLS estmates of the SIDF and SFPF Varables Mean SIDF SFPF OLS MLE OLS MLE INTERCEPT *** *** *** *** (0.200) (0.216) (0.140) (0.145) PROD *** *** (0.021) (0.021) - - LAND *** *** *** *** (0.022) (0.024) (0.031) (0.027) LAB *** *** ) *** *** (0.021) (0.023) (0.029) (0.029) FERT *** ** *** ) *** (0.003) (0.003) (0.004) (0.004) OTHER a *** *** (0.011) (0.010) SIGMA-SQUARED ** ** (0.006) (0.009) GAMMA *** *** (0.060) (0.051) LLF Returns to scale *** Sgnfcant at 1% level. Standard errors are shown n parenthess. a The estmate of 4 s computed by the homogenety condton where C s the cost of producton for the th farmer. s the rental prce of land per hectare estmated at N s the prce of labour per day estmated at N s the prce of norganc NPK fertlzer per kg estmated at. N57.9. s mplct prce ndex of other nputs estmated at N68.64 per kg. The derved cost functon s equally well behaved. Smlarly, based on the estmated parameters of the SFPF, the nput ratos, and the adusted observed output levels, the parameters of the correspondng dual cost functon were derved and ths formed the bass of computng the cost and allocatve effcency. The dual cost fronter s gven as: ln C = lnw Land ln W Labour (8) W Fert ln W Other ln PROD where the varables are as defned above for the cost functon derved from the SIDF. 4.2 Comparson of SIDF and SFPF Effcency Estmates and Dstrbutons The results of effcency dstrbutons and some descrptve statstcs from the SIDF and SFPF are presented n Table 2. For the SIDF, techncal effcency ranges from 64.3 to 97.1 wth a mean of 86.7%. Ths mples that f farm households wll operate on the fronter, they wll acheve a cost savngs of 13.3% wthout reducng output. On the other hand, f the average farm household n the sample was to acheve the techncal effcency level of ts most effcent counterpart, then the average farm household could realze a 10.7% cost savngs (that s, 1 [86.7/97.1]). A smlar calculaton for the most techncally neffcency farm household reveals cost savng of 33.7% (that s, 1 [64.3/97.1]). Techncal effcency from the SFPF ranges from 43.3 to 99.7 wth a mean of 85.3%. Here, the presence of techncal neffcency ndcates potental output gans wthout ncreasng nput use. Ths mples that f farm households were to operate on the producton fronter, they wll acheve a cost savngs of 14.7%. Smlar hgh techncal effcency scores were obtaned by Alene et al. (2006). The average allocatve effcency from the SIDF model s 57.8% wth a low of 23% and a hgh of 88.8%. Ths mples that there s room to mprove allocatve effcency of the farm households by 42.2%, f they operate on the fronter. It also suggests that f the average farm household was to acheve the allocatve effcency level of ts most effcent farm household, then the average farm household could acheve a cost savng of 34.9% whle the least effcent farm household would acheve a cost savng of 74%. The average allocatve effcency from the SFPF s 52.6% wth a low of 22.9% and a hgh of 79.9%

7 DISTANCE FUNCTION AND PRODUCTION FRONTIERS 183 Table 2: Estmates and dstrbuton of effcency from SIDF and SFPF Effcency level (%) SIDF SFPF TE AE CE TE AE CE < Mean Mn Max SD CV Mn = Mnmum; Max = Maxmum; SD = Standard devaton; CV = Coeffcent of varaton; TE = Techncal Effcency; AE = Allocatve Effcency; CE = Cost Effcency whch mples that allocatve effcency of the farm households can be mproved by 47.4% through approprate polcy nterventons. The mean allocatve effcency reported for each of the models ndcates that some nputs are beng used n ncorrect proportons. To check for overutlzaton or under-utlzaton of the producton nputs by farmers, the rato of the techncally effcent nput quantty over the cost-effcent nput quantty (for each observaton) s calculated for each of the fronter models. For the SIDF, the mean rato s 0.61, 2.86, 0.46 and 4.71 for land, labour, fertlzer and other nputs respectvely. For the SFPF the correspondng values are 0.72, 5.20, 0.63 and Ths mples that gven the respectve market prces of the varous nputs, fertlzer s consstently beng under-utlzed, labour s consstently over-utlzed, land s under-utlzed n most cases whereas results of other nputs are mxed. Therefore, for the farmers to operate effcently, the use of fertlzer and land needs to be ncreased whereas the use of labour needs to be contracted. The cost effcency from the SIDF model ranges from 19.6 to 85.9 wth a mean of 50.3% gvng room for cost effcency mprovement by 49.7%, f farm households were to operate on the fronter and also suggests a gan economc effcency of 41.5% for the average farm household and 77.2% for the least effcent farm household. cost effcency from the SFPF model ranges from 15.8 to 69.6 wth a mean of 44.6% gvng room for overall mprovement n effcency by 55.4%. The two approaches have demonstrated that maze farmers n Benue State operate wth consderable neffcency domnated by cost neffcency. Ths provdes an avenue for polcy nterventons that would help reduce neffcency. It s observed that the estmated techncal, allocatve and cost effcency from the dstance fronter are greater than those from the producton fronter. Smlarly, the effcency scores from the SIDF model are less varable than those from SFPF. A formal test was conducted to evaluate the statstcal sgnfcance of the dfference between the SIDF and SFPF techncal, allocatve and cost effcency scores. Ths was acheved by testng dfferent complementary hypotheses relatve to: () the equalty of means (t-test), () the equalty of dstrbutons (Wlcoxon sgned rank-test), and () the ndependence of the results wth regard to ther rank (Spearman s correlaton test). Table 3 presents the results, concludng that n the case of the t-tests, the dfferences between the SIDF and SFPF effcency scores are statstcally sgnfcant wth a confdence of 95 Table 3: Tests of hypotheses between SIDF and SFPF effcency scores T-test- Wlcoxon Speart-stat- test man s stc Z-statstc Rho ρ Techncal effcency (0.106) (0.245) (0.755) Allocatve *** *** *** effcency 0.000) (0.000) (0.000) Cost ** *** *** effcency (0.000) (0.000) (0.000) *** Sgnfcantly dfferent from zero at 5% level; p- values n parenthess

8 184 G. C. AYE AND E. D. MUNGATANA per cent. The Wlcoxon test further renforces ths result by ndcatng that the dstrbutons are also statstcally dfferent. Although the dfferent approaches produced effcency measures that are quanttatvely dfferent from each another, t s stll possble to acheve consstency of results wth respect to the rankng of ndvdual farm households, whch n many polcy analyses may be more mportant than the quanttatve estmates of effcency. Therefore, to assess the overall consstency of the two methods n rankng ndvdual farms n terms of effcency, the coeffcent of Spearman s rank-order correlaton was calculated between the two models. Spearman s correlaton suggests that the dfferent farm households rank smlarly when they are ordered accordng to ether ther SIDF or SFPF effcency scores. Based on ths, one can draw vald polcy conclusons from the results of ths study especally wth respect to allocatve and cost effcency. 4.3 Polcy Impacts on Techncal, Allocatve and Cost Effcency of Maze Farmers Smth-Blundel test of exogenety was conducted on the technologcal nnovaton varables. It was observed that the exogenety of each varable n each model was reected n at least one case. Detaled results are avalable from the authors upon request. An endogenety-corrected Tobt model was employed n the second-step regresson n the case of reecton of the null hypothess. The results of the secondstage endogenety-corrected Tobt model are presented n Table 4. The sgnfcance of the lkelhood rato (LR) test n each model mples the ont sgnfcance of all varables ncluded n Table 4: Tobt model results of mpact of polcy factors on TE, AE and CE Varable Mean SIDF SFPF TECoeff AECoeff CECoeff TECoeff AECoeff CECoeff Gender (0.009) (0.019) (0.017) (0.018) (0.018) (0.015) Age *** *** (0.000) (0.001) (0.001) (0.001) (0.001) (0.001) Edu *** * (0.000) (0.001) (0.001) (0.001) (0.001) (0.001) Hhs *** * *** * (0.000) (0.001) (0.001) (0.001) (0.001) (0.001) Land *** ** *** (0.008) (0.020) (0.018) (0.018) (0.020) (0.016) Offwork * (0.010) (0.006) (0.013) (0.012) (0.012) (0.012) -(0.010) Mfg *** ) * (0.010) (0.021) (0.019) (0.021) (0.020) (0.017) Ext ** * ) (0.002) (0.004) (0.003) (0.003) (0.003) (0.003) Credt *** *** ** ** *** *** (0.008) (0.018) (0.016) (0.017) (0.017) (0.014) Market ** (0.000) (0.001) (0.001) (0.001) (0.001) -(0.001) Hyv ** *** *** * *** (0.006) (0.013) (0.011) (0.012) (0.011) (0.010) Afert ** ** *** *** *** (0.009) (0.027) (0.024) (0.017) (0.025) (0.021) Herb *** *** (0.006) (0.013) (0.008) (0.009) (0.008) -(0.007) Practces *** (0.002) (0.005) (0.004) (0.004) (0.004) (0.004) Intercept *** *** *** *** ** (0.019) (0.041) (0.038) (0.040) (0.039) (0.033) LLF LR Test *** *** *** *** *** *** *** Sgnfcant at 1 % level; ** Sgnfcant at 5 % level; * Sgnfcant at 10 % level. Standard errors are shown n parenthess.

9 DISTANCE FUNCTION AND PRODUCTION FRONTIERS 185 the model. Thus, the hypothess that the technology and other polcy varables ncluded n each model have no sgnfcant mpact on effcency s reected. The effect of age could be postve or negatve. AGE had a postve sgn and sgnfcant mpact on techncal effcency n the two models. Thus, the varable ndexes experence and serve as a proxy for human captal showng that farmers wth greater farmng experence wll have better management sklls and thus hgher effcency than younger farmers. Increased farmng experence may lead to better assessment of the mportance and complexty of good farmng decson, ncludng effcent use of farmng nputs. The second human captal varable, EDU was consstently postve though has sgnfcant mpact on only the techncal effcency case only. Smlar postve and sgnfcant mpact of educaton on techncal effcency of maze farmers n Ngera was found by Oyewo and Faby (2008). HHS was found to be postvely and sgnfcantly related to techncal and cost effcency n the two models. A possble reason for ths result mght be that a larger household sze guarantees the avalablty of famly labour for farm operatons to be accomplshed n tme. The varable LAND s amed at capturng the effect of scale producton on effcency. A revew by Lundvall and Battese (2000) establsh a vared relatonshp between farm sze and techncal neffcency n developng countres usng the fronter producton functon. In ths study, t s observed that the n most cases, LAND had a postve effect on the three effcency measures. It then appears that small-scale operatons are a source of neffcency and hence low productvty n the area. These results are consstent wth the fndngs of Karaganns et al. (2000). OFFWORK can ncrease productvty by producng ncome that can be used to purchase modern nputs. Here, t was consstently negatve but wth a sgnfcant mpact on techncal effcency only n the SIDF. Ths mples that farmers who engage n off-farm work are lkely to be less effcent n farmng. Productvty suffers when any part of producton s neglected. Ths fndng s consstent wth that of Marano et al. (2010). Membershp of a farmers group (MFG) ndexes socal captal and affords farmers the opportunty to share nformaton on modern maze practces by nteractng wth others. It also provdes them wth barganng power n the nput, output and credt markets. As expected, MFG was found to be consstently postve, but wth a sgnfcant mpact on techncal and cost effcency n the SIDF and SFPF respectvely. Extenson (EXT) s expected to be postve as t enhances farmers access to nformaton and mproved technologcal packages. However the mpact of the extenson varable here s mxed. It had a negatve and sgnfcant mpact on techncal effcency but postve and sgnfcant mpact on allocatve effcency n the SIDF. It could be that when extenson agents do not have new nformaton for farmers, contact wth those agents would only amount to a waste of resources, leadng to a negatve mpact. Ths fndng s consstent wth the fndngs of Ha (2006) and Demrcan et al. (2010). CREDIT s consstently postve and sgnfcant. Ths s as expected snce the avalablty of credt loses the producton constrants thus facltatng tmely purchase of nputs and therefore ncreases productvty va effcency. The result s consstent wth the fndngs of Muhammad (2009). The varable MARKET serves as a proxy for the development of road and market nfrastructures. It s generally beleved that farms located closer to the market are more techncally, allocatvely and economcally effcent than the farms located farther from the market as ths mght not only ncrease producton cost but also affect farmng operatons, especally the tmng of nput applcaton. Ths expectaton was satsfed n ths study as the MARKET varable was correctly sgned n most cases but t was only had sgnfcant mpact on techncal effcency n the SFPF Although mproved technologes wll generally rase producton cost n absolute terms, the yeld enhancement arsng from ther usage can reduce per unt cost of producton thereby rasng not only techncal effcency but cost effcency as well. Results show that HYV had postve and sgnfcant mpact on techncal, allocatve and cost effcency n almost all cases. Chrwa (2007) employed a producton fronter model and found a postve and sgnfcant mpact of hybrd seed use on techncal effcency of smallholder maze farmers n Malaw. Smlar mpact of mproved maze seed on cost effcency from a cost fronter model was reported n Zavale et al. (2006). These fndngs further strengthen the need for hybrd seed mprove-

10 186 G. C. AYE AND E. D. MUNGATANA ment and dffuson n Ngera n lne wth the current doublng of maze producton programme of the federal government. AFERT had postve and sgnfcant mpact on allocatve and cost effcency n the two models. Its mpact on techncal effcency was only sgnfcant n the SIDF. Msuya et al. (2008) who found a postve mpact of norganc fertlzer on allocatve and techncal effcency, respectvely. Thus, falure to use fertlzer may result n rretrevable output loss. The sgn of the varable, HERB, s mxed though negatve n most cases. The domnatng negatve sgn of herbcdes could be due to the farmers percepton of the health and envronmental effects of herbcdes coupled wth ts hgh cost and nadequate applcaton knowledge, whch constraned ts adopton and usage. The use of conservaton practces mproves land qualty and hence yeld as well as reduces the unt cost of producton. As expected, PRACTICES have postve mpact on all the effcency measures n the two models though ths mpact was only sgnfcant for techncal effcency. Ths s consstent wth Sols et al. (2009) result for the case of techncal effcency. Therefore, economc and envronmental sustanablty should be vewed as complementary rather than compettve goals. CONCLUSION A number of agrcultural polces and or ntatves have been put n place to foster the growth of maze n Ngera. However, productvty stll remaned low. Ths study evaluates the techncal, allocatve and cost effcency of farm households usng stochastc dstance and producton functon fronters. Based on the fndngs of ths study, resources are not effcently used by maze farmers as was evdenced by both the stochastc dstance and producton functon fronters. The dfferences between the SIDF and SFPF effcency scores are statstcally sgnfcant wth a confdence of 95 per cent. The Wlcoxon test further renforces ths result by ndcatng that the dstrbutons are also statstcally dfferent. Although the dfferent approaches produced effcency measures that are quanttatvely dfferent from each another, the overall consstency check shows that the farm households were ranked smlarly by both approaches. Ths s partcularly robust to allocatve and cost effcency. The study also examned factors whch mght affect techncal, allocatve and cost effcency. Result ndcates that lmted use of modern technologes such as mproved maze seed, norganc fertlzers and conservaton practces, smallness of farm holdngs, nadequate formal educaton, access to extenson servces, credt and market were sgnfcant determnants of effcency. RECOMMENDATIONS The postve and sgnfcant mpact of hybrd seed calls for the Ngeran government to nvest more n research and development that wll produce a vable seed sector n the country. Greater avalablty and accessblty of norganc fertlzers s very crucal as these could enhance the effcency of smallholder farmers. Ths was also evdenced n the under-utlzaton of fertlzer as a producton nput. Gven the escalatng prces of norganc fertlzers, alternatves such as sol conservaton practces whch reduce the effectve costs of sol fertlty management optons are necessary. Ths should essentally form an mportant extenson package to all farmers snce the goal of economc benefts and envronmental sustanablty must be balanced. In vew of the nteractons among the agrcultural technology packages, t s argued that adopton of the whole package would be more proftable than adoptng a component or some components of the technology package. From these fndngs, a further nvestment n agrcultural research and development s necessary for ncreasng effcency and productvty of maze producton and subsequently reducng food nsecurty and poverty allevaton n Ngera. Approprate polcy formulaton and mplementaton s an effectve nstrument to mprovement n farm effcency and productvty whch promotes overall growth of the economy. Although, the promoton of mproved technologes s an mportant nstrument n ncreasng agrcultural productvty, t s not suffcent to make the needed necessary mpacts on rural lvelhood and the economy at large. Therefore, complementary polces whch nclude nvestment n educaton, land expanson, mprovement n the extenson system, effcent credt delvery system ncludng access to credt from both mcro-credt and commercal banks and enablng market orented polces must also form part of the strategy. Fnally, concerted efforts amed at

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