Estimating technical efficiency and the metatechnology ratio using the metafrontier approach for cropping systems in Kebbi State,Nigeria

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1 International Journal of Development and Sustainability ISSN: Volume 3 Number 7 (2014): Pages ISDS Article ID: IJDS Estimating tecnical efficiency and te metatecnology ratio using te metafrontier approac for cropping systems in Kebbi State,Nigeria A.J. Jirgi 1*, B. Grové 1, H. Jordaan 1, M.F. Viljoen 1, J.N. Nmadu 2 1 Department of Agricultural Economics and Extension Tecnology, Federal University of Tecnology Minna, Niger State, Nigeria 2 Department of Agricultural Economics, University of te Free State, Bloemfontein, Sout Africa Abstract Te study applied a metafrontier model, wic is developed based on te idea tat different groups of cropping systems use different tecnology set. Te analysis is applied to te meta-cost efficiency of 98 monocroppers and 158 intercroppers. Te results reveal tat based on te metatecnology ratio, millet/cowpea group were more tecnically efficient followed by te sorgum/cowpea group. Te sorgum groups were less tecnically efficient. Tis suggests tat crop diversification in order to manage risk sources as te potential of improving crop productivity in Kebbi State. Crop combinations, owever, prove to play an important role. Care sould be taken to select te optimal combination of crops to include in te intercropping system. Keywords: Cropping systems; Data envelopment analysis; Metafrontier; Metatecnology ratio. Publised by ISDS LLC, Japan Copyrigt 2014 by te Autor(s) Tis is an open access article distributed under te Creative Commons Attribution License, wic permits unrestricted use, distribution, and reproduction in any medium, provided te original work is properly cited. Cite tis article as: Jirgi, A.J., Grové, B., Jordaan, H., Viljoen, M.F. and Nmadu, J.N. (2014), Estimating tecnical efficiency and te metatecnology ratio using te metafrontier approac for cropping systems in Kebbi State,Nigeria, International Journal of Development and Sustainability, Vol. 3 No. 7, pp * Corresponding autor. address: jirgi.abigail97@gmail.com

2 1. Introduction Te two main cropping systems practiced in Nigeria are mono and intercropping system. Te cropping systems considered in tis study are practiced under rain-fed conditions. Generally intercropping involves te growing of rain-fed crops in mixtures, using available resources and permits farmers to maintain low but often adequate and relatively steady production. Monocropping generates vast amounts of corporate wealt, gives iger yields, is more efficient tan intercropping, provides jobs, and gives iger economic returns (Nelson, 2006; Mmom 2009). Te question is; can tis type of system provide sufficient food to te ever increasing population in Nigeria and oter parts of sub-saaran Africa? Farmers in nortern Nigeria practice bot monocropping and intercropping. Intercropping is practiced as a means of diversification to safeguard against risk associated wit agricultural production. Te question of wic cropping system is better in terms of tecnical efficiency in te context of monocropping and intercropping systems in Nigeria as not yet been answered. Sould farmers continue wit te monocropping system wic gives ig production yield in te sort term; or continue wit intercropping wic gives low but often adequate and relatively steady production over te longer term? Te increase in productivity in any of te systems will depend on ow efficient resources are utilized by te farmers. Researc on te comparison of efficiencies in agriculture is scanty. Te researc tat compared te efficiency of tecnologies used te igest average DEA score to indicate te decision making units (DMU) tat are more efficient (Binici et al., 2006; Alene et al., 2006). Frey et al. (2012) argued tat suc comparison is inappropriate because ig efficiency scores among a group of DMUs only gives a measure of relative omogeneity among te efficiency of te DMUs. Battese (2004) introduced te use of Metatecnology ratio (MTR) to compare efficiencies between different groups. Te MTR is a more reliable approac of comparing efficiencies of different groups of enterprises. Te objective of te study is to compare te efficiencies of te monocrop and intercropping systems in order to know wic tecnology is better and to know weter te tecnologies ave equal efficiency. 2. Metodology 2.1. Sampling tecnique and data collection A multi-stage sampling tecnique was used to select 256 farmers comprising of 98 monocrop farmers and 158 intercrop farmers. Te reason for te sample size cosen is tat tere are more intercrop farmers tan monocrop farmers in te State. In te first stage, te four agricultural zones were purposively selected in order to ave a good representation of all te agro-ecological zones in te State. Te second stage involved a random selection of two Local Government Areas (LGAs) from eac of te four agricultural zones. In te tird stage, four villages were randomly selected from eac of te two LGAs. Te fourt stage involved te random selection of te 98 monocrop farmers and te 158 intercrop farmers. Since te population of te LGAs is not ISDS

3 omogeneous, te number of farmers selected from eac of te selected LGAs was calculated using te formula: P S N n were, P = Proportion, S= Desired sample size, N= Total population, n= Population of LGA in question. Te survey was carried out in January to February, 2012; data were collected on production practices for te 2011 cropping season. Te ouseold eads were interviewed by te researcer and te trained enumerators. Data were collected on farmer s inputs, outputs and teir prices Estimation procedure for te tecnical efficiency metafrontier Te objective of te study is to compare te tecnical efficiency of te mono and intercrop farms in order to know te differences between metafrontier and te group frontier. Following O Donnell et al. (2008) te metafrontier production function was used to acieve tis objective Te basic analytical framework Te production teory and te concept of distance function form te basis of te efficiency measurement. O Donnell et al. (2008) defined te metafrontier and group frontiers in terms of output sets and output distance functions Te metafrontier Let y and x be non-negative real output and input vectors of dimension M x1 and N x1, respectively. Te metatecnologyset contains all input-output combinations tat are tecnologically feasible. Ten, T ( x, : x 0; y 0; x can produce y } (1) Te metatecnologyset is associated wit input and output sets. Te output set is defined for any input vector, x, given by: P( x) { y : ( x, T} (2) Te boundary of tis output set is referred to as te output metafrontier. Te output set is assumed to satisfy te standard regularity properties described by Fӓre and Primont (1995). Wen measuring efficiency, te tecnology using te output metadistance function, is defined as: D( x, inf { 0 : ( y / ) P( x)} (3) 1540 ISDS

4 Given an input vector, tis function gives te maximum amount by wic a farm can radially expand its output vector. Te distance function inerits its regularity properties from te regularity properties of te output set. An observation ( x, can be considered tecnically efficient wit respect to te metafrontier if and only if D ( x, Group frontier Consider te case were te universe of te farms can be divided into ( 1) groups, and suppose tat a certain group is constrained by resources, regulatory and oter environmental factors wic may prevent te farms from coosing te full range of tecnologically feasible input-output combinations in te t metatecnology set, T. Rater, te input-output combinations available to farms in te group are contained in te group-specific tecnology set: T {( x, : x 0; y 0; x can be used by farms in group to produce, y } (4) Te H group-specific tecnologies can also be represented by te following group-specific output sets and output distance functions: P ( x) { y : ( x, T }, 1,2,..., H; (5) k D ( x, inf { 0 : ( y / ) P ( x)}, 1,2,..., H (6) Te boundaries of te group-specific output sets are referred to as group frontiers. If te output sets, P ( x), 1,2,..., H, satisfy standard regularity properties ten te distance functions, D ( x,, 1,2,..., H, also satisfy standard regularity properties. For details of te standard regularity properties refer to O Donnell et al. (2008) and Fӓre and Primont (1995) Tecnical efficiencies and metatecnology ratios An observation ( x, is tecnically efficient wit respect to te metafrontier if and only if D ( x, 1. Generally, an output orientated measure of tecnical efficiency of an observed pair ( x, wit respect to te metatecnology is represented by: TE( x, D( x, (7) Since te group- output distance function, D ( x,, can take a value no less tan te output metadistance function, D ( x,. In anoter way, te metafrontier envelops te group- frontier. Wenever a strict inequality is observed between te group- distance function and te metadistance function, we can ISDS

5 obtain a measure of ow close te group- frontier is to te metafrontier. Specifically, te output-orientated metatecnology ratio 1 (MTR) for group- farm is defined as: D( x, TE( x, MTR ( x, (8) D ( x, TE ( x, In tis study te groups comprise of te sorgum farms (monocrop), sorgum/cowpea and millet/cowpea (intercrops). Te decomposition of te tecnical efficiency of a particular input-output combination is provided by equation 9: k TE( x, TE ( x, MTR ( x, (9) Equation 9 sows tat tecnical efficiency measured wit reference to te metafrontier (representing te existing state of knowledge) can be decomposed into te product of tecnical efficiency measured wit reference to te group- frontier (representing te existing state of knowledge and te pysical, social and economic environment tat caracterise group- (wic measures ow close te group- frontier is to te metafrontier) Data Envelopment Analysis for te tecnical efficiency For te DEA tecnical efficiency metatecnology frontier comparison, te estimates were done normally witout using te bootstrapping approac. Te DEA is a linear programming metodology tat uses data on output and inputs of groups. Using te input orientated and assuming constant returns to scale, te DEA problem is given by: min xi X i 0, X 0, Subject to Q 0, q i were, is a scalar and is a I 1vector of constants. N 1input matrix X, M 1output matrix, Q, q i and x i are te column vector of output and input respectively. Te value of obtained is te efficiency score for te itfarm. Te value satisfies; 1, wit a value of 1 indicating a point on te frontier and ence a tecnical efficient firm (Coelli et al., 2005). Note tat te linear programming problem must be solved I times, once for eac farm in te sample. A value of is ten obtained for eac farm. For eac group- te above linear programming is solved L times for eac DMU. Te metafrontier is constructed using DEA model based on te pooled data for all te cropping systems in te study area. Since tere are a total of L L cropping systems, te above equation 9 will be re-run wit te inputs and outputs matrices wit data for all te cropping systems in te Kebbi State. Te outputs for te intercroppers (10) 1Battese et al. (2004, p.94) refer to tis measure as te tecnology gap ratio. However, increases in te (tecnology gap) ratio imply decreases in te gap between te group frontier and te metafrontier. In tis study te metatecnology ratio is used ISDS

6 were converted to teir monetary value i.e. te farm income. Te inputs used were labour, nitrogen, posporus and potassium as indicated previously. Te variable seed was omitted because te conversion of seed to its monetary values will not be appropriate for use in te cost function (Data Envelopment Programme (DEAP), since te programme will not run wen te input value is also te same as te input price. Te DEAP 2.1 was used to obtain bot te tecnical efficiency scores Wilcoxon Rank-Sum Test In order to test for te differences in te tecnical efficiency and cost efficiency of te monocroppers and intercroppers, te Wilcoxon Rank-Sum Tests was used. Te Mann-Witney test is essentially identical to te Wilcoxon test even toug it uses a different test statistic. Wilcoxon Rank-Sum test is a nonparametric statistical test based on te ranking of data (Copper et al., 2006). Wilcoxon tries to detect if tere are local sifts in te distribution of te population of sample A to B. For small samples, independent groups, Wilcoxon for n 1 10 and n2 10 is given by: Test statistic: Z TA n1 ( n1 n2 1) / 2 n n ( n n 1) / (11) were, T A is sum ranking. Te rejection region: one-tailed Z Z, two-tailed Z Z / 2. Comparing te Z statistic to Z value is equivalent to comparing te P value to. 3. Results and discussion 3.1. Comparison between te tecnical efficiency of te monocroppers and intercroppers metatecnology ratio (MTR), in Kebbi State Te comparison between metatecnology ratio of te tecnical efficiency of monocroppers and intercroppers was done for te purpose of comparing te tecnical efficiency for te different groups of cropping systems in Kebbi State; te results are presented in Table 1. For metatecnology ratio (MTR); a iger value implies a smaller tecnology gap between te group frontier and te metafrontier. A value of 100% is equivalent to a point were te group frontier is equal to te metafrontier. Te results for te sorgum, sorgum/cowpea and millet/cowpea groups sows tat on average, sorgum farmers produce output under te conditions tat are more restrictive tan te sorgum and millet/cowpea group. Te average (MTR) for sorgum group (0.79) implies tat te sorgum group could at best; produce 79% of te output tat could be produced using te (unrestricted) metatecnology. Sorgum group as 0.79 MTR compared to te sorgum/cowpea and millet/cowpea groups wo ave MTR of 0.87 ISDS

7 and Te ig value of te MTR for millet/cowpea group suggests tat te group is closest to te metafrontier. Sorgum farmers can borrow tecnology from millet/cowpea and/or sorgum/cowpea group. Table 1. Data Envelopment Analysis estimates of tecnical efficiency and metatecnology ratios of te monocroppers and intercroppers, Kebbi State, January 2012 Enterprise group Mean SD Minimum Maximum Tecnical efficiency wit respect to te (DEA-) group frontiers Sorgum Sorgum/cowpea Millet/cowpea Metatecnology ratio (DEA-MTR) Sorgum Sorgum/cowpea Millet/cowpea Tecnical efficiency wit respect to te metafrontier (DEA-MF) Sorgum Sorgum/cowpea Millet/cowpea DEA-: Deta Envelopment Analysis for group, DEA-MTR: Data Envelopment Analysis for Metatecnology Ratio and DEA-MF: Data Envelopment Analysis for Metafrontier. Te ig value of te MTR for te millet/cowpea group could be due to te fact tat millet/cowpea cropping system (intercropping) under small older setting is often superior to monocropping, because te former lends itself to better disease control, better use of available labour, reduced risk from natural calamities and better monetary income tan monocropping (Beuerlien, 2001; Banik and Sarma, 2009). Palitza (2010) pointed out tat te negative consequences of climate cange can be addressed by increasing crop diversity (and a move away from monocropping) to diminis te risk of crop failure troug intercropping. Tese advantages of te millet/cowpea intercropping system could ave contributed to te ig efficiency Te relatively low average MTR for sorgum group could be because te cropping system is associated wit soil depletion and erosion, plant disease epidemics of enanced severity, increased use of pesticides and nutrients and vulnerability to climate cange (Saleem et al., 2000; Nelson 2006; Iyega, 2000). Tese disadvantages of monocropping could ave contributed to te lower tecnical efficiency of te sorgum group. Te variation in te DEA metafrontier (DEA-MF) of te tree groups of cropping system suggests tat tere is a scope for increasing te tecnical efficiency in te cropping systems in Kebbi State. Te maximum 1544 ISDS

8 values of 1 for te DEA-MF sow tat tere must ave been at least one DMU tat used an input-output combination tat placed it at te point of tangency between teir group frontier and te metafrontier 2. Comparison of efficiency across different cropping systems is to ascertain te relevance of catcing-up, i.e. of productivity gains attainable by increasing tecnical efficiency (Battese et al., 2004; O Donnell et al., 2008; Moreira and Bravo-Ureta, 2010). Te result from tis study reveals tat te sorgum and sorgum/cowpea groups can improve teir tecnology by learning from te prevailing agricultural practices of te millet/cowpea group wo are operating close to te metafrontier Comparison of te DEA tecnical efficiency metafrontier (MF) scores of te monocroppers and intercroppers using Wilcoxon Rank-Sum Test Table 2 presents te Wilcoxon Rank-Sum Test for te differences between te metafrontier scores of te sorgum and sorgum/cowpea farmers. Table 2. Wilcoxon Rank-Sum Test for te differences between te tecnical efficiency metafrontier scores of te sorgum and sorgum/cowpea farmers, Kebbi State, January 2012 Enterprise Ranks Count Wilcoxon sum rank Mean of Wilcoxon STD DEV of Wilcoxon Sorgum MF Sorgum/cowpea MF Ties 13 Z 0.68 P value 0.49 Te Wilcoxon Rank-Sum Test, wic is used to test for te differences between tecnical efficiency metafrontier scores of te sorgum and sorgum/cowpea farmers, is not significant. Te result sows tat tere is no statistical significant difference between sorgum and sorgum/cowpea farmers tecnical efficiency metafrontier scores. Based on te average tecnical efficiency metafrontier scores of te sorgum (0.46) and sorgum/cowpea (0.45) farmers (Table 6.7), te sorgum farmers ave te same efficiency in te utilisation of farm inputs as teir counterpart sorgum/cowpea farmers. However te results suggest tat tere is opportunity for bot groups of farmers to improve teir tecnical efficiencies. 2 Since te metafrontier and group frontiers are formed as te intersection of several yperplanes, tere is at least one DMU in te groups wo operated at a point were te yperplane of teir group frontier touced a yperplane of te metafrontier (O Donnell et al., 2008). ISDS

9 Table 3. Wilcoxon Rank-Sum Test for te differences between te tecnical efficiency metafrontier scores of te sorgum and millet/cowpea farmers, Kebbi State, January 2012 Enterprise Ranks Count Wilcoxon sum rank Mean of Wilcoxon STD DEV of Wilcoxon Sorgum MF Millet/cowpea MF Ties 7 Z P value 0.00 Te results in Table 3 sows tat te tecnical efficiency metafrontier scores for sorgum (monocrop) and millet/cowpea (intercrop), is significant Z = -4.73, P<0.01. Tis implies tat tere is statistical significant difference between te tecnical efficiency metafrontier scores of sorgum (monocrop) and teir counterpart millet/cowpea (intercrop). Te two groups ave different tecnical efficiency metafrontier scores. Te mean tecnical efficiency metafrontier scores for te sorgum and millet/cowpea is 0.46 and 0.62 respectively (Table 1). Te results suggest tat te millet/cowpea farmers are better in terms of resource utilisation tan teir counterpart sorgum farmers. Te possible reason wy te millet/cowpea farmer is better in terms of tecnical efficiency could be tat te intercrop requires less fertiliser because cowpeas fix nitrogen into te soil and te crops are less exposed to infestation of pests and disease (Beuerlien, 2001; Banik and Sarma, 2009). Particularly, millet is drougt tolerant, suffers less from pests and diseases tan sorgum, maize and weat NRC (1996), de Rouw (2004) and de Rouw and Winkel (1998). 4. Conclusion Based on te levels of te tecnical efficiency of te two cropping systems in te study area, bot mono and intercropping systems seem to ave te potentials of improving crop production in Kebbi State. Te result from tis study reveals tat te sorgum and sorgum/cowpea groups can improve teir tecnology by learning from te prevailing agricultural practices of te millet/cowpea group wo are operating close to te metafrontier. Policies towards enancing farmer s performance sould be promulgated. Acknowledgements Te autors acknowledge te contribution of te Tertiary Education Trust Fund (TETFund) and Federal University of Tecnology Minna, Niger State, Nigeria for funding te researc ISDS

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11 Palitza, K. (2010), Climate cange New tinking to tackle old problems, Inter press service news agency, ttp:// ipsnews.net/africa/nota.asp?idnews=45905, Retrieved May 22, Saleem, M.F, S.H. Sa, M.A. Malik and Munir, M.K. (2000), Bio-Economics of different upland rice-based intercropping system under strip plantation, International Journal of Agriculture and Biology, Vol. 2 No. 4, pp ISDS