Thesis. the Graduate School of The Ohio State University. Bernadette Chewe Chimai, B.Ag.Sc. The Ohio State University. Master's Examination Committee:

Transcription

1 Determnants of Techncal Effcency n Smallholder Sorghum Farmng n Zamba Thess Presented n Partal Fulfllment of the Requrements for the Degree Master of Scence n the Graduate School of The Oho State Unversty By Bernadette Chewe Chma, B.Ag.Sc Graduate Program n Agrcultural, Envronmental and Development Economcs The Oho State Unversty 2011 Master's Examnaton Commttee: Cameron S. Thraen, Advsor Donald Larson Gelson Tembo

2 Copyrght by Bernadette Chewe Chma 2011

3 Abstract Sorghum producton has been wdely promoted among smallholder farmers owng to ts ablty to thrve n drought prone condtons and low nput requrements compared to most staple cereals. However, sorghum producton and productvty among smallholder farmers remans low. Varatons n productvty among smallholder farmers are due to dfferences n effcency whch may be affected by varous regonal and farm specfc soco-economc factors. Ths study measured techncal effcency and ts determnants n sorghum producton, and the contrbuton of growng sorghum to techncal effcency n feld crop producton. The study used Data Envelopment Analyss (DEA) followed by an Ordnary Least Squares (OLS) regresson of the DEA scores on the household and farm characterstcs. Average techncal effcency n sorghum producton among the smallholder farmers was 34 percent. Techncal effcency n sorghum producton was affected by household sze, number of dependents, use of anmal draught power, gross value of feld crop producton, value of assets, ncome from lvestock actvtes, access to credt, seed rate and whether a household s located n a low ranfall area or not. On average, sorghum farmers were sgnfcantly more effcent n feld crop producton than non sorghum farmers. Therefore, sorghum producton mproves techncal effcency n overall feld crop producton among smallholder farmers.

4 Dedcaton I dedcate ths thess to my parents and daughter Mphatso.

5 Acknowledgements I would lke to thank the Internatonal Sorghum and Mllet Program (INTSORMIL) for grantng me a full scholarshp to study for a Master of Scence degree at the Oho State Unversty (OSU). My sncere grattude also goes Pat Rgby n Internatonal Programs n Agrculture at OSU for her admnstratve support, encouragement and frendshp durng my study perod. I would also lke to express my sncere grattude to my thess examnaton commttee members Prof. Cameron Thraen, Prof. Donald Larson and Dr. Gelson Tembo for ther advce, comments, encouragement and gudance n producng ths thess. I am also grateful to Dr. Mark Erbaugh for hs contrbutons to my thess. I gratefully acknowledge the Food Securty Research Project (FSRP) for the supplemental survey data used n ths thess. I am eternally ndebted to my parents for ther fnancal and emotonal support throughout my lfe. Specal thanks for encouragng me to pursue graduate studes and takng care of my daughter durng the entre study perod. To the rest of my famly, I say thank you for your support and encouragement. My fancé Bran, I am most grateful for you support and encouragement throughout my studes and your useful comments on my thess. v

6 Fnally, I would lke to thank all the teachng staff, admnstratve staff and my classmates at OSU who contrbuted to the successful completon of my Masters studes. v

7 Vta 2000.Roma Grls Secondary School July Bachelor of Agrcultural Scence, The Unversty of Zamba July 2007 The Lvestock Development Trust (LDT) award for the best graduatng student n Agrcultural Economcs and Extenson Educaton, The Unversty of Zamba Graduate Research Assocate, Department of Agrcultural, Envronmental, and Development Economcs, The Oho State Unversty Felds of Study Major Feld: Agrcultural, Envronmental and Development Economcs v

8 Table of Contents ABSTRACT... II DEDICATION... III ACKNOWLEDGEMENTS... IV VITA... VI TABLE OF CONTENTS... VII LIST OF TABLES... X LIST OF FIGURES... XI 1. INTRODUCTION PROBLEM STATEMENT AND JUSTIFICATION OBJECTIVES ORGANIZATION OF THE THESIS CONCEPTUAL FRAMEWORK EFFICIENCY THEORETICAL MEASUREMENT OF EFFICIENCY EMPIRICAL MEASUREMENT OF EFFICIENCY Parametrc methods The nonparametrc methods Identfcaton of potental determnants of neffcency v

9 2.4.4 Developments n effcency measurement MEASURING TECHNICAL EFFICIENCY USING DEA Determnants of Techncal Effcency DEA AND OLS MODELS DEA model Determnants of techncal neffcency DATA COLLECTION, ORGANIZATION AND ANALYSIS MODEL DIAGNOSTICS Outlers and nfluental observatons n DEA model Regresson dagnostcs n the effcency models EMPIRICAL RESULTS PRODUCTIVITY OF AGRICULTURE IN ZAMBIA SORGHUM PRODUCTION IN ZAMBIA DESCRIPTIVE ANALYSIS Soco-economc characterstcs of the sorghum farmers Economc actvtes Access to nformaton and nfrastructure Sorghum producton Comparson of characterstcs of sorghum farmers and non-sorghum farmers DEA AND OLS MODEL RESULTS Techncal effcency n sorghum producton Determnants of techncal effcency Techncal Effcency n feld crop producton Determnants of effcency and contrbuton of Sorghum producton v

10 5. CONCLUSIONS AND RECOMMENDATIONS REFERENCES APPENDIX A. TABLES x

11 Lst of Tables Table 1. Producton functon varables Table 2. Descrpton of varables n sorghum effcency model Table 3. Descrpton of varables n feld crop effcency model Table 4. Household and farm characterstcs of the sorghum farmers Table 5. Access to nformaton and servces Table 6. Summary of nputs, output and management practces n sorghum felds Table 7. Comparson of attrbutes between sorghum and non sorghum farmers Table 8. Dstrbuton of techncal effcency n sorghum producton n the sample Table 9. Determnants of techncal effcency n sorghum producton Table 10. Dstrbuton of techncal effcency scores n feld crop producton Table 11. Determnants of effcency and contrbuton of Sorghum producton Table 12. Comparson of VRS and CRS scores by category x

12 Lst of Fgures Fgure 1. Sorghum producton process... 8 Fgure 2. Input orented decomposton of effcency Fgure 3. Contrbuton of ncome generatng actvtes to total household ncome Fgure 4. Share of total area used for feld crops by crop Fgure 5. Dstrbuton of sorghum producton techncal effcency scores n the sample 51 Fgure 6. Dstrbuton of feld crop techncal effcency scores n the sample x

13 1. Introducton Sorghum producton has been wdely promoted among smallholder farmers owng to ts ablty to thrve n drought prone condtons and low nput requrements compared to most staple cereals lke maze. In Zamba, sorghum producton s promoted n mostly drer parts of the country to meet household food securty needs and famly ncome. Apart from ts producton advantages, utlzaton of sorghum has also evolved from supplementng household staple food needs to ndustral utlzaton n sectors such as commercal beer brewng, food processng and feed producton. The ncreased ndustral utlzaton has ncreased marketng opportuntes for sorghum producers that can result n ncreased ncome from crop producton. Sorghum producton n Zamba stands at about 30 thousand metrc tons per year. The general trend observed s that of stagnaton or declne n producton and yelds over the years. Low producton levels have been attrbuted to low productvty, unrelable ranfall, nadequate nfrastructure and producton and marketng enhancng support structures (Larson et al. 2006). Low productvty n sorghum producton has been attrbuted to, among other thngs, use of low yeldng cultvars especally among rural farmers, and low technology adopton and nput use (Chs, undated; Larson et al., 2006). Increasng productvty n smallholder agrculture has been dentfed as one of the man ways of mprovng farm ncomes and economc wellbeng of the farmers. Thus, promoton of productvty enhancng ntatves 1

14 has been a common component n polcy and programs by varous government and non government stakeholders. Improvng productvty could ncrease ncome obtanable from the lmted peces of land owned by the farmers and could result n mproved economc wellbeng among farmers (Onumah et al. 2009; Sols et al. 2009). In Zamba, smallholder agrculture s one of the most mportant forms of lvelhood among the rural households. Several publc polces have been targeted at mprovng smallholder agrcultural productvty through provson of agrcultural nputs, fnancal assstance, extenson servces, and promoton of sustanable methods of farmng such as conservaton farmng. Currently, the man publc polcy nterventon n mprovng smallholder staple food productvty s through the provson of nputs through the Fertlzer and Input Support Program (FISP) at subsdzed prces for maze producton. Efforts by publc polcy makers are supplemented by Non-Governmental Organzatons (NGOs) and other stakeholders such as Southern Afrca Development Communty (SADC), Internatonal Sorghum and Mllet Program (INTSORMIL) and Internatonal Crops Research Insttute for Sem-Ard Tropcs (ICRISAT), among others. Some of the nterventons that have been targeted at mprovng productvty n sorghum nclude breedng and dstrbuton of mproved hgh yeldng varetes that are pest and dsease tolerant, and promoton of resource conservng management practces. 1.1 Problem Statement and Justfcaton Varatons n productvty are a functon of dfferences n scale of operaton, producton technology, operatng envronment and operatng effcency (Fred et al. 2008). Improvng effcency n producton allows farmers to ncrease ther output wthout 2

15 addtonal nputs and changng producton technologes resultng n ncreased productvty (Bravo-Ureta and Pnhero, 1997). For smallholder farmers, varatons n productvty due to dfferences n effcency may be affected by varous regonal and farm specfc soco-economc factors. In order to dentfy these factors, there s need to fnd a way of representng the performance of the farmers. Several studes have measured techncal effcency and ts determnants among dfferent types of farmers and countres (see, for example, Alene et al. 2006; Sols et al. 2009; Ajbefun, 2008; Coell and Battesse, 1996; Cabrera et al., 2010; and Onumah et al. 2009). These studes provde useful nformaton on what affects techncal effcency n specfc crops and lvestock enterprses and the more general farm level. However, effcency n these studes s usually relatve, and tends to be specfc to the farmer group and country under study. Whle some of the factors dentfed n such studes can provde a general dea of what affects effcency, each country and agrcultural product has unque characterstcs from whch generalzatons may not be possble. Studyng farm level and enterprse specfc techncal effcency are both mportant n provdng useful nformaton about the performance of farmers. Effcency studes at farm level measure aggregate effcency takng nto account all the useful outputs that are produced and nteractons of all the nputs used especally n cases where the same nputs can be used n multple outputs as s common n ntercroppng. Some of the practces and nterventons that have been studed n relaton to farm techncal effcency n crop producton nclude effect of sol conservaton practces (Sols et al. 2007), land tenure 3

16 (Karuk et al. 2008) farm sze (Ros and Shvely, 2005; Alvarez and Aras, 2004) and the nfluence of growng cash crops (Uaene and Arndt 2009). However, none of these studes has consdered the nfluence of growng crops wth mportant producton attrbutes lke low nput ntensty such as sorghum on overall farm techncal effcency. Crop specfc effcency studes are mportant n revealng how effcently resources are utlzed n specfc crops that are of partcular mportance. Dfferences n producton processes and characterstcs of crops may result n dfferent household and farm attrbutes beng mportant. Whle some attrbutes may be general to all or specfc categores of crops, other factors may be unque to specfc crops. For nstance, factors affectng effcency n cotton may be dfferent from maze producton because of dfferences n sklls, equpment and nput levels needed n producng these crops. Most crop specfc studes of techncal effcency have been centered on staple and hghly commercalzed crops lke maze, cotton, coffee, rce and wheat. Few studes (see Omonona et al. 2010) have looked at less commercal crops wth growng economc mportance and attractve producton trats such as sorghum, cowpeas and other pulses. Few studes have attempted to analyze productvty n small holder agrculture n Zamba. For example, Smth (2008) uses OLS to dentfy the determnants of productvty of land and labor n crop producton, wth an emphass on the nfluence of access to cattle. Whle ths study dentfes the factors affectng land and labor productvty by lookng at sngle factor productvty n terms of value of crop yelds per unt of resource, t does not measure techncal effcency. 4

17 To the best of my knowledge, no study has measured techncal effcency n sorghum producton or the effect of growng sorghum on a farm s techncal effcency n feld crop producton. Ths study estmated techncal effcency n sorghum producton, ts determnants and the effect of sorghum producton on techncal effcency n feld crop producton usng data from smallholder farmers n Zamba. Techncal effcency was measured usng Data Envelopment Analyss (DEA) followed by a second stage least squares regresson to dentfy the determnants of techncal effcency. Measurng effcency provdes a way of quantfyng and comparng the performance of each farmer, and dentfcaton of factors explanng any neffcences and dfferences n performance. Identfcaton of factors affectng neffcency can assst stakeholders n the mprovement of productvty to dentfy controllable and uncontrollable factors affectng effcency that need to be taken nto account n desgnng nterventons. Stakeholders n the promoton of sorghum producton would be able to dentfy whch characterstcs or nterventons to focus on, and have an estmate of the expected effects. Identfcaton and mplementaton of approprate nterventons to ncrease effcency wll result n greater success n mprovng sorghum productvty among the farmers. Sorghum producton has the attractve characterstc of beng less nput ntensve and more tolerant to drought than other cereals lke maze. Measurng the effect of growng sorghum on techncal effcency n feld crop producton wll provde useful nformaton on how havng sorghum n a farmer s crop mx nfluences the farmer s effcency n nput use and gude stakeholders on the mpact of ther promotonal efforts on the wellbeng of the farm. The stakeholders wll be able to judge whether growng sorghum makes the farm more or less 5

18 techncal effcent. The effects of growng sorghum on techncal effcency n producton of all the feld crops can then be compared wth other farm objectves. 1.2 Objectves Ths study measured techncal effcency and ts determnants n sorghum producton among smallholder farmers and the effect of growng sorghum on techncal effcency n feld crop producton. The specfc objectves were ) To measure techncal effcency among smallholder sorghum farmers; ) To dentfy the factors affectng neffcency n sorghum producton; ) To determne the nfluence of growng sorghum on farm techncal effcency; and v) To dentfy measures of mprovng farmer productvty and ncome. 1.3 Organzaton of the thess The remander of the thess s organzed as follows: Secton 2 ntroduces effcency, productvty and the conceptual framework used to study techncal effcency n the thess. Secton 3 descrbes the emprcal model, data sources and dagnostcs performed on the DEA and OLS models. The results of the descrptve analyss, optmzaton and estmaton are presented n secton 5 followed by conclusons and recommendatons n secton 6. 6

19 2. Conceptual Framework A producton process nvolves the transformaton of nputs nto outputs. In crop producton, techncal nputs such as seeds, land, labor and fertlzer are combned to produce the crop. The transformaton process depends not only on the levels of nputs used, but also on the management practces that the farmers use to combne these nputs. Management practces used n producton represent an amalgam of knowledge and sklls that the farmer has or acqures overtme and characterstcs of the farm. The techncal nputs and the management practces jontly determne the quantty and qualty of output produced. The sorghum producton process s summarzed n Fgure 1. 7

20 Mcro Macro External Weather, dsease, Polcy, etc. Techncal nputs: Land, labor, seed, fertlzer Fa rm and household characterst cs Producton process Output Fgure 1. Sorghum producton process 2.1 Effcency Varatons n productvty are a functon of dfferences n scale of operaton, producton technology, operatng envronment and operatng effcency (Fred et al. 2008). Increases n productvty can be acheved by mprovements n technology such as ntroducton of new machnery, pestcdes, and mproved seed varetes among others. Alternatvely, productvty can be mproved by changng factors that mprove the effcency by whch nputs are beng transformed nto output such that hgher outputs are produced from the same level of nputs and technology (Bravo-Ureta and Pnhero, 1997; Coell, 1995). 8

21 Bravo-Ureta and Pnhero (1997) defne economc effcency as the capacty of a frm to produce a predetermned quantty of output at mnmum cost for a gven level of technology. Economc effcency s made up of allocatve and techncal effcency. Techncal effcency refers to the ablty of a producer to produce on the producton fronter whle allocatve effcency s about choosng the optmal proporton of nputs that allows for least cost producton gven nput prces. Accordng to Koopmans (1951), also quoted n Fred et al. (2008), a producer s techncally effcent f an ncrease n any output requres a reducton n at least one other output or an ncrease n at least one nput, and f a reducton n any nput requres an ncrease n at least one other nput or a reducton n at least one output. In sorghum producton, a techncally effcent farmer maxmzes output subject to nput constrants or attempts to mnmze the amounts of nput necessary to produce a gven output. Gven a producton fronter, a techncally effcent farmer s located on the fronter whle an neffcent farmer s located on the nteror of the producton functon. 2.2 Theoretcal measurement of effcency A farmer s sorghum producton functon can be expressed as: y f (x) (1) Where y s total sorghum output and x s an nx1 vector of physcal unts used n producton such as land, labor and captal. The producton functon s assumed to have the followng propertes; non-negatvty, weak essentalty, monotoncty and concavty. The non-negatvty assumpton ensures that the functon f(x) results n only zero or 9

22 postve outputs of sorghum from producton. Weak essentalty means that postve quanttes of at least one of the nputs, seed, are necessary to produce any sorghum. The weak essentalty assumpton s vald because t s not possble to produce any sorghum wthout plantng any seed. Monotoncty mples that addtonal unts of nputs used n producton do not decrease total producton. Thus, the margnal products of the nputs used n producton are expected to be non-negatve. The concavty assumpton restrcts the output obtanable from a lnear combnaton of nputs to be no less than the sum of the outputs obtanable from each nput on ts own. Assumng only two nputs, x1 and x2, the producton functon relatonshp can be represented n nput space as an soquant. X 1 X1 A D A C B I 0 O X2 A X2 Fgure 2. Input orented decomposton of effcency 10

23 Fgure 2 llustrates the concepts of nput orented techncal, allocatve and economc effcency n the producton of y 0 output of sorghum. The graph I 0 s an soquant representng the combnaton of nputs x1 and x2 needed to produce y 0 of output. Suppose farmer A s producng y 0 usng x1 A of nput x1 and x2 A of nput x2. Based on the soquant I 0, farmer A s usng more nputs than requred to produce y 0. Techncal effcency of each farmer can be computed as the rato of optmal performance to actual performance. In fgure 1, techncal effcency of farmer A can be computed as the rato of the lne segment OB to the lne OA. Mathematcally, ths s presented as the rato OB/OA. Snce OB s a segment of OA, techncal effcency of farmer A wll be less than one. All the farmers producng on the soquant I 0 are techncally effcent wth a score of 1. Farmer A could mprove hs techncal effcency by radally reducng both or one of the nputs up to the soquant I 0. If nput prces are taken nto consderaton, allocatve and economc effcency can also be calculated wth the ad of an socost lne. The allocatve effcency of farmer A s gven by the rato OC/OB. Economc effcency would then be the rato OC/OA. The optmal nput combnaton s the nput combnaton that costs the least relatve to the other combnatons on the soquant n the producton of y 0, pont D. A farmer producng at D s economcally effcent as he s usng the optmal combnaton of nputs of x1 and x2 that costs the least. 11

24 2.4 Emprcal measurement of effcency To measure effcency, the effcent producton functon needs to be known. In most emprcal studes, the effcent fronter s unknown and has to be estmated from data on whch effcency s to be measured. The nature of the assumptons made n estmatng the fronter dvdes the effcency measurement nto non-parametrc and parametrc. The parametrc methods of estmatng effcency make a pror assumptons about the functonal form of the producton functon and the neffcency term. In the nonparametrc methods such as Data Envelopment Analyss (DEA) and Free Dsposal Hull (FDH), the form of the producton functon s taken as unknown Parametrc methods The parametrc methods nvolve econometrc modelng of the producton process makng assumptons a pror on the functonal form of the producton functon and the dstrbuton of the neffcency term. The common functonal forms of the producton functon n the lterature are the Cobb-Douglas (and ts modfcatons) and the trans-log models. The estmated fronter can be determnstc or stochastc dependng on the treatment of devatons of an observaton from the fronter. Determnstc fronters are regresson based and attrbute all devatons to neffcency. Determnstc fronters may be estmated usng Corrected Ordnary Least Squares (COLS) or Modfed Ordnary Least Squares (MOLS). Unbased estmates of the slope parameters n both estmaton procedures are obtaned usng OLS followed by a correcton of the ntercept. In COLS, usng the largest postve observed resdual whle MOLS modfes the ntercept usng the mean of the assumed one-sded dstrbuted dsturbance term (Kumbhakar and Lovell. 12

25 2000). Stochastc fronters take nto account stochastc error by decomposng the error term nto stochastc and neffcency components. In Stochastc Fronter Analyss (SFA), the error term s decomposed by parameterzng the dstrbuton of the neffcency term (Fred et al. 2007). Ths entals makng assumptons on the dstrbuton of the neffcency term, usually half-normal or exponental, and that the stochastc error and neffcency are ndependent of each other and the ndependent varables (see for example, Coell and Battesse, 1998; Emokaro and Ekunwe, 2009 among others). Other dstrbutons of the neffcency term are avalable. The stochastc fronter can be estmated usng maxmum lkelhood estmaton (MLE) to obtan consstent estmates of the slope parameters. The condtonal dstrbuton of the estmates can be used to obtan condtonal expected values of neffcency for each observaton. Stochastc dstance fronters are also avalable for measurng effcency. The man weakness of stochastc fronter analyss les n ts parametrc nature. The need to specfy the functonal form of the producton functon a pror makes t susceptble to bas resultng from functonal form msspecfcatons. Another argument n the lterature relates to the comparson of ndvdual unts aganst an average practce fronter rather than best practce n the sample beng analyzed n SFA. Also, SFA fals to allow for analyss of techncal effcency n multple outputs wthout output prce nformaton (Coller et al. 2011). Wth multple outputs, the output varable s usually measured as an aggregate monetary value rather than physcal unts. The use of SFA for multple outputs s argued to be napproprate as t may underestmate effcency (Alene et al. 2006; Sols et al. 2009; Ajbefun, 2008). The use of methods lke Stochastc dstance fronters, DEA 13

26 or effcency scores computed from a combnaton of SFA and DEA s recommended as more approprate. Coller et al. (2011) also argue that cross sectonal SFA s no better than DEA wth regard to effcency rankngs of observatons because the condtonal expected values of neffcency are perfectly correlated wth the composte error term. As such, the rankngs of effcency that are based on dstrbutonal assumptons of the neffcency term are not expected to dffer from those based on DEA scores. Ondrch and Ruggero (2001) provde evdence supportng ths argument The nonparametrc methods The nonparametrc methods use mathematcal programmng methods to measure relatve effcency of unts commonly referred to as Decson Makng Unts (DMUs). The most common nonparametrc methods are the DEA and the more general FDH. A pecewse fronter s constructed based on data ponts that use the least nputs n producng a partcular level of outputs. Relatve effcency s measured by comparng observed performance aganst best-practce performance. The nonparametrc methods dffer from the parametrc n that the former does not make any a pror assumptons about the functonal form of the producton functon and the neffcency term. The DEA makes general assumptons of monotoncty and convexty, resultng n a flexble fronter that allows the producton functonal form to vary across DMUs. Relaxng the convexty assumpton n DEA leads to FDH whch has a step fronter (detaled treatment of FDH avalable n De Borger et al, 1994). The basc DEA and FDH are determnstc, thus attrbutng all devatons from the fronter to neffcency. 14

27 The most common method of estmatng effcency n DEA s a radal measure based on Farrell s (1957) concept of radal contracton of nputs to the least level necessary for producton of a specfc level of output. In output space, the radal measure can be thought of as radal expanson of output obtanable from a gven combnaton of nputs. Other methods of estmatng effcency n DEA nclude the use of a target DMU for each DMU under study, and other non-radal measures such as the addtve model, Russell measure, range-adjusted measure, slack-based measure, geometrc dstance functon, hyperbolc and dmensonal effcency models (see Fred et al for a detaled dscusson of each of these methods). The flexble functonal form of the nonparametrc methods has won favor n the effcency lterature. Also, other than just measurng effcency, the nonparametrc technques of DEA and FDH also provde nformaton on the shadow prces of nputs and outputs of the DMUs. These are obtanable from the weghts whch can be unrestrcted or restrcted wthn acceptable ranges (Mahlberg and Oberstener, 2001). DEA s also able to handle multple outputs and multple nputs wthout requrng prce data (Coller et al. 2011). The determnstc nature of the basc DEA s usually cted as ts man weakness as t fals to account for stochastc nose n data whch could potentally bas the estmated effcency scores (Coell and Battesse, 1996; Onumah et al. 2009). The DEA s also argued to be less robust to outlers and extreme values and lacks parameters for economc nterpretaton (Darao and Smar, 2007). 15

28 2.4.3 Identfcaton of potental determnants of neffcency In Stochastc fronter analyss, potental determnants of neffcency are usually ncluded as ndependent varables drectly n the producton functon and estmated as a one-stage procedure. Though two stage procedures of dentfyng potental determnants n the parametrc methods are possble, they are argued to produce based estmates of the nfluence of contextual varables on neffcency (Banker and Natarajan, 2008; Fred et al. 2009). In DEA, the determnants of effcency are usually dentfed n a second stage parametrc regresson of the DEA scores on varables n the envronment of the DMU that are expected to have an nfluence on effcency. The functonal form of the second regresson depends on the structure of the hypotheszed relatonshp between the scores and the envronmental varables. Whle some studes use OLS, most studes use Tobt regresson n the second stage (Ros and Shvely, 2005; Banker and Natarajan, 2008). However, the use of the Tobt regresson has been questoned. In partcular McDonald (2009) argues that the use of Tobt n the regresson of DEA scores on potental determnants of effcency s napproprate because the DEA scores are not a result of censorng, but rather, normalzaton. McDonald (2009) argues that least squares regresson s more approprate. The use of the two-stage approach n ether DEA or SFA has also been crtczed n the effcency lterature. The man argument s that the second stage regresson has no statstcal bass, thus any nference based on ths regresson s nvald (Fred et al. 2009). The use of bootstrappng technques for more vald statstcal nference s suggested. However, Banker and Natarajan (2008) propose a statstcal bass for the second stage n the case of DEA based methods that allow for stochastc error and 16

29 show that the second stage OLS or MLE yeld vald estmates on whch statstcal nference can be performed. Invaldty of the second stage regresson only occurs f the data generatng process restrcts output to beng determned by nputs and neffcency only Developments n effcency measurement Several new models and modfcatons have been proposed to deal wth weaknesses dentfed n the basc SFA and DEA/FDH. Attempts have been made to make SFA less parametrc by use of more general functonal forms form the producton functon such as the Fourer flexble form. Khumbakar et al. (2007) propose an approach to handle nonparametrc stochastc fronter models based on local maxmum lkelhood technques. By localzng the parameters of a local polynomal producton model and ts stochastc component, the procedure presented n Kumbhakar et al. (2007) releves functonal form concerns n the producton functon and the stochastc component. Coller et al. (2011) propose an extenson of the COLS to handle multple outputs n SFA wthout the use of prce nformaton. They use DEA based methods to provde a measure of aggregate output that corresponds to the hghest soquant. The aggregate output s then regressed on observed nputs usng a trans-log functonal form and COLS to estmate techncal effcency. Henderson and Smar (2005) also develop a fully nonparametrc stochastc fronter model for panel data. In the DEA framework, most of the attempts have been targeted at mprovng the robustness of estmates to statstcal nose. For example, Gstach (1998) ntroduced the 17

30 dea of DEA+ whch attempts to address the relablty of DEA n nosy envronments. In DEA+, a pseudo fronter s estmated usng DEA n the frst stage. Maxmum lkelhood estmaton s appled to the DEA effcency scores to estmate the scalar value by whch the pseudo-fronter should be shfted to get to the true producton functon, yeldng consstent estmates. Banker and Natarajan (2008) buld on Gstach (1998) s DEA+ to allow for the analyss of the nfluence of contextual varables on effcency. Banker and Natarajan (2008) specfy a producton functon that s monotone ncreasng wth a 3 part error term made up of a lnear functon of contextual varables, one sded neffcency term and a two-sded random nose term. Usng DEA+ n the frst stage followed by OLS, Tobt or MLE n the second stage produces consstent estmates, performng better than one stage parametrc methods. Other stochastc consderatons n DEA nclude the use of chance constraned programmng (Cooper et al. 1998), stochastc DMUs (Gong and Sun 1995). Kuosmanen (2006) ntroduced Stochastc Nonparametrc Envelopment of Data, StoNED, a technque of measurng effcency that uses constraned Nonparametrc Least Squares (NLS) regresson technques to estmate a stochastc producton fronter. The StoNED attempts to brng together the nonparametrc nature of the DEA fronter wth the stochastc nature of SFA. It entals a pecewse constructon of the producton functon and decomposton of the neffcency term from the composte error. In addton to accountng for stochastc error, StoNED allows for utlzaton of statstcal tools such as goodness of ft and statstcal tests commonly done n parametrc methods. However, n cross sectonal analyss, StoNED suffers nconsstency and only computes absolute levels 18

31 of effcency that are based on a pror assumptons of the dstrbuton of the neffcency. These weaknesses are also shared by the parametrc technques that rely on cross sectonal data. In the cross sectonal settng, StoNED s more of a sem-parametrc estmaton procedure because of the relance of dstrbutonal assumptons n the dstrbuton of the neffcency term (Kuosmanen and Kortelanen, 2007). Panel data could be used to provde more consstent estmates that are also free from dstrbuton assumptons of the neffcency term. 2.5 Measurng techncal effcency usng DEA Data Envelopment analyss was chosen as the method of estmatng effcency n ths study because t allowed for analyss of multple outputs wthout ntroducng output prces and avoded the possblty of encounterng problems assocated wth functonal form msspecfcatons 1. Several studes that have compared the results of DEA and SFA methods have reported no sgnfcant dfferences n scores obtaned (for example Ajbefun, 2008). Data Envelopment Analyss constructs a pece-wse fronter envelopng the most DMUs n the sample. In nput orentaton, ths entals constructng an Isoquant usng the DMUs that are closest to the nput axes. The closer a DMU s to an nput axs, the less of that nput the DMU s usng to produce a fxed output. In output orentaton, the fronter s 1 In recognton of the weaknesses of the tradtonal SFA and DEA methods of analyzng effcency, an attempt was made to use the more robust StoNED whch presented an opportunty to analyze techncal effcency n sorghum producton wthout the functonal form ssues assocated wth SFA and vulnerablty to nose and outlers assocated wth DEA. The producton functon for each household was estmated but the resultng resduals could not be decomposed nto stochastc nose and neffcency due to problems of a postvely skewed producton functon rather than a negatve skewness. In the nterest of tme, the choce was between SFA and DEA. 19

32 constructed based on the DMUs that are furthest from the orgn ndcatng that they are able to produce more from a fxed set of nputs and are, therefore, on a hgher producton possblty fronter. The nput orentaton reveals the case of radal contracton whle the output orentaton shows radal expanson. Mathematcally, effcency of a DMU s measured as a rato of the sum of weghted the outputs to the sum of weghted nputs. Charnes, Cooper and Rhodes (1978) proposed an nput orented DEA model to measure the relatve effcency of a DMU as: Maxmze u, v s k 1 m j 1 v u k j y x k, j, vk ykh k 1 Subject to 1 m u x s j 1 j jh v u 0 (2) k, j where y kh s the amount of output k produced by DMU h, x jh s the amount of nput j used by DMU, 20

33 v k s the weght gven to output k, u j s the weght gven to nput j. Ths can be converted nto a Lnear Programmng (LP) problem by normalzng the weghts to add to 1. The LP can be presented as: Maxmze u, v s k 1 v k y k, Subject to u 1 m j 1 j x j, s k 1 v k y k, h s k 1 u j x j, h u v 0. (3) j, k The LP can be solved usng GAMS (Kalvalagen, 2004). The model presented here reflects constant returns to scale (CRS) and assumes that the DMUs, the farmers n ths case, are operatng at the optmal based on ther scale. It s wdely argued that ths s too restrctve and unrealstc an assumpton and an alternatve varable returns to scale (VRS) based model s avalable. Usng the VRS model ensures that a DMU s performance s only compared wth other DMU s operatng at the same scale. The VRS DEA model as suggested by Banker et al (1984) can be presented as: 21

34 mn m ze z subject to h h y k, h yk, x j, h h x j, h h h h 1 h 0 (4) The VRS DEA model was chosen to measure techncal effcency n sorghum producton because the assumpton that the farmers n the sample are operatng at optmal based on ther scale s not approprate. In contrast, the CRS model was used to measure techncal effcency n feld crop producton because of nsuffcent memory to process the VRS model Determnants of Techncal Effcency Identfcaton of the determnants of techncal effcency can be done n a second stage regresson of the effcency scores from the LP problem on farm and household characterstcs expected to explan techncal effcency. In most DEA based studes, the second stage regresson s presented as Tobt model as the effcency scores fall n the range 0 to 1, attrbutng t to censorng (Ros and Shvely, 2005; Andreu and Grunewald, 2006). However, McDonald (2009) provdes evdence of lack of censorng or corner soluton n the Data Generatng process of the effcency scores, but, rather, 22

35 normalzaton resultng n fractonal or proportonal score. Johnson (2009) recommends the use of quas maxmum lkelhood estmaton (QMLE) to produce asymptotcally effcent estmates. An alternatve, and less statstcal demandng, s the use of OLS to produce unbased and consstent estmates, though asymptotcally neffcent. In the presence of non-normalty and heteroskedastcty, the dependent varable can be transformed through usng the natural logarthm. Based on ths argument, OLS s used n the second stage regresson wth robust standard errors and a natural log transformaton of the dependent varable. The natural logarthm of dependent varable makes t closer to normal than wthout the transformaton (Wooldrdge, 2009). Other studes have used the natural logarthm of the effcency or neffcency scores from DEA (Bravo-Ureta and Pnhero, 1997; Helfand and Levne, 2004). The second stage model was specfed as follows: ln effscore 0 X (5) Where lneffscore s the natural logarthm of the DEA effcency scores, β 0 s the ntercept, X s a vector of household and farm characterstcs, β s a vector of estmated parameters and ε s the stochastc dsturbance term for the th farmer. 23

36 3. DEA and OLS models Ths secton presents the emprcal model used to estmate techncal effcency n sorghum producton, dentfy the determnants of neffcency n sorghum producton and the nfluence of growng sorghum on techncal effcency feld crop producton 3.1 DEA model The man nputs used n agrcultural producton can be categorzed as land, labor and materals. Land refers to the total area of land used n the producton of the crop(s) under study (Ajebefun, 2007; Omononah, 2010). In some studes land s further sub-dvded nto rrgated and unrrgated land to account for the effects of rrgaton on the quantty of crop produced (Coell and Battesse 1996). The way labor s represented n the producton functon vares across studes. Some studes consder labor n aggregate rrespectve of the source, measured n days or hours over the producton perod (Ajebefun, 2007; Alene et al., 2006). Others segregate famly from hred labor to take nto account dfferences n productvty of the two types as they are not consdered to be perfect substtutes n developng countres (Sols et al., 2009; Coell and Battesse, 1996). Materals nclude nputs such as seed, fertlzer, pestcdes and mplements that can be ncluded ndvdually n physcal unts or costs, or as aggregate materal costs dependng 24

37 on avalablty of data. For nstance, Bravo-Ureta and Pnhero (1997) nclude fertlzer n hundred pound unts and total expendture on farm tools explctly n the model whle Sols et al. (2009) uses expendture on purchased nputs. To estmate techncal effcency n sorghum producton, output was quantty of sorghum harvested n klograms whle the nputs were area planted wth sorghum and quantty of sorghum seed planted. Lack of data on labor use, materal cost of other nputs from the survey made t mpossble to nclude them as nputs n the model. Another nput that could have been ncluded was fertlzer use. Whle data was avalable on fertlzer use n all the cropped felds, only one household used fertlzer n the sorghum felds. The DEA model varables are summarzed n Table 1. Table 1. Producton functon varables Varable name Sorghum producton a Descrpton Feld crop producton b Y Quantty of sorghum harvested n kgs Quantty of harvest for each feld crop n kgs land Cultvated land n ha cultvated land n ha seed Quantty of seed planted n kgs quantty of seed planted n kgs for each crop fertlzer Quantty of fertlzer used n kgs Notes: a :sorghum producton functon wll be used n the DEA model to measure techncal effcency n sorghum producton. b: the aggregate crop producton functon wll be used n the DEA model to analyze the contrbuton of growng sorghum to farm techncal effcency n crop producton 25

38 In the DEA model to determne the contrbuton of growng sorghum to farm techncal effcency, only land, seed, fertlzer are ncluded as nputs due to unavalablty of data on labor use n crop producton. 3.2 Determnants of techncal neffcency A number of determnants of effcency n producton have been dentfed from prevous studes. Gorton and Davdova (2004) suggest that the man factors affectng effcency n agrculture producton may be categorzed nto agency and structural factors. Factors ncluded n the agency category are human captal factors such as educaton, tranng and experence of the farm operator. The man structural factors are socal captal and farm locaton whch take nto consderaton the agrcultural envronmental condtons facng the farm such as sol qualty, alttude, clmate, ranfall and access to water. Sols et al. (2009) add lteracy and age to the agency factors and famly ncome, famly sze, access to credt, land tenure status, gender composton of the labor force and off-farm employment to the structural factors. Others nclude farm sze (Bravo-Ureta and Pnhero, 1997; Coell and Battesse, 1996; Ajbefun, 2007). Whle these categores represent the man factors consdered n analyses from prevous studes, ther sgnfcance and estmated effects n explanng techncal effcency vary across studes. In a study nvestgatng agrcultural producton of farmers n Inda, Coell and Battese (1996) dentfed age, level of schoolng of the farmer, farm sze and year of observaton 26

39 the factors affectng techncal effcency of the farms. The drecton of effect of age vared across the vllages under study. The level of schoolng attaned by the household head had a postve effect whle farm sze and year of observaton had negatve effects. The drecton of effect of age on techncal effcency tends to vary by study, for example the effect of age was negatve n Ajbefun (2007) and postve n Bravo-Ureta and Pnhero (1997). In a study to evaluate techncal effcency n dfferent categores of farms that have adopted sol conservaton practces, Sols et al. (2007) found that educaton, extenson, male farmers, and access to credt had postve nfluences on effcency. In Sols et al. (2009), partcpaton n farmer or socal organzatons and use of sol conservaton practces also had a postve effect. Ownershp of land had a negatve effect such that farmers that owned the land they were cultvatng were less techncally effcent n crop producton than those who dd not own the land. In fsh producton n Ghana, Experence and pond sze had postve effects on techncal effcency whle beng a male farmer and usng concrete ponds had negatve effects. Household and farm characterstcs ncluded n the effcency model were gender of the household head, age of the household head, household sze, head s educaton, tllage usng anmal draught power, tllage usng hred labor, value of off-farm ncome, gross value of feld crop producton (excludng sorghum), mproved seed, value of assets, access to crop producton advce, access to agrcultural credt, ncome from lvestock actvtes, gross value of frut and vegetable producton, farm sze, dependents, seed, square of seed, quantty of seed cubed and dummy for locaton n low ran areas. The effcency functon for the th farmer s: 27

40 ln effscore adptll dagcredt seed hlabortll 13 seed 2 malehead lvnc seed3 offncml vfprod 2 hage lowran hsze lfarmsze lfcrop u 4 hedu 10 mprovseed 16 5 dependents prodadvce 11 asset = 1, 2,..., n (6) where lneffscore s the sorghum producton techncal effcency score. Equaton (6) was used to dentfy the determnants of neffcency n sorghum producton by testng the hypothess that household soco- economc factors and farm characterstcs are not statstcally mportant n explanng techncal effcency usng the p-value of the t- statstc. The null hypotheses to test the ndvdual sgnfcance of the varables can be stated as: β j = 0 for each of the j explanatory varables. 28

41 Table 2. Descrpton of varables n sorghum effcency model Varable name Malehead Hage Hsze Hedu Prodadvce Adptll Hlabortll Offncml Lfcrop Assetml Dagcredt Lvncml Vf_gvprod Lfarmsze Dependents Sorgseed Sorgseed2 Sorgseed3 Lowran Improvseed Varable label Male headed dummy Age of household head Household sze Household head's educaton Dummy equal to 1 receved producton advce Dummy equal to 1 tlled wth anmal draught power Dummy equal to 1 tlled wth hred labor Off farm ncome n mllons ZMK Natural log of the gross value of feld crop producton Assets n mllons ZMK Dummy equal to 1 f receved an agrcultural loan Lvestock ncome n mllons ZMK Gross value of frut and veg producton n mllons ZMK Natural log of farm sze Number of dependents Quantty of sorghum seed Square of quantty of sorghum seed Cube of quantty of sorghum seed Dummy equal to 1 f located n low or lower ran area Dummy equal to 1 f used mproved seed Table 2 summarzes the varables used n the effcency model to dentfy determnants of techncal effcency n sorghum producton. The effcency model to analyze the contrbuton of growng sorghum to farm techncal effcency n crop producton s: 29

42 ln effscore rentn hlabortll vfprodml fsp u 1 borrown malehead hage lvnml 9 lowran 16 dprcenf o 22 2 hedu offncml 10 3 hsze tllbran prodadvce assetml dependents 11 sorghum credt seedpad 5 12 mechtll farmsze 19 vroadkm com0607 ownttle adptll =1,2,,n (7) A descrpton of the varables used n the effcency model for feld crop producton s presented n table 3. 30

43 Table 3. Descrpton of varables n feld crop effcency model Varable name Malehead Hage Hedu Hsze Dependents totland ownttle rentn borrown lowran tllb4ran sorghum mechtll adptll hlabortll dprcenfo prodadvce dagcredt vroadkm vf_gvprodml lvncml offncml assetml seedpad com0607 fsp0607 Varable label Male headed dummy Age of household head Household head's educaton Household sze Dependents Farm sze Households owned any farmland wth ttle deeds Households rented-n any farmland Households borrowed any farmland Households resdng n low or lower ranfall area Household tlled before rany season Household grew sorghum dummy Households usng mechancal power for tllage Households usng anmals to power tllage Households usng hred labor for tllage Households wth access to commodty prce nformaton Households that receved agrcultural producton advce Probablty of household recevng an agrcultural loan Dstance to vehcular transport (km) Gross value of frut and veg. producton n mllons ZMK Lvestock ncome n mllons ZMK Off farm ncome n mllons ZMK Assets n mllons ZMK Households that pad for seed Receved commercal fertlzer Receved FSP fertlzer Model (7) wll analyze the contrbuton of growng sorghum to farm techncal effcency n crop producton by test the hypothess that growng sorghum has an nfluence on 31

44 techncal effcency. The null hypothess to test the effect of sorghum producton on techncal effcency s: 0 11 (8) 3.1 Data collecton, organzaton and analyss Ths thess used natonally representatve data from the 2008 rural supplemental survey to the 1999/2000 post harvest survey collected by a team effort of the Central Statstcal Offce (CSO) of Zamba and the Food Securty Research Project (FSRP). The total sample sze was 8094 households, 369 of them were sorghum farmers. Generaton and Varables relevant for the study were generated and organzed n STATA verson 10. The effcency scores for the DEA models were computed usng GAMS IDE Descrptve analyss and estmaton of the effcency models was done n STATA verson Model dagnostcs Outlers and nfluental observatons n DEA model One of the weaknesses of DEA s ts vulnerablty to outlers. In order to dentfy possble outlers n the computaton of techncal effcency scores for sorghum producton, the quantty of sorghum harvested was regressed on area planted and quantty of seed planted n order to dentfy potental outlers and nfluental observatons. Three observatons were dentfed and removed from the sample. To further mprove robustness of the effcency scores to outlers, the effcency scores were computed based on two runs of the GAMS model. The effcency scores from the frst run had an average of 25 percent 32

45 and eght households had scores of one. The eght fully effcent households were treated as potental outlers and excluded from analyss and the fnal effcency scores computed n a second run of the model. Smlarly, effcency scores n the feld crop DEA model were computed n two runs. The average effcency from the frst run was 24 percent. The second run excluded the 131 households who had scores of 1 n the frst run Regresson dagnostcs n the effcency models Varous regresson dagnostcs were performed on the two effcency models to ensure unbasedness and effcency of the OLS regresson estmates, and valdty of the hypothess tests. The models were tested for multcollnearty n the ndependent varables usng varance nflaton factors (VIFs). All the VIFs, except for seed and the square of seed were less than 4 ndcatng an absence of multcollnearty. Tests for specfcaton errors showed that the sorghum effcency model dd not have sgnfcant specfcaton errors or omtted varables. The feld crop techncal effcency model, however, had sgnfcant specfcaton errors and omtted varables whch perssted n varous model specfcatons. The specfcaton errors n the feld crop effcency model could result n bas n the regresson coeffcents. Both models had sgnfcant heteroskedastcty based on the Breusch Pagan Godfrey test and were corrected usng robust standard errors. Kernel densty plots of the resduals from the two neffcency models before transformaton of the effcency scores showed non-normalty n the resduals. After transformng the effcency scores usng natural logarthms, the resduals were more 33

46 normally dstrbuted justfyng the use of the natural log of effcency scores. The DEA scores were all greater than zero; hence no observatons were lost after transformaton due to falure to determne the natural log of zero. Numerc tests of normalty usng the Shapro-Wlk W test for normal data confrmed the lack of normalty n the resduals from the sorghum effcency model before transformaton of the DEA scores. Wth the natural log of the scores, the resduals were normally dstrbuted. The feld crop effcency model resduals remaned non normal even wth the transformaton though mprovements were observed. Non lnearty n the relatonshps between the dependent varable and contnuous ndependent varables were also checked usng plots of ndvdual varables aganst the scores. In the sorghum effcency model, non lnear relatonshps were observed n farm sze, gross value of feld crop producton and seedng rate hence the use of the natural log for farm sze and gross value of feld crop producton and the polynomal functon seedng rate. None of the contnuous varables n the feld crop effcency model showed sgnfcant non lneartes. Access to credt s usually treated as an endogenous varable because a household s decson to get credt s determned by some of the unobserved factors n the household makng t potentally endogenous. Several studes have acknowledged the possble endogenety n access to credt and have corrected for the bas usng nstrumental varables (for example Ros and Shvely, 2005; Fleteschner and Zepeda, 2002). In ths study, endogenety n credt was found to be statstcally sgnfcant n the feld crop 34

47 effcency model but nsgnfcant n the sorghum effcency model. The endogenety problem n the feld crop effcency model was corrected for usng resdency n a vllage, knshp tes, value of non productve assets, whether a household receved ad and quantty of maze harvested as nstruments n a two stage least squares (2SLS) regresson. In the frst stage, a Probt regresson was performed to estmate the probablty of a household accessng credt. The predcted value of the probablty that a household would receve credt was ncluded n the second stage OLS estmaton of the effcency model. Endogenety was also suspected n the varable representng whether a household grew sorghum or not due to observed dfferences between sorghum and non sorghum farmers n several household and farm characterstcs durng descrptve analyss of the sample. A formal test for endogenety showed that the decson to grow sorghum s exogenous. 35

48 4. Emprcal results 4.1 Productvty of Agrculture n Zamba Agrcultural s the man source of lvelhood for most rural households n Zamba wth the most mportant farm enterprse beng maze producton for these households. Zamban agrculture s characterzed by poor access to mproved seed and fertlzer, low farm ncomes, hgh nput costs, lmted prvate sector nvolvement n nput and output markets (Mnstry of Agrculture and Cooperatves et al. undated) and government nvolvement n nput and output markets. Access to credt s also low among the smallholder farmers due to, among others, the cessaton of government supported agrcultural loans durng the market lberalzaton changes of the 1990s, reluctance of commercal banks to gve agrcultural loans to low collateral farmers wth a reputaton of falng to repay loans n lean producton years, and the concentraton of mcrofnance on fnancng urban populatons nvolved n non agrcultural ncome generatng actvtes (Chumya, 2006). These, and other factors, have resulted n productvty n smallholder agrculture beng generally low. Demnger (2000) also attrbutes low agrcultural productvty n Zamba to polcy strateges that have specfcally been drected at fertlzer and maze resultng n maze beng cultvated n less sutable areas and more concentraton of research on maze producton than other crops. 36

49 4.2 Sorghum producton n Zamba Sorghum has hstorcally been grown as a tradtonal crop manly for household brewng and gran needs. Sorghum producers are dotted throughout the country, especally n the drer parts lke southern provnce and the valley areas of the eastern provnce. Productvty n sorghum s generally low wth actual farmer yelds beng below potental yelds. Low productvty has been attrbuted to among others, use of low yeldng cultvars especally among rural farmers, and low technology adopton and nput use (Chs, undated; Larson et al., 2006). Several mproved varetes have been realzed onto the seed market such as Sma, Kuyuma, ZSV12, ZSV15, WP-13, MMSH-375, MMSH- 413, MMSH-1324 and MMSH-1257 (Mnstry of Agrculture and Cooperatves et al. undated). Potental yelds for these varetes are between 4.5 and 8 tons per hectare. However, adopton of the mproved seed varetes s low due to mperfect nformaton and poor seed delvery channels among others (Chs, undated). Water requrements are lower n sorghum than maze. A fne seed bed s recommended for good germnaton of the seed. Recommended seed rates are about 10 kgs/ha for gran and kg per hectare for forage n Zamba. Other practces recommended for mproved sorghum yelds nclude performng at least one weedng, fertlzer applcaton and pest control (Mnstry of Agrculture and Cooperatves et al. undated). 37

50 4.3 Descrptve analyss Ths secton presents the results of the descrptve analyss for the households n the sample. Secton descrbes the sorghum farmers n the sample n relaton to household composton, ncome generatng actvtes and household access to socal captal and nfrastructure. Secton summarzes sorghum producton among the farmers n the sample. Comparsons of household and farm characterstcs of the sorghum and non sorghum farmers are presented n secton Soco-economc characterstcs of the sorghum farmers The sample was made up of 369 sorghum farmers, 9.49 percent categorzed as medum scale holdngs and the rest small scale holdngs. Table 4 presents the household and farm characterstcs of the sorghum producng households under analyss. The average household sze n the sample was equvalent to 6.21 adults, 43 percent of whom were ether chldren below the age of 12 years, elderly above 60 or household members that had been ll n the three months before the survey. Most of the household heads were prme-aged males. Educaton levels among the sorghum farmers n the sample are qute low, especally among the household heads that, on average, dd not have a complete prmary educaton. Educaton and lteracy have been dentfed as mportant factors n determnng decsons to adopt productvty enhancng technologes among farmers. 38

51 Table 4. Household and farm characterstcs of the sorghum farmers Characterstc Average Proporton of male household heads 77% Age of the household head Household sze n adult equvalents 6.28 Number of members aged years 3.09 Number of dependents 2.72 Head's number of years of schoolng 4.86 Number of years of schoolng of the most educated member 7.12 Value of household assets owned n 2008 n ZMK 512, Value of productve assets owned n 2008 n ZMK 3,210, Household ncome n 2008 n ZMK 3,359,669 Exchange rate was ZMK3, 561 per US Dollar On average, the sorghum households n the sample owned ZMK 512, 328 worth of assets, manly bcycles, sprayers and ox-ploughs. The value of assets used n agrcultural producton such as mplements and anmal stocks was ZMK 3, 210, Economc actvtes The man ncome generatng actvtes that the sorghum farmers n the sample where nvolved n are agrcultural producton and off-farm such as wage or salary employment and ownershp of busnesses earnng an average of ZMK 3,359,669 per household n a year. In terms of contrbuton to total household ncome however, more than half of the household s ncome came from agrcultural producton wth feld crop producton contrbutng the most (fgure 3). 39

52 3.8% 6.4% 7% 49% 13% 21% Cash remttances receved frut and vegetable producton busness actvtes wage/salary employment lvestock actvtes feld crop producton Fgure 3. Contrbuton of ncome generatng actvtes to total household ncome Gven the mportance of agrcultural and feld crop producton n partcular, mprovng effcency and productvty n crop producton can result n a large ncrease n total household ncome. Hgh relance on feld crop producton whch s mostly ran fed could make the sorghum farmers susceptble to crop falure as a result of extreme weather. Average farm szes were 2.99 hectares, much hgher for medum scale farmers wth an average of 7.23 hectares compared to 2.54 hectares for the small scale farmers. Each farmer was growng approxmately 3 crops on hs/her pece of land. In terms of planted area, maze remans the most mportant crop followed by sorghum (Fgure 4). 40

53 11% 7% 6.4% 49% 26% Maze ha planted groundnuts ha planted other Sorghum ha planted cassava ha planted Fgure 4. Share of total area used for feld crops by crop Access to nformaton and nfrastructure Access to nformaton among the sorghum farmers was qute hgh wth more than half havng receved producton advce and or nformaton on commodty prces (Table 5). On the other hand, access to agrcultural credt was very low such that only 7 percent had receved loans. Interestngly, none of the households that had receved the loans reported to have used them for sorghum producton. The loans were used to support maze, seed cotton and tobacco producton. 41

54 Table 5. Access to nformaton and servces Varable Mean Receved producton advce 59% Receved agrcultural credt 7% Value of loan n ZMK 30, Receved prce nformaton 65% Dstance to vehcular road 7.42 Used fertlzer 19% Pad for fertlzer 99% Receved fertlzer on tme 80% Access to fertlzer was equally low wth most of the farmers who had fertlzer havng purchased t through the Food and Input Support Programme (FISP) or commercal sellers. Recept of fertlzer was tmely for most of the farmers who had fertlzer Sorghum producton The scale of sorghum producton and productvty n the sample was qute low wth lower or, n some cases, hgher than recommended levels of nput use. Table 6 presents a summary of nput use, management practces and outputs for sorghum n the sample. Area used for sorghum producton was only about half a hectare on average. The man tllage methods used n the sorghum felds were conventonal hand hoe cultvaton by household members and plowng usng anmal draught power. Only a few of the households tlled the sorghum felds before the onset of the rany season. The seed rate computed as quantty of seed planted per hectare was more than the recommended 10 kgs per hectare for food and wthn the recommended range of 15 to 20 kgs per hectare for forage (Mnstry of Agrculture and Cooperatves et al., undated). Unfortunately t s dffcult to determne wth certanty f seed was used excessvely because the survey dd 42

55 not collect any nformaton on the ntended use of the sorghum planted. It s hghly lkely though, that the seed rate was n excess gven that most of the sorghum n Zamba s produced for food gran. Most of the households used local seed varetes wth only a few usng hybrd seed. Ths could, perhaps, contrbute to the low observed productvty of land of less than a ton per hectare. Local varetes tend to be lower yeldng and less responsve to good management practces. Seed productvty was equally low at only 35 kgs of sorghum from a klogram of seed planted. In order to determne tmelness of plantng for sorghum, the varety whch determnes tme requred maturng and the prevalng ranfall condtons have to be taken nto consderaton. For ths sample, a lttle less than half of the households planted ther sorghum on tme. Tmng of weedng was also good for about half of the sample who planted local varetes before December and hybrds between the frst week of December and md January. Smlarly, the number of complete weedngs, an average of about one and a half complete weedngs, was wthn recommended. Despte ts mportance n nfluencng sorghum yelds, only one farmer used fertlzer n sorghum even f a lot more had receved fertlzer. Low fertlzer use s lkely to further reduce varatons n sorghum yelds among the households n the sample. 43

56 Table 6. Summary of nputs, output and management practces n sorghum felds Varable Value Area planted n ha 0.47 Seed planted n kgs 7.36 Seed rate n kgs per ha Sorghum harvested n kgs Value of sorghum harvest n ZMK 12, Sorghum yeld n kgs per hectare Households usng conventonal hand hoe tllage 39% Households that prepared felds by plowng 39% Households that prepared felds by rdgng 14% Households that prepared felds by bundng 3% Households that prepared felds by moundng 1% Households usng anmals to power tllage 39% Households usng mechancal power for tllage 1% Households usng famly labor to power tllage 56% Households usng hred labor to power tllage 5% Households that tlled before the rans 32% Household usng hybrd seed 9% Households usng recycled hybrd seed 3% Households usng local seed 84% Households usng open pollnated seed varetes 1% Households whch planted on tme 47% Households whch weeded on tme 50% Households that practced crop rotaton n current sorghum feld 77% Number of complete weedngs Comparson of characterstcs of sorghum farmers and non-sorghum farmers A comparson of varous household and farm characterstcs of the sorghum and non sorghum farmers was done to test for systematc dfferences n the two sub groups. The results of the mean comparson t-tests ndcated that the sorghum farmers were dfferent from the non-sorghum farmers on several aspects relatng to the household and the farm ( 44

57 Table 7). Statstcally sgnfcant dfferences were observed n household soco-economc characterstcs, farm characterstcs, feld management practces, and access to nformaton and credt servces. The sorghum growng households were larger and had a hgher number of chldren, elderly and ll members than the non-sorghum growng households. Households wth larger household szes tend to have more access to famly labor. Household sze has been lnked to avalablty of farm labor such that larger households would have more access farm labor (Benjamn, 1992). Wth more famly labor, households could be able to ncrease ther cultvated land szes and produce more. However, access to large amounts of famly labor may result n under apprecaton of the value of labor n producton such that large households may end up over utlzng labor per unt of other nputs. The presence of large numbers of dependents n the sorghum growng households could deplete the amount of famly labor that s actually avalable for use n agrcultural producton. A comparson of the age of the household heads between the two sub groups reveals a statstcally sgnfcant dfference. The household heads are older among the sorghum farmers by about 2 years. Despte the dfference n the average ages, the heads of both groups fall wthn the same age range. Educaton levels n the sample were generally low among the households as evdenced by the low number of years n school of the household heads and the most educated prme aged household member. The average educaton level of the household heads n the sample of 5.61 years ndcates a lack of 45

58 completon of prmary educaton. The average educaton level of the most educated household members (7.61) ndcates completon of prmary educaton but stll less than the number of years for basc educaton n Zamba. Educaton levels are sgnfcantly lower for sorghum farmng households than for the others. Sgnfcant dfferences were also observed n average total land holdngs between the sub groups wth sorghum farmers havng lower land holdngs of 2.99 hectares compared to 3.75 hectares among the non sorghum farmers. The tenure status of the land holdngs for most almost all the households n the sample (94 percent) was owned land wthout ttle, a characterstc that s shared by most rural households n Zamba resdng on tradtonal land. Ownershp of land wth ttle provdes securty for the household whch has been reported to encourage nvestment n productvty enhancng technologes resultng n hgher effcency (Gorton and Davdova, 2004; Karuk, 2008). Use of borrowed land was sgnfcantly lower among the sorghum farmers. No dfferences were observed n cultvated area and area under feld crop producton. However, gross value of feld crop producton was lower among the sorghum farmers. A rato of gross value of feld crop producton to planted area was computed n an attempt to measure productvty of land n feld crop producton. A comparson of the mean of the rato among the sub groups revealed that sorghum farmers were sgnfcantly less productve than the non sorghum farmers by ZMK 624, 000 per hectare. Ths dfference n productvty of land warrants further exploraton as the two sub groups have shown sgnfcant dfferences n varous attrbutes, other than the decson to grow sorghum or 46

59 not, that may affect productvty of nputs and effcency n general. Several crop and feld management practces also dffered among the two sub groups. For nstance, more sorghum growng households ploughed ther felds when preparng ther land whle less used anmal draught power compared to ther counterparts. Anmal draught power has the potental to mprove productvty and effcency of nputs n producton and dffcultes n access among smallholder farmers has been cted as one of the man causes of low agrcultural productvty n Zamba (Smth, 2008; Dennger and Olnto, 2000). Use of conservaton tllage practces also vared wth sgnfcantly more sorghum growng households usng zero tllage or plantng basns and sgnfcantly more non sorghum farmers usng contour bundng. More sorghum farmers prepared ther felds before the onset of the rany season. Ths could result n more tmely plantng as tllng before the rans allows the farmer more tme to prepare for and perform other feld management actvtes. Access to agrcultural producton advce and prce nformaton was hgh wth at least half of the sample havng receved producton advce and 76 percent havng access to nformaton on commodty prces. On the contrary, use of agrcultural producton credt was low, especally among the sorghum farmers. Access to vehcular transport was hgher among the sorghum farmers. 47

60 Table 7. Comparson of attrbutes between sorghum and non sorghum farmers characterstc Overall dd not grow sorghum grew sorghum t-test HHs resdng n low or lower ranfall area 46% 46% 46% Age of household head (years) *** Male headed household 77% 78% 77% Level of educaton hh head n years *** Maxmum educaton level of prme-aged *** Sze of household n adult equvalents ** Number of dependents n adult equvalents * Households usng conventonal hand hoe tllage 43% 43% 47% Households prepared land by plowng 30% 29% 41% *** Households prepared land by rdgng 30% 31% 27% Household prepared land by bundng 15% 15% 5% *** Households usng plantng basns 1% 1% 3% ** Households usng zero tllage 3% 2% 5% ** Households used slash and burn to prepare land 7% 7% 4% *** Households usng hred labor for tllage 14% 15% 7% *** Used household famly labor for tllage 64% 64% 59% ** Households usng anmals to power tllage 32% 32% 11% *** Households usng mechancal power for tllage 2% 2% 1% Household tlled before rany season 41% 41% 47% ** Households that pad for seed 53% 54% 44% *** Total land owned (ha) *** Land cultvated n ha Owned any farmland wth ttle deeds 4% 4% 2% Owned any farmland wthout ttle deeds 94% 94% 97% *** Households rented-n any farmland 2% 2% 1% Households borrowed any farmland 3% 3% 1% *** Households usng fertlzer 32% 33% 19% *** Income from lvestock actvtes n ZMK' Gross value of feld crop producton n ZMK'000 2,066 2,087 1,635 *** Area cultvated wth feld crops n ha Gross value of feld crop per ha n ZMK 000 1,627 1,659 1,035 *** Off-farm ncome n ZMK'000 2, , , *** Value of productve assets owned n ZMK'000 3,885 3,917 3,210 Contnued 48

61 Table 7. Contnued characterstc Overall dd not grow sorghum grew sorghum Value of assets owned n ZMK'000 1,340 1, *** Receved agrcultural producton advce 55% 55% 59% Receved a loan for agrc producton 10% 10% 0.07% ** Value of agrc loan n ZMK' Access to commodty prce nformaton 76% 76% 65% *** Dstance to vehcular transport (km) ** *,**,*** denote statstcal sgnfcant at 10 percent, 5 percent and 1 percent respectvely. t-test 4.4 DEA and OLS model results Ths secton presents the emprcal results of the computaton of techncal effcency and ts determnants n sorghum producton and the contrbuton of sorghum producton to effcency Techncal effcency n sorghum producton Techncal effcency n sorghum producton was computed usng a VRS DEA model n GAMS. The CRS model effcency scores were also computed to compare n terms of average effcency and dstrbuton of the households n the sample (Table 12 n Appendx secton). The output varable was sorghum producton defned as quantty of sorghum harvested n klograms. The nputs for the DEA model were land measured n hectares under sorghum producton and quantty of sorghum seed planted n klograms. The results of the optmzaton ndcate that techncal effcency n sorghum producton for ths sample of smallholder farmers was low wth an average of 34 percent. Ths 49

62 represents an neffcency of about 66 percent. In terms of sorghum producton, ths mples that households are producng 66 percent less of potental output gven ther prevalng level of technology and nput use. Alternatvely, the farmers could stll produce ther current outputs of sorghum wth fewer nputs f they were more effcent. Table 8 and Fgure 5 present the dstrbuton of households n the sample. Of the 317 households analyzed, 15 households (4.7 percent) had an effcency score of one ndcatng full effcency. About three quarters of the households (78.55 percent) were 50 percent or less effcent. Such low effcences n producton ndcate potental for mprovements n sorghum producton gven the current levels of technology among the farmers. Table 8. Dstrbuton of techncal effcency n sorghum producton n the sample Effcency category Number of households proporton of sample > > > > > > > > >

63 Fgure 5. Dstrbuton of sorghum producton techncal effcency scores n the sample Determnants of techncal effcency Ths secton attempts to explan the determnants of techncal effcency n sorghum producton n the sample. The determnants of techncal effcency were dentfed through a second stage regresson of the DEA effcency scores on household and farm characterstcs. The model to explan techncal effcency n the sample was statstcally 51

64 sgnfcant at one percent. Table 9 summarzes the OLS regresson results alternatve specfcatons of the model. Model (1) s the man model for ths study. Techncal effcency n the sample was affected by household sze, number of dependents, use of anmal draught power, gross value of feld crop producton, value of assets, ncome from lvestock actvtes, access to credt, seed rate and whether a household s located n a low ranfall area or not. Household sze s negatvely assocated wth techncal effcency such that larger households are less effcent. Household sze tends to be lnked to avalablty of famly labor n developng countres wth poor or non-exstng labor markets. As such, as famly labor ncreases, productvty per unt of labor decreases. Lnked to household sze s the number of dependents n a household whch has a sgnfcant postve effect on effcency n ths sample. The presence of dependents n the household reduces the amount of famly labor avalable forcng households to make better use of the lttle labor avalable, producng more from each of the remanng unts of famly labor n the household. In cases where the number of dependents ncreases to the extent of causng labor shortages for farm producton, households may resort to hrng labor. The cost of hrng labor may act as an ncentve for farmers to be more effcent. Other household characterstcs lke age of the household head, educaton level and gender of the household head were not mportant for ths sample despte beng mportant for other crops and samples n other studes. Educaton, n partcular, s not mportant despte havng the expected sgn. The nfluence of educaton on effcency s usually attrbuted to the ablty of more educated farmers to understand and adopt producton practces that may enhance productvty. In 52

65 ths sample, however, educaton levels were very low wth only a few havng fnshed prmary educaton. Table 9. Determnants of techncal effcency n sorghum producton Varables Coeffcent Coeffcent Coeffcent Model (1) (2) (3) Malehead Hsze ** ** Hedu Hage Prodadvce Adptll ** ** * Hlabortll Offncml Lfcrop ** ** Vf_gvprodml Assetml * * ** Dagcredt *** *** *** Lvncml *** *** *** Ltotland *** *** ** Dependents ** ** * Srate *** *** *** Srate *** *** *** Srate *** *** *** Lowran *** *** *** Improvseed Constant ** ** *** Observatons R-squared Dependent varable lvrsscore lvrsscore lcrsscore *,**,*** denote statstcal sgnfcant at 10 percent, 5 percent and 1 percent respectvely. 53

66 Use of mechancally or anmal powered mplements n land preparaton allows for better plowng and preparaton of seed beds for crop producton. In ths sample of sorghum farmers however, tllage of sorghum felds usng anmal draught power had a negatve and sgnfcant effect on techncal effcency n sorghum producton. Households that ploughed ther sorghum felds wth anmal draught power were less effcent than ther counterparts who used famly labor hand hoeng. Ths result s hghly unusual and s not consstent wth the lterature or expectatons. Possble explanatons could be that use of ploughs may result n a plough depth that s too deep (greater than fve centmeters) for proper germnaton of seed, or bg clods of sol that would make the seed bed not fne enough for germnaton compared wth usng a hand hoe. Use of hybrd seed varetes s also productvty enhancng and has been found to be postvely related to techncal effcency n producton n crops lke maze (see, for example, Chrwa, 2007). However use of hybrd seed was nsgnfcant n ths sample. Ths could be because very few households used hybrd seed. The mportance of feld crop producton to the household ndcated by the gross value of feld crops produced was statstcally sgnfcant n explanng effcency n sorghum producton. As the scale of producton of feld crops ncreases, so does the mportance of sorghum producton provdng an ncentve to ncrease effcency of nput use. Also, f part of the ncome obtaned from sale of feld crops s renvested nto mproved nputs and producton technques for the crops, effcency s mproved. However, changes n scale of producton n other farm enterprses lke hortcultural and lvestock producton are not mportant for effcency n sorghum producton. 54

67 The rate at whch seed s appled, measured n klograms per hectare, has a sgnfcant effect on techncal effcency n sorghum producton. Intally the effect of ncreasng the seed rate reduces effcency at a decreasng rate untl ts effect reaches zero then starts to ncrease effcency. Further ncreases n the seed rate eventually negatvely affect effcency ndcatng dmnshng returns to ncreases n seed rate. Access to agrcultural credt sgnfcantly mproved techncal effcency n sorghum producton such that households that receved agrcultural loans were more effcent than smlar households who dd not. Access to credt may ncrease ablty of farmers to fnance the acquston of usually expensve mproved nputs lke hybrd seed and practces that may requre more nvestment than tradton producton technques. Whle none of the loans receved by the farmers were reported to have been for sorghum producton, the presence of the loan n the household could have helped to smooth the ncome needs of the households n general resultng n more fnancal resources avalable for all the actvtes the household may be nvolved n. Another actvty that may mprove access to fnance n the household s off farm ncome, whch n ths sample was not statstcally sgnfcant. The value of a household s assets may be an ndcaton of the wealth status of the household. In ths group of smallholder farmers, the value of assets owned had a postve effect on techncal effcency. Effcency n sorghum producton ncreases the wealther a household becomes. Assets also act a cushon to shocks when sold off n tmes of need. 55

68 The ncome from the sale of assets can be used to mprove access to productvty enhancng nputs and producton practces. Farm sze had a sgnfcant nverse relatonshp wth effcency ndcatng that effcency n sorghum producton decreases wth ncreases n sze of land under the farmer s control. Ths s consstent wth other studes that have found that small farms are more effcent than large farms (Reardon et. al 1997; Fleteschner and Zepeda, 2002) but contrary to others who found large farms to be more effcent (Carter, 1984; Ros and Shvely, 2005). The nverse relatonshp n ths sample may be explaned by farmers wth small farms ntensfyng producton to get the most out of the land gven ther lmted land parcels. Geographcal locaton of a household determnes the level of clmatc varables such as ranfall and temperature that households are subjected to. The nteracton of these varables has a bearng on how productve households and nputs are n the producton of certan crops. The low and lower ranfall agro-ecologcal zones represent the drer and hotter parts of the country. As such, productvty of nputs n growng crops s expected to be lower for households n low ranfall areas. Farms located n low or lower ranfall areas were sgnfcantly less effcent than those n hgher ranfall areas. Ths s expected as sorghum producton responds favorably to avalablty of mosture even though t s drought tolerant. The other 2 models presented n Table 9 demonstrate the effect of usng dfferent model specfcatons on explanng techncal effcency n sorghum producton. Model (2) presents the results of a regresson of the natural logarthm of the VRS DEA scores on 56

69 only the explanatory varables that were ntally sgnfcant at 10 percent. The statstcal sgnfcance and coeffcents of the varables n model (2) do not dffer much from those n model (1) ndcatng no effect of excludng the nsgnfcant varables on statstcal sgnfcance and coeffcents of the remanng varables. Model (3) presents a regresson of the natural log of the CRS DEA scores on the varables n model (1) to compare how the determnants of techncal effcency varable by DEA model used. In terms of statstcal sgnfcance, household sze and the scale of feld crop producton represented by the gross value of feld crop producton are no longer mportant n explanng techncal effcency n feld crop producton. The drecton of nfluence of each of the varables on techncal effcency remans the same although the magntude dffers slghtly n some cases Techncal Effcency n feld crop producton Techncal effcency n feld crop producton was computed usng CRS DEA model n GAMS due to nsuffcent memory for the VRS model. The average techncal effcency n feld crop for the farmers n the sample was 35 percent. The 65 percent neffcency presents opportuntes for mprovng productvty n the sample by ether usng lower quanttes of nputs to produce current levels of output or produce more output from current levels of nputs. Most of the households (79 percent) had effcency scores equal to or less than 50 percent. The mnmum effcency was about 0.3 percent whle 222 households (3.23 percent) were fully effcent. Table 10 and Fgure 6 present the dstrbuton of techncal effcency n the sample. 57

70 Table 10. Dstrbuton of techncal effcency scores n feld crop producton Effcency category Number of households proporton of sample > , > , > , > > > > > > Average techncal effcency n feld crop producton among the sorghum farmers was 41 percent; sgnfcantly hgher than the average of the non-sorghum farmers of 34 percent (p-value 0.000). 58

71 Fgure 6. Dstrbuton of feld crop techncal effcency scores n the sample Determnants of effcency and contrbuton of Sorghum producton The determnants of techncal effcency n feld crop producton n the sample were dentfed by an OLS regresson of the natural logarthm of the DEA effcency scores on several farm and household characterstcs. The model explanng varaton n the natural logarthm of effcency was sgnfcant at one percent. 59