Crop diversification and technical efficiency in food crop production :A study of peasant farmers in Nigeria

Crop diversification and technicalefficiency in food crop production

A study of peasant farmers in NigeriaKolawole Ogundari

Department of Food Economics and Consumption Studies,Christian-Albrechts-Universitat zu Kiel, Kiel, Germany

AbstractPurpose – The purpose of this paper is to identify the trends in crop diversification (CD) whileexamining its impact on the technical efficiency of peasant farmers in Nigeria.

Design/methodology/approach – The paper employs the Herfindahl and Ogive indices tocompute the diversification indices and the stochastic frontier production model (SFPM) to estimatethe technical efficiency (TE) level of the farms using unbalanced panel data covering three farmingseasons (2006/2007 to 2008/2009).

Findings – The results of both the Herfindahl and Ogive indices showed that cropping patternincreased significantly with the intensification of crop diversification in the study across the threeseasons. The result of the SFPM shows evidence of decreasing returns-to-scale and technical progressin the food crop production in the region. Education, extension, and CD are identified as efficiencyincreasing policy variables while an average TE level of about 81 percent was obtained from theanalysis.

Originality/value – To the best of the author’s knowledge, this the very first study that employspanel data to analyze technical efficiency of farms in Nigeria.

Keywords Food crops, Crop diversification, Peasant farmers, Technical efficiency, Nigeria, Agriculture

Paper type Research paper

1. IntroductionThere is widespread agreement that agriculture is central to economic growth incountries of sub-Saharan African (Delgado, 1995) including Nigeria. For instance,Nigeria’s agricultural sector is particularly important in terms of employmentgeneration, contribution to gross domestic product (GDP), and export revenue earnings(Manyong et al., 2005). Besides, Nigerian agriculture is overwhelmingly dominated bysmallholder-subsistence farm economy responsible for over 90 per cent of the country’sagricultural output with rudimentary farm implements, low capitalization, and lowyield per hectare (Olayemi, 1998).

In terms of growth, the agricultural sector of Nigeria’s economy has achievedsignificant success in recent times. As at 2009, it attained the 7 per cent growth targetedin the National Economic Empowerment and Development Strategy (NEEDS) – amacro-economic policy framework currently implemented in the country.Unfortunately, the 2.7 per cent growth rate in the food sub-sector currently observed

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JEL classifications – C81, Q18, R15The author gratefully acknowledges the financial support of the German Academic

Exchange Service (DAAD) towards his PhD program at the University of Gottingen from whichthis article was produced.

Efficiency in foodcrop production

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International Journal of SocialEconomics

Vol. 40 No. 3, 2013pp. 267-288

q Emerald Group Publishing Limited0306-8293

DOI 10.1108/03068291311291536

is far too low for a country whose population is growing at the rate of 3.5 per cent (CBN,2006). This low growth rate in the food sub-sector is largely responsible for theworsening food insecurity in some parts of the country as domestic food productioncannot keep pace with the rapid growing population of over 150 million people.

The most fundamental constraint to agricultural growth in Nigeria, despite theenormous agricultural potential in the country, is the peasant nature of the productionsystem, poor response to technology adoption, fragmentation of land, and loss/failure inthe cropping activities that in turns cause variability in the production (Manyong et al.,2005). The later observation suggests why majority of the smallholder farmers in thecountry embrace a cropping pattern that is characterized by growing a wide variety ofcrop mix under multiple cropping systems in space adapted to various agro-ecologicalzones known as crop diversification (Ajibefun, 2006)[1].

Crop diversification is regarded as a phenomenon which has attracted considerableinterest among peasant farmers around the globe because of the following inherentcharacteristics:

. as a potential risk management tool against uncertainty;

. income and employment generation opportunity;

. ability to reduce diseases, weed and insect build up; and

. possibility to increase soil fertility and among others (Singh, 2000).

Besides, policy relevance of crop diversification with likely influence on the growth andsustainability of agricultural production has been stressed in the developingagriculture further by Ellis (1993). For example, Bamji (2000) shows that diversificationwithin food crops and between food crops and livestock helps nutrition security,particularly for small and marginal farmers.

Efficiency in food crop production is a topical issue in food security programs ofmany developing countries. The crucial policy role of efficiency in increasingagricultural output has been widely recognized by researchers and policy makersaround the globe (Bravo-Ureta et al., 2007). According to Ajibefun (2006), themeasurement of efficiency is more important, given the fact that efficiency of farmers isdirectly related to overall productivity of the agricultural sector.

A search of the literature however, suggests that the impact of crop diversification onthe production efficiency is quite mixed. While Guvele (2001) and van den Berg et al.(2007) revealed that crop diversification reduces income variability in Sudan andsustains a reasonable income level for Chinese farmers, respectively, andKar et al. (2004)conclude that crop diversification increases agricultural production in Bangladesh.Also, Lleweln and Williams (1996) and Haji (2007) reveal that diversificationsignificantly decreases efficiency of farmers in Indonesia and Ethiopia, respectively,while Coelli and Fleming (2004) and Rahman (2009) report that diversification improvesefficiency of farmers in Papua New Guinea and Bangladesh, respectively. The mixedfindings from these studies indicate that the effect of crop diversification on agriculturalproductivity might vary from region to region or case to case.

The findings from the empirical studies highlighted above appear mixed withregard to the impact of crop diversification on production efficiency in the developingagriculture. And, considering the fact that studies have shown that crop diversificationis a recognized phenomenon of interest among the dominated peasant farmers in the

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Nigerian agricultural production systems (Ajibefun, 2006; Fawole and Oladele, 2005), itis important to raise the following research questions:

RQ1. How has crop diversification developed in Nigeria?

RQ2. What is the relationship between crop diversification and technical efficiencyof farmers in the country?

RQ3. Is crop diversification capable of increasing food production/food security tomeet the rising demand in the country?

Answers to these questions makes analysis of this nature worthwhile, as the resultswill shed light on whether crop diversification is a desired strategy for promotingagricultural development and perhaps food security in the country.

The rest of this paper is divided into the following sections. Section 2 outlines thereview of efficiency and diversification literatures. Section 3 discusses themethodology. Section 4 presents the empirical results while Section 5 providesconclusions and policy implications from the paper.

2. A review of efficiency and diversification literature2.1 Frontier efficiencyThe standard production economic theory assumes that all producers are efficientwhilstimplicit assumption in frontier efficiency analysis suggests that some producers areinefficient (Hailu et al., 2005). Given this, the crucial role of efficiency in increasingagricultural output has been widely recognized by researchers and policy makersaround the globe. Broadly, two quantitative approaches are developed for measurementof production efficiency: parametric (deterministic and stochastic frontier models) andnon-parametric (data envelopment analysis (DEA)) approaches. The advantages andlimitations including model specification issues regarding these approaches areextensively discussed in Kumbhakar and Lovell (2000) and Coelli et al. (2005).Nonetheless, since DEA assume deviation from the frontier to be entirely attributed toinefficiency effects, the present study employs the stochastic frontier models because ofits inherent stochasticity which assumes deviation from the frontier to the existence ofrandom effects such as climatic conditions and inefficiency effects[2].

The stochastic frontier analysis (SFA) was developed independently by Aigner et al.(1977) and Meeusen and van den Broeck (1977). It consists of two-part error terms: aninefficiency component (ui) and a purely random component (vi). According to Greene(2008), SFA is simply an extension of the familiar regression model on the theoreticalpremise that a production function represents an ideal, maximum output attainable,given a set of input bundles. SFA framework could be extended to the traditionalprimal representation of production technology (such as production or distancefunctions), or dual representation of production technology (such as profit, revenue orcost functions).

2.2 Crop diversificationThe concept of diversification conveys different meaning to different people at differentlevels. In research related to marketing for example, diversification implies ameasure ofmarket concentration. Within the agricultural enterprise, diversification may be viewedas a process with three stages (Chaplin, 2000). The first stage is considered as the


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cropping level which involves a shift away from monoculture. At the second stage, thefarms havemore than one enterprise and producemany crops that they could potentiallysell at different times of the year. The final stage is understood as mixed farming wherethere is a shift of resources from one crop (or livestock) to a larger mix of crops(or livestock) or mix of crop and livestock. The second stage describes definition of cropdiversification on which this paper is really based.

Mengxiao (2000) described crop diversification as the complex diversificationpatterns of agricultural cropping systems found under the conditions of farmingenvironments. According to Johston et al. (1995), crop diversification has threedimensional benefits which the author described as economic, social, and agronomic.The economic benefits include: seasonal stabilization of farm income tomeet other basicneeds of life like education of the children; coverage of their subsistence need, mostespecially meeting family food security; and a reduction of risk of the overall farmreturns by selecting a mixture of activities whose net returns have a low or negativecorrelation while lessening price fluctuations. Social benefit include seasonalemployment for farm workers while the agronomic benefits include: conservingprecious soil and water resources, reduced diseases, weed and insect build up, reducederosion, increased soil fertility, and increased yields (Caviglia-Harris and Sills, 2005;Gunasena, 2000; Ali and Beyeler 2002)[3].

In a related development, Paul and Nehring (2005) observed that diversification is asignificant factor explainingdifferences in the level andvariability of farm incomebetweenhigher and lower performing small farms. However, several other micro-level studiessupport the above proposition (von Braun, 1995; Ramesh, 1996; Ryan and Spencer, 2001).

However,manydeveloping countries have incorporated a cropdiversification strategyin several development programs (Gunasena, 2000). A significant example of this is thewell documented Asia experience in the successful use of diversification strategy in thecommercialization of agriculture in the 1990s (Hoque, 2000; Mariyono, 2007).

2.2.1 Economic measures of crop diversification. There are different measures ofeconomic diversity indexwith each having strength and weakness in the literature. Someof these indices include; Herfindahl index, Ogive index, Simpson index, Entropy Index,Modified Entropy Index, Index of Maximum Proportion, and Composite Entropy amongothers Index. But in the present study, we employ Herfindahl and Ogive indices becausethe two arewidelyused inmeasuring cropdiversificationor specialization in the economicliterature which is a genuine justification through which our results could be comparewith other findings. Besides, the indices are easy to compute.

2.2.2 Herfindahl index. The Herfindahl index ðHDÞ is the sum of the squaresof the acreage/revenue proportion of each crop in total cropped area/revenue. Theindex has widely been used in marketing and corporate firm studies as a measure ofmarket concentration (Rhoades, 1995; Ali and Byerlee, 2002; Oluwadare et al., 2009).Recent application of this index to capture crop diversification or degree ofspecialization in agricultural production includes (Rahman, 2009; Brummer, 2001;Brummer et al., 2006).

A detailed description of the Herfindahl index as used in the present study isdescribed below:

HD ¼XJ

j¼1

YjPJj¼1Yj

!2

0 # HD # 1 ð1Þ

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where Yj represents the area/revenue share occupied by the jth crop in total area/totalrevenue Y. J is the total number of crops, that is, when maximum diversificationoccurs. The index ranges from zero, reflecting complete diversification(i.e. an infinite number of crops in equal proportion), to one, reflecting completespecialization (i.e. just one crop). It can be shown that this index attains a minimumvalue equal to 1/J.

2.2.3 Ogive index. Application of the Ogive index to measure firm/farm leveldiversification includes; St. Louis (1980), Coelli and Fleming (2004) and Mekhora andFleming (2004). A detailed description of this index as used in the present study isdescribed below:

Ogivei ¼XNJ

j

ðYj 2 1=NJ Þ21=NJ

! "ð2Þ

where NJ represents the number of the jth crop activities cultivated by the ith farmer,1=NJ denotes a measure of precision which captures perfect diversification of theactivities on the farm. Y represents the area/revenue share occupied by the jthactivities. The economic interpretation is that as Ogivei !1, it implies perfectspecialization.

3. Methodology3.1 The data and study areaThe data used in this study came from a farm households’ survey that was carried out inSouthwestern Nigeria covering 2006/2007, 2007/2008 and 2008/2009 farming seasons.The region is made up of six states (Ekiti, Ogun, Ondo, Osun, Oyo and Lagos). Of allthese states, Lagos state is regarded as the financial capital of the country known forcommerce rather than agriculture. Based on this, Lagos is not included in the surveywhile Ogun, Ondo, Osun, Oyon and Ekiti states were adequately represented in thesurvey.

The food crops farmers were randomly sample with help of the extension personnelof the state’s agricultural development program (ADP) via a well-structuredquestionnaire. 282, 260, and 304 farms were sampled in 2006/2007, 2007/2008, and2008/2009 farming seasons, respectively. At the state level, a total number of 181, 206,173, 141, and 145 farms were sampled in Ekiti, Ondo, Oyo, Osun, and Ogun states,respectively. In all, we have 846 observations consisting of unbalanced panel datacovering three farming seasons in the region[4].

The data for the analysis consist of information on the value of crops produced inNaira which is the Nigeria currency (i.e. cassava, yam, maize, cocoyam and sweetpotatoes as extracted from the survey) and input used in producing the crops.Specifically, we collected information on inputs such as farm size (hectare), labourutilization which includes family and hired labour measured in mandays with mandayof an adult male and female equal 1 and 0.75, respectively, while that of a child equals 0.5.Detail information on fertilizer (kg), pesticides (litre) and planting materials usedwere also collected. Furthermore, we collected information on the socio-economiccharacteristics of the farmers which include age, gender, family size, year of formaleducation, number of extension visit, accessibility to credit, and non-farmparticipation. Thus, Table AI of the Appendix contains the summary statistics ofthe information collected from the survey and subsequently used in the analysis.


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3.2 Analytical frameworkThe basic stochastic frontier production function is specified as:

yit ¼ f ðxit ;bÞ expðVit 2 UitÞ ð3Þ

where yit denotes the value of the production of the ith farm (i ¼ 1,. . . N) at t periodwith t ¼ 2006=2007; 2007=2008; 2008=2009 farming seasons; xit is a (1xk) vector of theassociated inputs of the ith farm at t period; b is a (kx1) vector of unknown parametersto be estimated; vit is a random error term (statistical noise) distributed symmetricallyand uit[5] is the asymmetric error term assumed to be independently and identicallydistributed (uit . 1) that captures technical inefficiency and is independent of vit.

In line with equation (3), we defined technical efficiency of a peasant farmer as theratio of the mean output, given the values of the inputs xit and its technical inefficiencyeffect (uit), to the corresponding mean output if there was no technical inefficiency inthe production (uit ¼ 0). This however can be expressed as:

TEit ¼EðYitjuit;XktÞ

EðYijuit ¼ 0;XktÞ¼ expð2y itÞ ð4Þ

where E denotes the expectation operator while TEit takes a value on the interval (0, 1).TEit ¼ 1 indicates a fully efficient farm and 0 implies a fully inefficient farm.

Generally, the objective of the stochastic production frontier model is not only toserve as a benchmark against which technical efficiency of producers are estimated,but to also explore how exogenous variables or policy variables exert influence onproducer performance (Kumbhakar and Lovell, 2000). To explore this in a single stageapproach, Kumbhakar et al. (1991) parameterized the mean of the pre-truncateddistribution of inefficiency error term ui while Caudill and Ford (1993) parameterizedthe variance of the pre-truncated distribution of inefficiency error term ui. The laterapproach is employed in the present study. A detailed description of these approachesis well documented in Kumbhakar and Lovell (2000).

3.3 Empirical modelThe translog production frontier function which is flexible and most frequently used inempirical work is assumed for this study and expressed as:

lnyit¼

z0 þfHLDHlitþffDfitþfpDpitþX6

j¼1

bjlnXjitþtTAðtÞ

þ 12

X6

j¼1

X6

k¼1

bjlnXjit:lnXkitþ1

2tTTA

2ðtÞ

þX6

j¼1

kjT lnXjit ·AðtÞþv1Dekitiþv2Dondo

þv3Dosunþv4Doyoþ61D2008þ62D2009þpHIit

0

BBBBBBBBBBBBBBBB@

1

CCCCCCCCCCCCCCCCA

þvit2uit ð5Þ

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where In: natural logarithm; yit: total value of farm produce for the ith farmin the tth time period; X1: land; X2: hired labour which is equal toln½MaxðHlabour; 12 DHlÞ&; X3: family labour; X4: fertilizer which is equal toln½Maxð fertilizer; 12 Df Þ&; X5: pesticides which is equal to ln½Maxð pesticide; 12 DpÞ&;X6: cost of planting materials; A(t): time dummies for each farming season ofthe sample. This dummy reflects a linear trend with 2006/2007 ¼ 0, 2007/2008 ¼ 1,and 2008/2009 ¼ 2 is included in the model to account for technological change. DHl isa dummy which has a value of one if number of hired labour is positive and a value ofzero if otherwise, Df is a dummy which has a value of 1 if fertilizer usage is positive and0 if otherwise, and Dp is dummy with a value of 1 if pesticide usage is positive and 0 ifotherwise.

In an attempt to minimize bias in the coefficient of some of the variablesin the equation (5), ln½MaxðHlabour; 12 DHlÞ&, ln½Maxð fertilizer; 12 Df Þ& andln½Maxð pesticide; 12 DpÞ& are included to account for zero usage of these variableinputs in the regressionwhileDHl,Df, andDp account for intercept change (Battese, 1997).

States dummies are also included in the production frontier to account for statespecific effect in the production frontier. This include: Dekiti, Dondo, Dosun, and Doyo,which are Ekiti, Ondo, Osun, and Oyo states, respectively, (Dogun is left out forestimation). Seasonal dummies were also included in the production frontier whichinclude; D2008 and D2009 for 2007/2008 and 2008/2009 seasons, respectively, (D2007 for2006/2007 is left out for estimation). Finally, the Herfindahl index of cropdiversification (HI) is included in the frontier regression to assess the impact ofdiversification on the technology frontier of the farmers.

In this study, we follow standard assumption on the stochastic error term that vitand uit are assumed to be uncorrelated. Also we assumed, vit is normally distributed asN ð0;s 2

vitÞ with s 2vt ¼ gðxjt;Dkt ; tiÞ while uit is assumed to be half-normally distributed

as N þð0;s 2uitÞ with s 2

ut ¼ qðZmt;Dpt ;aiÞ.A preliminary examination of the OLS residuals of the estimated

relationship between the variables included in equation (5) reveals the possibilityof heteroskedascity[6]. Based on this, the analysis allows a double heteroskedascityerror structure in the SFA. Heteroskedascity in both vit and uii are tested for andestimated in the paper. Thus, for the likely variables to correct for the presence ofheteroskedascity in the two-sided error term, we follow the suggestion of Hadri et al.(2003) and Loureiro (2009) that heteroskedascity in uii is likely to be affected bysize-related variables. In this regard, we include the farm size to capture differences inthe farm harvest while site specific location variables such as states dummies wereincluded to capture size and location differences across the region as:

s 2vt ¼ exp t0 þ t1lnXlandit þ t2Dekitit þ t3Dondot þ t4Dosunt þ t5Doyot

# $ð6Þ

wheres 2vt represents the variance of the two sided error (vit), lnXlandit is the logarithm for

land while the state dummies are as indicated by the subscripts. However, a model withhomoskedastic statistical variance from the restriction results that all the t parametersexcept the intercept are equal to zero is tested for.

Following traditional technical inefficiency effect model in the literature, thevariance of the inefficiency error is modeled as a function of the farmers’socio-economic variables, state and seasonal dummies as:


273

s 2ut ¼ exp

v0 þ a1Zaget þ a2Zgendert þ a3Zfamilyt þ a4Zeduct þ a5Zcredit

þa6Zextent þ a7Znonfarmt þ a8Z indext

þd1Dekitit þ d2Dondot þ d3Dosunt þ d4Doyot þ d5D2008

þd6D2009 þ G1Index:D2008 þ G2Index:D2009

0

BBBBB@

1

CCCCCAð7Þ

where s 2ut represents variance of one-sided error term (ui), Zage: age of the primary

decision makers in the study area, Zgender: gender dummy of the primary decisionmakers in the study area (male ¼ 1, 0 otherwise), Zfamily: family size (this representsonly the core family members), Zeduc: years of schooling the farmer, Zcredi: creditdummy (access ¼ 1, 0 otherwise), Zexten.: number of contacts with extension agents,Znonfarm,: nonfarm income dummy (participation ¼ 1, 0 otherwise), Zindex: cropdiversification index. The states and seasonal dummies are included as earlier definedand described. The interaction between seasonal dummies and the crop diversificationindex includes; IndexD2008 and IndexD2009. However, a model with homoskedasticinefficiency variance from the restriction results that all the parameters of equation (7)except the intercept v0 are equal to zero is tested for.

The estimation of the parameters of equations (5-7) is jointly carried out usingmaximum likelihood procedures in STATA10 for the analysis.

4. Results and discussion4.1 The development and trends in crop diversificationTable I presents the average score for the computed Hefindahl and Ogive indices ofcrop diversification based on cropped area and revenue from each crop portfolios forthe 2006/2007-2008/2009 farming seasons and also across the states. The surveyedpeasant farmers were observed to have portfolios consisting of a maximum of fiveactivities (or enterprises). These activities include; cassava, yam, maize, potatoes, andcocoyam. These crops are either solely cropped or mixed by the farmers.

The result of the correlation between these indices shows that the index in pair issignificant and positively correlated as indicated by p-value of 0.000. Subsequently, wefocus our discussion on the Harfindahl index of cropped area. Thus, it is clear from the

Herfindahl_area indexHerfindahl_total rev

index Ogive indexMean Max. Min. Mean Max. Min. Mean Max. Min.

2006/2007 0.498 1 0.224 0.568 1 0.230 1.362(2.6) 4(5) 0.121(1)2007/2008 0.457 1 0.210 0.515 1 0.216 1.192(3.2) 4(5) 0.052(1)2008/2009 0.425 1 0.213 0.434 1 0.208 1.032(3.3) 4(5) 0.063(1)Ekiti 0.494 1 0.225 0.561 1 0.294 1.361(2.8) 4(5) 0.325(1)Ogun 0.451 1 0.224 0.417 1 0.216 1.156(3.2) 4(5) 0.062(1)Ondo 0.456 1 0.184 0.541 1 0.235 1.172(2.9) 4(5) 0.102(1)Osun 0.440 1 0.191 0.479 1 0.208 1.104(3.2) 4(5) 0.052(1)Oyo 0.449 1 0.201 0.490 1 0.214 1.137(3.1) 4(5) 0.098(1)Pooled 0.459 1 0.210 0.504 1 0.208 1.191(3.0) 4(5) 0.052(1)

Note: Figure in parentheses represents average number of activities

Table I.Trends in cropdiversifcation by farmingseason and states

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table that the proportional measures of crop diversification reveal a shift towards morediversification cropping patterns among the peasant farmers in the study. This isinterpreted as evidence of intensification of crop diversification in the region[7]. Forexample, the computed average 0.498, 0.457, and 0.425 for 2006/2007, 2007/2008, and2008/2009 farming seasons, respectively, lend support to observation. Also, furthercalculation shows about 15 per cent downward trends in the computed Herfindahlindex from 2006/2007 to 2008/2009 farming seasons which was found to be significantat p-value of 0.0012[8]. The implication of this is that there is evidence that croppingpattern increased (by about 15 per cent) significantly with intensification of cropdiversification in the Southwestern Nigeria.

A further confirmation of this observation is the result of Cuzick’s non-parametrictrend test of the index condition on the seasons. The z-score of 25.87 with p-value0.000 shows that there is indeed strong evidence of downward trends in diversification(meaning increased crop diversity) in the region.

However, a second look at the dataset, we observed that out of the 62 farms thatwere repeatedly sampled throughout the three seasons, 43 farms (representing69 per cent) increased the number of portfolios of activities/enterprises on their farms,eight farms (13 per cent) maintain the number of activities/enterprises on their farmswhile 11 farms (18 per cent) decreased the number of activities/enterprises on theirfarms. This observation could be interpreted as a further indication of increaseintensification of crop diversification among the smallholder farmers in the region.

Summarizing the index by state shows that crop diversification is higher in Osunstate with an average index of 0.440. This is followed by 0.449, 0.451, 0.456 and 0.494,respectively, for Oyo, Ogun, Ondo and Ekiti states in that order.

The overall average Herfindahl index of 0.459 with standard deviation of 0.205 wasobtained. The distribution of this index is shown in Figure 1. As shown in the figure,

Figure 1.Distribution of Herfindahl

index for cropped area

0.1

0.05

00.2 0.4 0.6 0.8 1

0.15

Frac

tion

AreaHerfindahl


275

majority of the farms are located in the region with the index of less than 0.5 suggestingthat most of the farm households embraces crop diversification in the study area.

4.2 Hypotheses testsThe results of the likelihood ratio tests employ during the analysis are presented inTable II[9]. The first null hypothesis indicates the rejection of Cobb-Douglasspecification at 5 per cent level of significance (second row). The implication of this isthat the used of translog stochastic frontier production function is more suitable toderive a conclusion from the data. The null hypothesis of homoskedastcity vit and uit isrejected as revealed by the third row. The null hypothesis of homoskedasticity vitwith heteroskedasticity uit is also rejected as shown in the fourth row. The fourthhypothesis of homoskedasticity uit with heteroskedasticity vit which also doubles asthe test of the effects of technical inefficiency is rejected (fifth row). The implication ofthe fourth hypothesis is that there is presence of technical inefficiency effects in thestudy.

4.3 The elasticities and returns to scaleThe maximum likelihood estimates (MLE) of preferred heteroskedasticity correctedstochastic frontier production function model are presented in Table III. Before theestimation, all the input and output data are normalized by their respective samplemeans, which makes it possible to interpret the first-order parameters directly aspartial production elasticities at the sample mean (Coelli et al., 2005). At the pointestimate, the estimated output elasticity of land, hired labour, family labour, fertilizer,pesticide and materials were positive and therefore consistent with economic theory.The variables were significantly different from zero, with at most a 10 per cent level ofsignificance with the exception of family labour and materials. Non-significantof family labour in food crop production in Nigeria was also observed in the work ofOyekale (2006), and Oyewo and Fabiyi (2008). Hired labour with the highest elasticityimplies that this variable is important in food production among peasant/smallholderfarmers in the country.

This study checked for the monotonicity condition with respect to all inputs at theirindividual point estimates in accordance with Sauer et al. (2006). This result is based onthe number of individual point estimates with production elasticities that arenon-positive. In this regard, the results show that 13 per cent of the elasticities arenegative for land; hired labour: 9 per cent; family labour: 26 per cent; fertilizer:21 per cent; pesticides: 23 per cent and materials: 34 per cent.

Null hypothesesLog

likelihood LRCritical-

value (5%) Decision

Translog, i.e. full heteroskedasticity preferred model 473.68H01: bjki ¼ 0, i.e. Cobb-Douglas vs Translog 412.17 123.02 41.34 Reject H0

H02: lns 2v ¼ lns 2

u ¼ const., i.e. homoskedasticity inboth vi and ui errors 402.41 142.54 32.67 Reject H0

H03: lns 2v ¼ const, i.e. homoskedasticity in vi error 408.35 130.66 11.07 Reject H0

H04: lns2u ¼ const, i.e. homoskedasticity in ui error and

no. technical effect 432.16 83.04 23.69 Reject H0

Table II.Likelihood-ratio tests

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Variables Parameters Coefficients SE p-value

Production variablesD_Hiredlabor w1 0.1052 * 0.0557 0.059D_Fertilizer w2 0.0747 * * * 0.0127 0.000D_Pesticide w3 20.0361 * 0.0203 0.075In(land) b1 0.1089 * 0.0642 0.089In(Hired labour) b2 0.3713 * * * 0.1075 0.000In(Family labour) b3 0.0862 0.0812 0.288In(Fertilizer) b4 0.2958 * * * 0.0746 0.000In(Pesticide) b5 0.0617 * * 0.0321 0.054In(Materials) b6 0.0354 0.0297 0.233Time trend tT 0.0498 * * * 0.0196 0.0110.5[In(land) £ In(land)] b11 0.0045 0.0519 0.9380.5[In(Hired labour) £ In(Hired labour)] b22 20.1421 * * * 0.0525 0.0070.5[In(Family labour) £ In(Family labour)] b33 0.0953 0.1022 0.3510.5[In(Fertilizer) £ In(Fertilizer)] b44 20.2014 * * 0.0951 0.0340.5[In(Pesticide) £ In(Pesticide)] b55 0.2504 0.8135 0.7580.5[In(Materials) £ In(Materials)] b66 0.0146 0.0254 0.5650.5[Time trend £ Time trend] tTT 0.0173 * * * 0.0047 0.000In(land) £ In(Hired labour) b12 0.7951 * * 0.4589 0.083In(land) £ In(Family labour) b13 21.4501 1.3459 0.281In(land) £ In(Fertilizer) b14 0.0029 * * 0.0013 0.026In(land) £ In(Pesticide) b15 0.2152 0.3715 0.562In(land) £ In(Materials) b16 0.2374 * * * 0.0825 0.004In(land) £ Time trend k1T 0.0105 0.0128 0.412In(Hired labour) £ In(Family labour) b23 20.5469 * 0.3062 0.074In(Hired labour) £ In(Fertilizer) b24 0.2063 0.1614 0.201In(Hired labour) £ In(Pesticide) b25 20.5529 0.3791 0.145In(Hired labour) £ In(Materials) b26 0.2216 0.2272 0.329In(Hired labour) £ Time trend k2T 0.0978 * * * 0.0305 0.001In(Family labour) £ In(Fertilizer) b34 20.0008 0.0019 0.998In(Family labour) £ In(Pesticide) b35 2.0604 1.3809 0.673In(Family labour) £ In(Materials) b36 21.8611 1.2241 0.128In(Family labour) £ Time trend k3T 0.3035 0.2437 0.213In(Fertilizer) £ In(Pesticide) b45 20.3386 * 0.1968 0.085In(Fertilizer) £ In(Materials) b46 20.0062 0.0127 0.592In(Fertilizer) £ Time trend k4T 0.2452 * * 0.1101 0.026In(Pesticide) £ In(Materials) b56 0.0369 0.2821 0.895In(Pesticide) £ Time trend k5T 0.1073 0.1484 0.469In(Materials) £ Time trend k6T 0.0194 0.0204 0.341D_Ekiti v1 20.0278 0.0377 0.460D_Ondo v2 0.0952 0.1498 0.523D_Osun v3 0.1723 * 0.0937 0.066D_Oyo v4 0.1098 * 0.0629 0.081D_2008 61 0.0345 * * * 0.0126 0.006D_2009 62 0.0134 * * 0.0061 0.028Herfindahl index of crop diversification (HI) p 0.0533 0.0439 0.227Constant z0 2.1025 * * * 0.1341 0.000Stochastic variance (lns 2

v )In(land) t1 20.0621 * * 0.0271 0.022D_Ekiti t2 20.0923 * * * 0.0286 0.001D_Ondo t3 1.3293 * * * 0.5456 0.015

(continued )

Table III.Estimates of the

stochastic frontierproduction model


277

The sum of the first-order elasticities suggests that an average farm from the sampleexperiences decreasing returns-to-scale (DRTS) of 0.959 which was found to besignificantly different from zero at 5 per cent level. The implication of this is that if allthe inputs are jointly increased by 1 per cent, the food production would increase byabout 0.96 per cent which is an indication that quantities of some inputs in theproduction function exceed the scale efficient point. A search of the literatures showsthat a similar finding was obtained in the developing agriculture by Binam et al. (2004),Tijani (2006), Chirwa (2007) and Solis et al. (2009).

The variable “time trend” accounts for technical change. At the point estimate, thepositivity and significance of this variable implied technical progress in food cropproduction from the analysis. The positive significant dummies of Oyo and Osunstates implied a higher frontier for farms in these states, with reference to Ogun state.Also the positive significance of seasonal dummies is an indication of the positiveseasonal effects on the production frontier in the study.

In the middle panel of Table III are the results of heteroskedasticity of vit.The findings show that land and the states dummies for Ekiti, Osun, andOyo decreased the stochastic variance with the exception of the dummy for Ondo statewhile only the dummy for Osun state is not significantly different from zero. Theimplication of this is that variable such as farms size influences output variability orproduction risk associated with food crop production in the study.

4.4 Technical inefficiency effectsThe relationship between the variance of the inefficiency term and socio-economicvariables of the farmers, production characteristics, and seasonal and state dummies is

Variables Parameters Coefficients SE p-value

D_Osun t4 21.0366 0.6704 0.122D_Oyo t5 21.4164 * * * 0.7812 0.069Constant t0 24.7422 * * * 1.3254 0.000Inefficiency variance (lns 2

u )Age a1 20.0322 0.0241 0.182Gender a2 0.3051 * * 0.1523 0.045Family size a3 0.0618 0.0547 0.259Education a4 20.1726 * * * 0.0539 0.001Extension contacts a5 20.0260 * * 0.0118 0.027Credit a6 0.1712 0.1551 0.269Non-farm income a7 20.1026 0.1374 0.455Herfindahl index of crop diversification (HI) a8 1.0712 * * * 0.3598 0.003D_Ekiti d1 20.2524 0.5623 0.654D_Ondo d2 2.4731 1.866 0.185D_Osun d3 1.6874 * 0.9104 0.064D_Oyo d4 1.9081 1.2981 0.194D_2008 d5 20.3369 * * * 0.0938 0.000D_2009 d6 20.2577 * * * 0.1269 0.042Herfindahl index of crop diversification £ D_2008 G1 0.6355 * * * 0.2073 0.002Herfindahl index of crop diversification £ D_2009 G2 0.2684 * * 0.1157 0.020Constant C0 23.6913 * * * 0.8175 0.000

Note: Statistically significant at *10, * *5 and * * *1 per cent, respectivelyTable III.

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presented in the lower panel of Table III. This result also doubles as a measure oftechnical inefficiency effects.

The results however, show that gender, family size, and credit increased the varianceof technical inefficiency (i.e. decreased technical efficiency) of the farmers[10]. Onlygender is significantly different from zero. The implication of this is that variance oftechnical inefficiency of household heads that are male increase significantly comparedto that of their female counterparts. This observation conform to the findings of Adesinaand Djato (1997), Bozoglu and Ceyhan (2007) and Erhabor and Emokaro (2007).Nonetheless, a possible explanation for this could be attributed to the time of supervisiondevoted to the activities on the farms by the female household heads compared to theirmale counterparts as most male household heads spend most of their time in pursingnon-farm activities as observed by Oladeebo and Fajuyigbe (2007).

In a related development, age, education, extension, and non-farm income decreasedthe variance of the inefficiency term (i.e. increased technical efficiency). Education inthis study is defined as years of formal education and extension is the number of visitby the extension agents to the farmer’s farms and these two variables are significantlydifferently from zero. This observation follows a priori expectation, given thateducation is an important factor in technology adoption. Educated farmers areexpected to be receptive to improved farming techniques and therefore should have alower variance of technical inefficiency than less educated farmers.

However, an important objective of this study is to examine the relationshipbetween crop diversification and variance of technical inefficiency of the farms. To thisend, the sign of the Herfindahl index of crop diversification (a8) suggests thatspecialization increases the technical inefficiency variance (i.e. diversification improvetechnical efficiency TE)[11][12]. A plausible reason for this observation can beattributed to the fact that under multiple cropping systems, crops not only compete fornutrients but can mutually benefit each other as noted by Ajibefun (2006). However,such agronomic benefits of crop diversification as highlighted in the literature includeimprovement in soil fertility; tendency to reduce diseases, weed and insect build up andpossibility to reduce erosion among others. In addition to this, outputcomplementarities in terms of unobserved factors (e.g. farming experience gainedfrom one crop could be replicated on another crop) and observed factors (method ofproduction/technical knowledge) under such a system of production have the tendencyto positively impact the performance and production of another crop in the region. It isequally important to stress that improvement in the efficiency level associated withcrop diversification as observed in the present study, could also be a link to Schultz’s(1964) “poor-but-efficient hypothesis”. For example, using the same level of inputs thatcould have been used to produce one crop under crop diversification system of farmingimplied that the efficiency is probably enhanced by input reduction rather than outputexpansion by the smallholder croppers under investigation in the region. Also, it ispossible that labour force is used in a more balanced way among the activities therebyenhanced the level of efficiency of the farmers.

Although, the result obtained in this study is consistent with the work of Coelli andFleming (2004) and Rahman (2009), but it is contrary to the finding of Lleweln andWilliams (1996), Oyekale (2007) and Haji (2007). This means that the impact of cropdiversification on technical efficiency is quite mixed and perhaps varies from region toregion.


279

The results of the states dummies were quite mixed. The coefficients of the dummiesfor Ondo, Osun, and Oyo implied increased technical inefficiency, with reference to theOgun state. TheOsun states dummy is significantly different from zero at the 10 per centlevel of significance. The dummy forEkiti was found to increaseTEwith reference to theOgun state dummy which is not significantly different from zero. Also, for the seasonaleffects, the coefficients of 2007/2008 and 2008/2009 seasonal dummies show thattechnical inefficiency of the farms decreased in 2007/2008 and 2008/2009 farmingseasons relative to the farms in the 2006/2007 farming season.

Likewise, the cross-effects of the crop diversification index and seasonal dummiessuggest that technical inefficiency of the farms increased as farm embracesspecialization in 2007/2008 and 2008/2009 farming season compared to the farms in the2006/2007 farming season.

4.5 Estimated technical efficiencyTable IV provides average technical efficiency scores for the pooled sample across theseasonal and states level while the distribution of technical efficiency scores is shownin Figure 2. For the pooled data, the results show that technical efficiency scores rangesfrom 0.457 to 0.996 with average of 0.807 (0.128). The implication of this is that anaverage farm in the sample requires 19 per cent more resources to produce the sameoutput (or meet the same objectives) as an efficient farm on the frontier.

The 2008/2009 farming season recorded the highest efficiency score of0.846(0.103). This is followed by 0.805(0.126) and 0.766(0.109) for 2007/2008 and2006/2007 farming seasons, respectively. Thus, the estimated technical efficiencyscores shows that there is an increasing trend in the efficiency in the region based onthe three farming seasons considered in the study. For example, there is a significanceincrease in the estimated technical efficiency score from 2006/2007 to 2007/2008 and2006/2007 to 2008/2009 indicated by superscript “a” with p-value of 0.000 (Table IV).We also found evidence of a significant increase from 2007/2008 to 2008/2009 indicatedby superscript “b” with p-value of 0.000. The implication of this is that over theseasons, there is evidence of significant improvement in the technical efficiency level ofthe farms in the region. This could be attributed to the level of education of the farmersand the number of contacts with extension services as demonstrated in the lower panelof Table III.

A scrutiny of the states’ technical efficiency scores indicates that Osun staterecorded the highest technical efficiency estimate with an average of 0.837(0.115). Thisis followed by Ondo, Ogun, Oyo and Ekiti states with average efficiency of 0.818(0.115),0.816(0.097), 0.801(0.102) and 0.766(0.167), respectively.

Thus, a comparison of the average technical efficiency score obtained in this studywith other studies focusing on food crop production in the region is discussed asfollows. The 0.81 obtained in the present study is consistent with 0.82 reported byAjibefun et al. (2002) compared to 0.70 and 0.52 reported by Fasasi (2007) andAwoyinka et al. (2009), respectively.

5. Conclusions and policy implicationsThis paper examines trends in crop diversification and its impact on technicalefficiency of peasant farmers in Southwestern Nigeria using heteroskedastic correctedstochastic production frontier model on unbalanced panel data covering three farming

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Number of farms Mean efficiency

Pooled resultsMean 846 0.8065SD 0.1281Minimum 0.4572Maximum 0.9958By seasons2006/2007 farming seasonMean 282 0.7657SD 0.1097Minimum 0.4572Maximum 0.9789

2007/2008 farming seasonMean 260 0.8045a

SD 0.1269Minimum 0.4787Maximum 0.9828

2008/2009 farming seasonMean 304 0.8461a,b

SD 0.1034Minimum 0.4973Maximum 0.9956

By statesEkiti stateMean 181 0.7659SD 0.1669Minimum 0.5665Maximum 0.9668

Ogun stateMean 145 0.8162SD 0.0965Minimum 0.5278Maximum 0.9752

Ondo stateMean 206 0.8184SD 0.1153Minimum 0.5207Maximum 0.9957

Osun stateMean 141 0.8373SD 0.1155Minimum 0.4787Maximum 0.9869

Oyo stateMean 173 0.8014SD 0.1017Minimum 0.4572Maximum 0.9863

Notes: aSignificant increase in this mean score compared to that of 2006/2007; bsignificant increase inthis mean score compared to that of 2007/2008

Table IV.Mean efficiency scores bythe whole sample, season,

and states estimates


281

seasons (2006/2007-2008/2009) with 846 observations. The results reveal evidence ofincreasing diversification as indicated by various indices employed in the study. Theimplication of this is that crop diversification as opposed to specialization is regardedas an important cropping system in the region.

The elasticity of output with respect to land, hired labour, family labour, fertilizer,pesticide and materials are positive and significant with the exception of family labourand plantingmaterials. There is evidence of technical progress in food crop production inthe region.The computed returns to scale suggestdecreasing returns to scale in the study.

The result of technical inefficiency effects shows that education, extension, and cropdiversification significantly decrease variance of technical inefficiency (or increasetechnical efficiency) of the farmers in the study. The implication of this is thatdiversification of crop enterprises enhances the technical efficiency level of farmers inthe region. This however, implies that intensification of diversification is advantageousfor farmers’ economic performance in the Nigerian agricultural food production process.

The overall technical efficiency of about 81 per cent obtained from the analysisimplies that an inefficiency level of about 19 per cent is observed from the analysis.

Finally, from the perspective of increasing food crop production in Nigeria, cropdiversification is demonstrated in this study as a policy goal in the country taking Asiaexperience in 1990s as a challenge. Thus, given the results of the empirical findings,especially the drivers or determinants of technical efficiency, the study makes thefollowing policy recommendations.

Policies that increase extension-farmer contact ratio and motivation of educatedfarmers into farming.

Policies that educate farmers to diversify into high-value crops such as fruits andvegetables in combinationwith traditional crops as such novel encouragement is capableof improving rural farm income generation and better nutrition/diet intake in the region.

Notes

1. Multiple cropping is the system whereby farmers cultivate many crops/intercropsimultaneously on the same piece of land. It is a resilience mechanism adopted byfarmers in many regions of the world (Ellis, 1993). Petit and Barghouti (1992) identified cropdiversification as a stage at which many developing agriculture are currently practicing.

Figure 2.Distribution of thetechnical efficiency scoresby whole sample andseasons

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2. This observation suggests why stochastic frontier models is preferred model for analyzingfarm level efficiency in the developing agriculture where most variability in agriculturalproduction is attributed to uncertainty related to climatic conditions such as drought, floodsamong others.

3. The benefits of crop diversification have both value-enhancing and value-reducing effectssuch that the net effect is ambiguous in some instances (Chaplin, 2000).

4. Less than 10 per cent of the farmers were repeatedly sample within the seasons.

5. Various distributional assumptions have been proposed in the literature to model theone-sided uit. These includes half normal, exponential, truncated, and gamma distributions(see more details in Kumbhakar and Lovell, 2000).

6. Earlier we check for heteroskedasticity in the residual using Breusch-Pagan test, the resultfailed to reject the null hypothesis of no heteroskedasticity at p-value of 0.000.

7. The index is constructed such that a value tends towards one (HiD ! 1) impliesspecialization or a value tends towards zero (HiD ! 0) implies diversification.

8. This is computed byHD08=092HD06=07

HD06=07

h i£ 100 ¼ 0:42520:498

0:498

% &£ 100 ¼ 214:65%:

9. We constructed the likelihood ratio test using the statistics LR ¼ 22½lnðLHR 2 LHUÞ&,where LHR is the value of the maximized log-likelihood for the restricted and LHU

represents that of unrestricted. This statistics follows a x 2 distribution with TR 2 TU

denoted degree of freedom, where TR and TU represents the number of variables in therestricted and unrestricted samples, respectively.

10. Gender, male-headed households ¼ 1; female-headed households ¼ 0 while the femaleheaded households are mostly widows and the rest divorce.

11. The index is constructed such that a positive sign on coefficient of this variable implies anegative impact of specialization and vice versa.

12. It is important to mention that the square of the Herfindahl index in theinefficiency variance function was found to be insignificant and thereby dropped fromthe final model.

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Corresponding authorKolawole Ogundari can be contacted at: [email protected]

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287

Appendix

Statistics

Variables

Unit

Symbol

Mean

SDMin.

Max.

Total

farm

output

aNaira

Y2,553.65

2,345.39

60.067

14,532.80

Land

Hectares

X1

2.318

1.651

18.6

Hired

labour

Mandays

X2

141.17

103.103

0378

Fam

ilylabour

Mandays

X3

109.1

76.247

8437

Fertilizer

Kilogram

X4

219.81

135.595

01,650

Pesticide

bLitre

X5

0.975

1.3781

010

Materialsc(m

onetaryvalue,naira

)Naira

X6

34,755.16

19,359.74

6,200

262,855

Tim

etrend

2006/2007¼

0,...,2008/2009¼

2X7

1.026

0.832

02

Dfertilizer(used¼

1)Dum

my

Df

0.728

0.4452

01

Dpesticide(used¼

1)Dum

my

Dp

0.521

0.4998

01

DHlab(used¼

1)Dum

my

Dhl

0.668

0.3751

01

Age

Years

Z1

51.304

10.745

2576

Gender(m

ale¼

1)Dum

my

Z2

0.715

0.4516

01

Fam

ilysize

Counts

Z3

5.382

2.369

015

Edu

cation

Years

Z4

9.514

5.371

016

Extension

Count

Z5

6.746

3.66

019

Credit(access¼

1)Dum

my

Z6

0.667

0.471

01

Non-farm

income(participation

¼1)

Dum

my

Z7

0.387

0.487

01

Diversification

index

Count

Z8

0.459

0.206

0.21

1State

andseasonsdu

mmies

Ekiti

Dum

my

D1

0.214

0.41

01

Ond

oDum

my

D2

0.243

0.429

01

Osun

Dum

my

D3

0.167

0.373

01

Oyo

Dum

my

D4

0.204

0.404

01

Year_2007

Dum

my

D5

0.333

0.471

01

Year_2009

Dum

my

D6

0.359

0.48

01

Noof

observation

846

Notes:

a The

totalfarmoutput

includ

esaggregated

totalrevenue

from

cassava,yam,m

aize,sweetpotatoandcocoyamdeflated

bythe2008

consum

erprice

indexof

179.80

nairaforfood;bpesticides

isexpressedas

weigh

tedcost

ofherbicides

andinsecticides

dividedby

thesum

oftheirrespective

(Tornq

uist)

priceindices;

c materialsisthetotalcostsof

planting

materialswhich

includ

ethecost

ofseeds,cuttings,and

tubers

plantedby

thefarm

ers

Table AI.Summary statistics ofvariables for theregression

IJSE40,3

288

Crop diversification and technical efficiency in food crop production :A study of peasant farmers in Nigeria

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