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Research ArticleAnalysis of Economic Efficiency and Farm Size A Case Study ofWheat Farmers in Nakuru District Kenya

Samuel Mburu1 Chris Ackello-Ogutu2 and Richard Mulwa2

1 Department of Household and Consumer Economics Universitat Hohenheim Fruwirthstraszlige 48 70599 Stuttgart Germany2Department of Agricultural Economics University of Nairobi PO Box 30197 Nairobi 00100 Kenya

Correspondence should be addressed to Samuel Mburu mburusamyahoocom

Received 21 April 2014 Revised 17 August 2014 Accepted 20 September 2014 Published 16 October 2014

Academic Editor Jean Paul Chavas

Copyright copy 2014 Samuel Mburu et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The primary objective of this study is to examine the effect of farm size on economic efficiency among wheat producers andto suggest ways to improve wheat production in the country Specifically the study attempts to estimate the levels of technicalallocative and economic efficiencies among the sampled 130 large and small scale wheat producers in Nakuru District The social-economic factors that influence economic efficiency in wheat production have also been determined Results indicate that themean technical allocative and economic efficiency indices of small scale wheat farmers are 85 96 and 84 respectively Thecorresponding figures for the large scale farmers are 91 94 and 88 respectively The number of years of school a farmerhas had in formal education distance to extension advice and the size of the farm have strong influence on the efficiency levelsThe relatively high levels of technical efficiency among the small scale farmers defy the notion that wheat can only be efficientlyproduced by the large scale farmers

1 Introduction

The relationship between farm size and land productivityhas been widely debated in literature for decades and severalreasons and explanations for the inverse relationship betweenfarm size and land productivity have been put forward andtested

The first reason is imperfect factormarkets including fail-ures in the land market credit market [1] insurance market[2] and labour market [3 4] Malfunctioning or absence ofthese markets will lead to suboptimal resource allocation atthe farm level implying inefficiencies An important causeof labour market imperfections in developing countries islabour supervision cost as hired labour is assumed to beless motivated and effective it takes more productive familylabour to supervise hired labour which decreases overalllabour productivity at farm level [5] This would explainwhy labour and farm productivity are lower on large farmswhich require more hired labour Studies by Assuncao andBraido [4] and Barrett et al [6] argue that the imperfect

market hypotheses imply the presence of unobservable vari-ation between households that leads to differences in theinput intensity levels which are correlated with farm areaTherefore they add a set of household-specific characteristicssuch as household size dependency ratio and gender ofthe household head in testing the inverse relation betweenfarm size and productivity However no previous study hasshown that household characteristics completely explain landproductivity

A second important explanation questions whetherthe land productivity between farm size and productivityemerges (or not) from omitted variables Importantly differ-ences in soil quality lead to differences in soil productivitywhich clearly affect output with small farmers being moreproductive because of having plots of better quality Inaddition farming practices and production methods mightvary according to farm size leading to differences in yieldsand productivity [4 7] All these studies show a decrease inthe severity of land productivity when controlling for soilquality [6 8] but none has found that the land productivity

Hindawi Publishing CorporationEconomics Research InternationalVolume 2014 Article ID 802706 10 pageshttpdxdoiorg1011552014802706

2 Economics Research International

declines Lipton [5] used differentiation in farmmanagementskills as an explanatory variable of farm productivity usingpanel data which allows for household-specific fixed effectsHowever the evidence does not suggest thatmanagerial skillsexplain land productivity

A third explanation of the land productivity is relatedto methodological issues As one of the unsettled issuesLipton [5] mentions that large farms cannot be consideredlinear replicas of small ones Incentives to use inputs varywith production scale that is larger farms use differenttechnologies than small farms Most empirical studies onthe land productivity are based on cross-sectional data andeconometric models can fail to capture nonlinearities andoften impose a common specification (parameters) for thewhole sample Moreover the scale ranges that are allowed inthe models may be too small to measure scale effects [9]

11 Background of the Study Wheat is the second mostimportant crop after maize in Kenya with regard to bothproduction and consumptionUntil the early 1970sKenyawasa net exporter of wheat but currently the country importsabout 60 of the total domestic demand Wheat is grown inthe cooler andmedium-rainfall regions covering the NakuruUasin Gishu Trans-Nzoia and Narok districts and is mostlyrain-fed Production is carried out by small medium andlarge scale farmers numbering about 9000 The industrysupported by about 20 millers contributes 14 and 30 tooverall and cereal GDP respectively The small scale farmersare the majority of the producers but their productionaccounts for only one-quarter of the total wheat producedThe domestic demand for wheat is growing at the rate of 7per year even though production is increasing marginallyWheat and its by-products have gained importance in thehouseholdsrsquo consumption patterns in the last decade In2005 wheat and its by-products accounted for 44 of totalexpenditure of main staples in urban areas up from 35in 1999 [10] Kenya is a high cost wheat producer and forthis reason the country requested the Common Marketfor Eastern and Southern Africa (COMESA) for safeguardmeasures to allow the country to address weaknesses incompetitiveness of the subsector

The increasing domestic demand for wheat is drivenlargely by the rapidly growing population increased urban-ization rising incomes and a change in food preferencesfrom traditional cereals towards wheat and wheat productsThough the country has the potential of increasing theproduction of wheat the sector is faced by several challengesnotably expensive inputs (chemicals seeds and fertilizers)insufficient farm machineries high fuel prices unstableproducer prices and subdivision of large scale farms intosmaller units The small scale farmers are the majorityof the producers but they differ significantly in the useof inputs agronomic practices and productivity from thelarge scale farmers [10] The actual levels of efficiency andsources of inefficiencies among the different size categoriesare however unknown Measuring economic efficiency inwheat production is important for a number of reasonsthe significance of the subsector in terms of farm incomes

to the rural economy regional integration (more openborders especially under COMESA and the East AfricanCooperation) is spawning higher levels of competition thatrequire increased production and distribution efficiency andthe importance of the subsector to the countryrsquos strategiesrelating to achievement of broad food self-sufficiency ruralemployment creation and poverty reduction

Following the experiences of the 200708 global foodcrisis when many food net-importing countries especiallythose in sub-Saharan Africa were unable to secure suppliesfrom the international market the country has embarkedon an aggressive plan to boost its domestic food productionunder the auspices of the Agriculture Sector DevelopmentStrategy (ASDS) This is essentially an import substitutionstrategy that requires increased investments to the agriculturesector reformation of the agricultural research and informa-tion dissemination systems and improving access to creditin order to increase technological innovation particularlyamong the growers of the major cereal grains (maize wheatand rice)

12 Objectives of the Study The analysis of the link betweeneconomic efficiency and farm size in Kenya is partly moti-vated by the increasing pressure on agricultural land thatarises from increasing population and the persistence of highrural populations despite increasing urbanization Agricul-tural land is also under pressure from other sources climatechange that aggravates the already diminished fallow periodsdue to fragmentation in the more populous and high rainfallpotential regions declining soil fertility and the need forequity in land ownership that brings the large wheat farmsinto high prominence The study therefore addresses animportant question of whether or not there are significanteconomic efficiency differences between large scale farms andsmallholder units that are the most likely to predominatein the future as the different pressures mount on the landresource

The general objective of this study is to examine theeffect of farm size on economic efficiency among wheatproducers in Nakuru District and to suggest ways to improvewheat production in the country The specific objectives areto estimate the levels of technical allocative and economicefficiencies among the large and small scale wheat producersto assess the effect of farm size on technical allocative andeconomic efficiency and to determine socioeconomic factorsinfluencing efficiency among small and large scale wheatproducers The following null hypotheses will be tested

H0 farm size has no effect on economic efficiency

H0 none of the identified socioeconomic factors influ-ences efficiency

2 Farm Size and Efficiency

Several studies have investigated the levels of technicaland allocative efficiencies on various farm enterprises withdifferent findings Obare et al [11] applied a dual stochasticefficiency technique and a two-limit Tobit model to analyzeresource allocative efficiency in Irish potato production in

Economics Research International 3

Kenya The authors established that Irish potato productionin Nyandarua North District is characterized by decreasingreturns to scale with a mean allocative efficiency of 057The paper further established that farming experience accessto extension and credit and membership in a farmersrsquoassociation positively and significantly influenced allocativeefficiency

Mulwa et al [12] used a two-step estimation technique(DEA metafrontier and Tobit Regression) to highlight theinefficiencies inmaize cultivation and their causes inWesternKenya The study found that farmers could reduce theirinput use by about 20ndash30 and still achieve their currentproduction level The costs could be reduced by over 50without affecting production thereby indirectly increasingthe farmersrsquo incomes A study by Abate et al [13] applyinga stochastic frontier model in Ethiopia found that tenure sta-tus significantly influences technical efficiency The authorsreport that more than half of the farmers cultivating wheaton their own plots operated above the average efficiency levelcompared to less than one-quarter for those cultivating onborrowed plots Beside land tenure systems several othersocial economic and resource factors were identified to havean influence on technical efficiency Technical efficiency washigher for older farmers due to experience gained over timeMale headed households were found to be more efficientthan female headed households and households with moreeducated heads were found to be more efficient This studyhowever had its emphasis on wheat production and theresults would not be generalized to other enterprises

Ogundari and Ojo [14] estimated technical and allocativeefficiency of smallholder crop farmers in Nigeria using CobbDouglas production and cost functions The finding of thestudy was that farmers operated under increasing returns toscale and therefore had the potential of improving their effi-ciencyThe educational level of the head of farmer (schoolingyears) farm size quantity of fertilizer age of farmer creditavailability and farming experience of the farmer were foundto influence technical efficiency significantly

The evidence on the farm-size efficiency relationship ismixed It is important to clearly define the terms andmethod-ologies adopted in investigating the relationship betweenfarm size and the efficiency of farms based on the particularregion Most frontier studies have focused only on technicalefficiency even though it is by improving overall economicefficiency that major gains in output could be achieved Thefew studies reviewed above suggest there is still a gap inour understanding of the relationship between farm size andeconomic efficiency This paper attempts to fill the gap byexamining overall efficiency on wheat production

21 Theoretical Framework This study uses the parametricstochastic efficiency technique that follows the Kopp andDiewert [15] cost decomposition procedure to estimate tech-nical allocative and economic efficiencies Its advantage liesin the application of a stochastic frontier model with a dis-turbance term specification that captures noisemeasurementerror and exogenous shocks beyond the farm The two-stepregression model has been used to analyze the effects of

the social-economic factors on economic efficiency using acensored Tobit model

Over fifty years ago Farrell [15] introduced a methodol-ogy to measure economic efficiency (EE) technical efficiency(TE) and allocative efficiency (AE by definition EE is equalto the product of TE and AE) According to Farrell TEis associated with the ability to produce on the frontierisoquant while AE refers to the ability to produce at agiven level of output using the cost-minimizing input ratios(Figure 1) Alternatively technical inefficiency is related todeviations from the frontier isoquant and allocative inef-ficiency reflects deviations from the minimum cost inputratiosThus EE is defined as the capacity of a firm to producea predetermined quantity of output at minimum cost fora given level of technology [15 16] Productive units canbe inefficient either by obtaining less than the maximumoutput available from a determined set of inputs (technicalinefficiency) or by not purchasing the lowest priced packageof inputs given their respective prices and marginal produc-tivities (allocative efficiency) Efficiency measurement can becategorized as either input or output oriented input-orientedtechnical efficiency evaluates how much input quantities canbe reduced without changing the quantities produced whileoutput-oriented measures of efficiency estimate the extent towhich output quantities can be expanded without alteringthe input quantities used [17] Efficiency estimation can bestbe demonstrated by relating both allocative and technicalefficiency Farrellrsquos methodology has been applied widelywhile undergoing many refinements

3 Empirical Framework Stochastic FrontierProduction and Cost Functions

As in Bravo-Ureta and Evenson [18] and Bravo-Ureta andRieger [19] the parametric technique used in this studyfollows the Kopp and Diewert [15] cost decompositionprocedure to estimate technical allocative and economicefficiencies The firmrsquos technology is represented by thestochastic frontier production function as follows

119884119894= 119891 (119883

119894 120573) + 119890

119894 (1)

where119884119894= the output of the 119894th farmer 119883

119894= a vector of input

quantities of the 119894th farmer and 120573 = a vector of unknownparameters to be estimated Consider the following

119890119894= (119881119894minus 119880119894) (2)

The 119881119894are assumed to be independent and identically dis-

tributed 119873(0 1205902V ) random errors independent of the 119880119894 The

119880119894are nonnegative technical inefficiency effects representing

management factors and are assumed to be independentlydistributed with mean 119906

119894and variance 120590

2 The 119894th farm

exploits the full technological production potential when thevalue of 119880

119894comes out to be equal to zero and the farmer

is then producing at the production frontier beyond whichhe cannot produce The greater the magnitude of 119880

119894from

the production frontier the higher the level of inefficiency of


YTE

CTECOB

CEEO X1

X2

DC

A

B

YTE technically efficient isoquantCTE technically efficient costCEE economically efficient costCOB observed cost

X1

lowast

X2

lowast

Figure 1 Graphical Representation of observed and technicallyand economically efficient cost Measures Technical efficiency (TE)allocative efficiency (AE) and economic efficiency (EE) are equalto the following TE = OBOA = CTE COB AE = ODOB =

CEECTE and EE = TE lowast AE = ODOA = CEECOB

the farmer [20] The maximum likelihood estimation of (1)provides estimators for the beta coefficients The variances ofthe random errors1205902V and those of the technical and allocativeinefficiency effects 1205902

119906and overall variance of themodel 1205902 are

related thus

1205902= 1205902

V + 1205902

119906 (3)

The ratio 120574 = 1205902

1199061205902 measures the total variation of output

from the frontier which can be attributed to technical orallocative inefficiency [21]

Subtracting V119894from both sides of (1) yields

119884lowast

119894= 119910119894minus V119894= 119891 (119883

119894 120573) minus 119880

119894 (4)

where 119884lowast119894is the observed output of the 119894th firm adjusted for

the stochastic noise captured by V119894

Equation (4) is the basis for deriving the technicallyefficient input vectors and for analytically deriving the dualcost frontier of the production function represented by (1)For a given level of output 119884lowast

119894 the technically efficient input

vector for the 119894th firm 119883119905119894 is derived by simultaneously

solving (4) and the ratios 1198831119883119894= 119896119894(119894 gt 1) where 119896

119894is

the ratio of observed inputs 1198831and 119883

119894 Assuming that the

production function in (1) is self-dual the dual cost frontiercan be derived algebraically and written in a general form as

119862119894= 119891 (119875

119894 120572 119884lowast

119894 120572) (5)

where 119862119894is the minimum cost of the 119894th firm associated with

output 119884lowast119894 119875119894is a vector of input prices for the 119894th firm and 120572

is a vector of parametersThe economically efficient input vector for the 119894th firm

119883119890

119894 is derived by applying Shephardrsquos Lemmaand substituting

the firmrsquos input prices and output level into the resultingsystem of input demand equations

120597119862119894

120597119875119894

= 119883119890

119894(119875119894119884lowast

119894 120573) 119894 = 1 2 119898 inputs (6)

where 120573 is a vector of estimated parametersThe observed technically efficient and economically

efficient costs of production of the 119894th firm are equal to 1198751015840119894119883119894

1198751015840

119894119883119905

119894 and 119875

1015840

119894119883119890

119894 respectively These cost measures are used

to compute technical efficiency (TE) and economic efficiency(EE) indices for the 119894th firm as follows

TE119894=1198751015840

119894119883119905

119894

1198751015840

119894119883119894

(7a)

EE119894=1198751015840

119894119883119905

119894

1198751015840

119894119883119894

(7b)

Following Farrell [16] the allocative efficiency (AE) index canbe derived from (7a) and (7b) as follows

AE119894=1198751015840

119894119883119890

119894

1198751015840

119894119883119905

119894

(8)

Thus the total cost or economic efficiency of the 119894th firm(1198751015840

119894119883119894minus 1198751015840

119894119883119890

119894) can be decomposed into its technical (1198751015840

119894119883119894minus

1198751015840

119894119883119905

119894) and allocative (1198751015840

119894119883119905

119894minus 1198751015840

119894119883119890

119894) components

31 The Production Function A production function canbe expressed generally as 119884 = 119891(119883

119894) where 119884 is output

level per unit of time and 119883119894denote quantities of different

inputs Using only labor (119871) and capital (119870) and other factorsof production held constant (in the short run) we have119884 = 119891(119871119870) Generally labor units can be changed at ashort notice but it takes more time to install machinery orequipment represented here by 119870 Production functions canbe expressed in different forms depending on the techno-logical relationship between 119884 and 119883 indeed the functionalrelationship between output and inputs is referred to asthe firmrsquos technology Due to duality knowledge of a firmrsquostechnology automatically reveals a firmrsquos cost function (therelationship between 119884 and total cost of all inputs includingfixed costs) One of the most commonly used productionfunction specifications for agricultural production relation-ships is the Cobb-Douglas function generally expressed asfollows in the case of two inputs

119884 = (119871119870) = 119860119871119886119870119887 (9)

where 119860 is a scale parameter (constant) and 119886 and 119887 areelasticity of output response due to changes in 119871 and 119870respectively the coefficients 119886 and 119887 are generally restrictedto ensure that the technology exhibits decreasing returns toscale thus allowing for a profit maximum

A variation of the Cobb-Douglas function applied inthis study is the stochastic frontier model defined in (10)(The Cobb-Douglas production form is chosen because itspracticality and ease in the interpretation of its estimated


coefficients Despite its limitations of constant elasticity ofsubstitution the Cobb-Douglas is found to be an adequaterepresentation of our data) It is simply a linearization of theabove general form using logs

ln119884119894= 1205730+ 1205731ln fert

1+ 1205732ln seed

2

+ 1205733ln chem

3+ 1205734ln foliar

4+ 1205735ln hlab

5

+ 1205736ln flab

6+ 119881119894minus 119880119894

(10)

where ln = natural logarithm1198841=wheat output (in kg) of the

119894th farmer per acre fert2= quantity of fertilizer used in kg

per acre seed2= quantity of seeds used in kg per acre chem

3

= quantity chemicals used in kg per acre foliar4= quantity

of foliar used in liters per acre hlab5= cost of hired labor

per acre flab6= imputed cost of family labor per acre V

119894=

random error 119906119894= inefficiency measure and 120573

119894= parameters

to be estimatedThe 119906

119894is the nonnegative truncation (at zero) of the nor-

mal distributionwithmean 120583119894 and variance 1205902The variables

specified in themodel were subjected to a correlation test thatshowed that all the variables were not highly correlated

32 The Cost Function The economic cost of an input isthe minimum payment required to keep the input in itspresent employment It is the payment the input wouldreceive in its best alternative employmentThe correspondingdual stochastic frontier cost function which is the basis ofestimating the allocative efficiencies of the farmers is specifiedas follows

119862119894= 119891 (119875

119894 120572 119884lowast

119894+ 119880119894) 119894 = 1 2 3 119873 (11)

where119862119894=minimum cost of the 119894th firm associated with out-

put 119884119894119891 = Cobb-Douglas functional form 119875 = input prices

employed by 119894th farm in wheat production120572 = parameter tobe estimated 119884lowast

119894= the observed wheat output per acre of the

119894th firm adjusted for the statistical noise captured by 119881119894 and

119880119894provides information on the levels of allocative efficiency

of the 119894th farmThe Cobb-Douglas cost frontier function for the wheat

farmers is specified as follows

ln119862119894= 1205720+ 1205721ln119884lowast1+ 1205722ln pfert

2

+ 1205723ln pseed

3+ 1205724ln119901chem

4+ 1205725ln pfoliar

5

+ 1205726ln phlab

6+ 1205727pflab7+ 119880119894

(12)

where119862119894= total cost of production of 119894th farm per acre119884lowast

1

= observed wheat output per acre adjusted for statisticalnoise pfert

2=price of fertilizer per kg pseed

3=price of seeds

per kg pchem4= price per liter of chemical pfoliar

5= price

per liter of chemical phlab6= wage rate per day and pflab

7=

imputed family labor per day

33 Determining Factors Influencing Efficiency Severalauthors have investigated the relationship between efficiencyand various socioeconomic variables using two alternative

approaches (for a review of several of these paperssee Bravo-Ureta and Rieger [19]) One approach is tocompute correlation coefficients to conduct other simplenonparametric analyses The second way usually referredto as a two-step procedure is to first measure farm levelefficiency and then to estimate a regression model whereefficiency is expressed as a function of socioeconomicattributes Kalirajan [22] observed that socioeconomicattributes have roundabout effects on production and henceshould be incorporated into the analysis directly whileRay [23] argued that the two-step procedure is justifiableif one assumes that production function is multiplicativelyseparable in what he calls discretionary (included inproduction function) and nondiscretionary (used to explainvariations in efficiency) inputs Analysis of the effects offirm-specific factors on economic efficiency has generatedconsiderable debate in frontier studies In this study thetwo-step procedure has been adopted to analyze the effectsof socioeconomic factors in the economic efficiency ofthe wheat producers The economic efficiency estimatesobtained are regressed on some socioeconomic factors usingthe Tobit model This use of a second stage regression modelof determining the socioeconomic attributes in explaininginefficiency has been suggested in a number of studies (eg[24 25])

TheTobit ModelConsider the theoretical Tobit model whichtakes the following form

119884lowast

119896= 119883119896120573 + 119880

119896 (13)

where 119884119896is the latent (hidden) independent variable for the

119896th farm 119883119896is the vector of independent variables which

have been postulated to affect efficiencyThe vector 120573 comprises the unknown parameters asso-

ciated with the independent variables for the 119896th farmand 119880

119896is an independently distributed error term assumed

to be normally distributed with zero mean and constantvariance Dummy variables were added to represent thevarious socioeconomic factors such as age gender and levelof education of the head of household among others Becausethe dependent variable in (13) is a measure of efficiency thevariables with a negative (positive) coefficient will have apositive (negative) effect on efficiency levels

34 Data and Sampling Procedure The study was carried outin Rongai and Ngata divisions in the new Nakuru districtwhere a representative sample of 138 wheat farmers wasrandomly selected The district covers an area of 14841 km2where 79623 km2 is arable land 45 km2 is water mass forestsare 7 km2 and national parks cover 188 km2 The district islocated in the high potential (over 1800 meters above sealevel) and low potential (less than 1800 meters above sealevel) agroecological zonesThe high potential zone generallyreceives more rainfall over a longer period of time than thelow potential zoneThe average farm size for small scale is 25acres while for large scale is 200 acres The district has threedistricts agroecological zones lower highland (LH3-LH4)mainly the wheatmaizebarley zone the lower midland


(LM3) zone and the upper midland (UM2-5) which isthe upper sisal zone According to the Ministry of Agricul-ture these two divisions produce 75 and 25 of the totalwheat produced in the district respectively A list of farmersin the district was provided by the Ministry of Agricultureat the divisional offices that was used to select the sampledfarmers

The sampling procedure used was stratified proportionalsampling method since the population of the wheat farmerswas not homogeneous The sampling frame comprised allwheat farmers (in the 2008 season) in Ngata and Rongaidivisions Two separate lists from the sampling frame weredeveloped One list consisted of all the farmers who grewwheat onmore than twenty (gt20) acres to form the first stratawhile the second list comprised farmers growing wheat ontwenty acres and less (20 and less) of land The sample sizewas determined using a formula developed by Krejcie andMorgan [26] which is shown as follows

119878 =1205942119873119875 (1 minus 119875)

1198892 (119873 minus 1)+ 1205942119875 (1 minus 119875) (14)

where 119878 = required sample size 1205942 = table value of chi-squarefor 1 degree of freedom at the desired confidence level whichis 3841 for 95 confidence level119875 = population proportionassumed to be 05 since this would provide the maximumsample size119863 = degree of accuracy expressed as a proportion(005) and119873 = population of wheat farmers in the division

Using the above formula the sample size computed for apopulation of 150 small scale farmers was 108 farmers whilethe sample size for the 30 large scale farmers was 28 farmersNgata division had more large scale and small scale farmersthan Rongai divisionTherefore to determine the sample sizefor each division for the small scale farmers the sampling wasproportional to size at 60 for Ngata division and 40 forRongai Division For the large scale farmers the proportionwas 57 in Ngata division and 43 in Rongai divisionThe farmers were then randomly selected from each stratumusing the proportionate random sampling to form the studysample A total number of 138 farmers were sampled

The household data was collected using a structuredquestionnaire by trained enumerators The survey soughtinformation on wheat acreages quantity of inputs and theirprices quantity harvested credit extension and demo-graphic characteristics of household members as well as thequality of life indicators

The data was compiled and cleaned using SPSS data entrybuilder and SPSS data editor The analysis was done usingFrontier 40 and STATA statistical packages

4 Key Results and Discussion

This section highlights the key results on the productionsystems productivity and efficiency levels

41 Production Systems and Farmersrsquo Profile Majority of thefarmers (both small scale and large scale) were growingwheaton rented landThe high cost of renting land had implicationson the area that farmers were able to put under production

Wheat production was highly mechanized with mostof the farm activities being carried out by use of tractorsThe large scale farmers reported high use of inputs such ascertified seeds and fertilizers while most small scale farmersused recycled seeds during planting The main reason forthe use of recycled seeds was that they were cheaper thanthe purchased hybrid seeds As a result the productivityamong the small scale farmers was lower than the large scalefarmers Wheat productivity in the district was below thenormal yields mainly due to inadequate rainfall during the2007 cropping season The use of inputs such as certifiedseeds was quite low and farmers relied on recycled seedsFertilizer use was also low especially among the small scalefarmers The main cost components were cost of chemicalsland preparation costs and fertilizer and seed costs

Majority of the farmers had achieved the primary level ofeducation The literacy level determines the rate and extentof technology adoption and with such level of education theuptake of technology can be enhanced Most farmers wereself-employed in agriculture implying that theywere availableon their farms most of the times The results indicate thatmost farmers were not accessing extension services mainlydue to unavailability of extension workers and farmers hadto travel long distances to access extension advice Similarlyfew farmers accessed credit facilities mainly due to lack ofcollateral and very strict conditions of accessing credit Onaverage the gross margins were Kenya shilling 9787 andKenya shilling 7260 per acre for large scale and small scalefarmers respectively All other costs held constant the grossmargins looks attractive for both categories of farmers Thisindicates that wheat production can be a profitable enterpriseamong the small scale farmersWith the supply of labor in therural areas the small scale farmers would manage to producewheat in a cost-effective mannerThis argument is supportedbymaize sectorKenyawheremajority of the farmers are smallscale farmers practicing labor-intensive farming techniquesand they supply the bulk of maize produced in the country

42 Technical Allocative and Economic Efficiencies Themaximum-likelihood (ML) estimates of the parameters ofthe stochastic production frontier were obtained using theprogram FRONTIER 41 [17] These results are presented inTable 1 which also presents the OLS results of the averageproduction function for comparison The signs of the slopecoefficients of both OLS andML estimates are positive exceptfor family labor that has a negative coefficient implyingthat increasing the family labor affects wheat productionnegativelyML estimated coefficients such as seeds fertilizersand chemicals are significant while for OLS only chemicalscoefficient is statistically significant The estimate of thevariance parameter gamma (120574) is also significantly differentfrom zero which implies that the inefficiency effects aresignificant in determining the levels of wheat output of thesampled farmersThe estimated production function is givenas

ln119884119894= 45 + 048 ln seed

119894+ 011 ln fert

119894

+ 011 ln chem119894+ 009 ln foliar

119894

+ 004 ln hiredlab119894minus 0027 ln famlabor

119894

(15)


Table 1 Ordinary least squares (OLS) estimates of the average production function and ML estimates of the stochastic production frontierfor the sampled wheat producers

Variable OLS estimates119905-ratio ML estimates

119905-ratioCoefficient Standard error Coefficient Standard error

Intercept 459 1003 457 446 0882 506lnseed 028 0228 124 048 0205 235

lowast

lnfertilizer 008 0054 149 011 0043 263lowast

lnfoliar 01 0114 089 009 0083 113lnchemical 019 0066 302

lowast 011 0042 264lowast

lnhiredlabor 004 0029 152 004 0025 176lnfamilylabor minus004 0034 minus134 minus0027 0031 minus085

sigma squared 054 126 0216 582gamma (120574) mdash 093 0036 259

lowast

Log likelihood minus14054 minus1312lowastSignificant at the 5 level

where 119884119894= wheat output per acre in kilograms seed

119894=

quantity of seeds per acre in kilograms fert119894= the quantity of

fertilizer per acre in kilograms foliar119894= the quantity of foliar

used per acre in kilograms chem119894= the quantity of chemicals

used per acre in liters hiredlab119894= the cost of hired labor per

acre famlabor119894= the imputed cost of family labor per acre

Thedual cost frontier derived from the stochastic produc-tion frontier shown in Table 1 is as follows

ln119862119894= minus 1507 + 0267 (pseed

119894) + 0010 (pfert

119894)

+ 0012 (pfoliar119894) + 0223 (pchem

119894)

+ 0147 (ln pwage119894) + 1042 (ln119884lowast

119894)

(16)

where119862119894= the cost of production per acre of 119894th farm pseed

119894

= the price of seed per kg pfert119894= the price of fertilizer per

kg pfoliar119894= the price of foliar per kg pchem

119894= the price

of chemical per liter pwage119894= the wage rate per day119884lowast

119894=

the wheat output in kg per acre adjusted for statistical noise(Table 2)

43 Distribution of Technical Efficiency (TE) Allocative Effi-ciency (AE) and Economic Efficiency (EE) Measures Resultsas indicated in Table 3 show that the mean technicalallocative and economic efficiency indices of small scalewheat farmers are 85 96 and 84 respectively whilefor the large scale farmers the mean technical allocativeand economic efficiency indices are 91 94 and 88Thus the results from both small and large scale farmersreveal some considerable levels of inefficiencies in wheatproduction inNakuruDistrict However the large scale farmshave relatively higher technical and economic efficienciescompared to small scale farmers

The mean technical efficiency scores were quite high forboth small and large scale farmers but were higher amonglarge farms than for the small farms However the resultsshow that there is still some considerable level of inefficienciesin the use of inputs for the corresponding output levels Theallocative efficiency was higher among small scale farmersthan for large scale farmers implying that small scale farmers

Table 2 The OLS estimates of the stochastic cost function

Cost per acre Coefficient Standard error 119905 119875 gt 119905

lnpseed 0267 015 176 008lnpfertilizer 0010 003 034 0731lnpfoliar 0012 001 089 0378lnpchemical 0223 005 435 0000lnplabor 0147 027 054 0589lnobserved 119884lowast 1042 013 778 0000Constant minus1507 182 minus083 0410

Table 3 Mean TE AE and EE scores by farm size

Farm size TE AE EESmall scale 085 096 084Large scale 091 094 088Overall 088 095 086

were quite price-sensitive to the input prices than the largescale farmers The overall economic efficiency was quite highfor both farm categories though it was higher among largescale than small scale farmersThemean technical allocativeand economic efficiency estimates between large and smallscale farmers was statistically significant

The relatively high levels of technical efficiencies amongthe small scale farmers defies the notion that wheat produc-tion in the country can only be efficiently produced by thelarge scale farmers This study shows that it is possible forsmall scale farmers to produce wheat efficiently In manyparts of Africa including Kenya small farms remain at thecenter of agriculture and rural development However oneof the main causes for the low agricultural productivity isthe lack of appropriate machineries that cater to and suitthe requirements of small scale farms For this reason manysmall farms are deemed as unproductive and inefficient Toraise the productivity of wheat among small scale farmersin the country basic farm mechanization requirements tocater to small farm needs must be met such as suitabilityto small farms simple design and technology versatility


for use in different farm operations affordability in termsof cost to farmers and most importantly the provisionof support services from the government and the privatesectorsmanufacturers

44 Farm Size and Efficiency Statistical tests were carried outon the relationship between the size of the farm and technicalefficiency The test results shows that the mean differencesin technical scores are significantly different from zero at1 and 5 levels of significance The null hypothesis thatthe mean difference equals zero is rejected thus acceptingthe alternative that the mean difference between small scaleand large scale is less than zero These results indicate thatlarge scale farms have a higher technical efficiency than smallscale farms Results on the statistical tests on the associationbetween farm size and allocative efficiency show that themean difference in allocative efficiency scores is statisticallydifferent from zero at 1 and 5 level of significanceThe nullhypothesis that there is no mean difference between smallscale and large scale is rejected This implies that there isstatistical difference in allocative efficiencies between smallscale and large scale wheat farms A similar test was done onthe association between farm size and economic efficiencyThe results show that the mean difference in economicefficiency scores between small scale and large scale farmersis statistically different from zero at 1 and 5 levels ofsignificance The null hypothesis is rejected and this impliesthat the large scale farmers have higher economic efficiencythan small scale farmers

45 Findings on Factors Influencing Efficiency For this pur-pose the parameters technical efficiency (TE) allocativeefficiency (AE) and economic efficiency (EE) indices wereestimated censured Tobit procedure for the following socioe-conomic characteristics

(1) farm size equal to zero for small scale and equal toone for large scale

(2) age given by age of the household head(3) gender equal to zero for female head and one formale

head(4) marital status equal zero for single one for married

and two for widowed(5) level of education of head equal to zero for no

education one for primary education and two forpostprimary education

(6) main occupation of household head equal to zero forsalaried and one for self-employed

(7) belonging to a farmer group equal to zero for No andone for Yes

(8) distance to the nearest certified seed seller (km)(9) distance to nearest extension services (km)(10) land tenure equals zero for owned land and one for

rented land(11) source of seed equal to zero for recycled seed and one

for purchased seed

The Tobit results presented in Table 4 show that there is thelack of consistent pattern of association between efficiencyand some socioeconomic characteristics such as farm sizeage of the head and years of experience in growing wheatThe clearest pattern that emerges is that most of these social-economic characteristics were positively related to efficiencyThe positive sign of farm size implies that technical efficiencyincreases with the size of the farm The size of the farm isalso significant with allocative efficiency The negative signfor the age of the head implies that efficiency of productiondeclined with the age of the head The significant influenceof education on farm efficiency is critical indicating thathouseholds headed by more educated heads were moreeducated compared with households headed by less educatedheads The interpretation is that farmers who had a higherlevel of training were more technically and economicallyefficient than those with low level of training

The positive relationship between the education level ofhousehold head and economic efficiency can be supportedby similar results reported in studies which have focusedon the association between formal education and technicalefficiency [18 27 28] In general more educated farmers areable to perceive and interpret and respond to new infor-mation and adopt improved technologies such as fertilizerspesticides and planting materials much faster than theircounterparts This result is consistent with the findings byAbdulai and Eberlin [29] which established that an increasein human capital will augment the productivity of farmerssince they will be better able to allocate family-suppliedand purchased inputs and select and utilize the appropriatequantities of purchased inputs while applying available andacceptable techniques to achieve the portfolio of householdpursuits such as income The result that shorter distancesto extension providers influenced farm efficiency is alsoconsistent with findings by Seyoum et al [30] who founda 14 difference in technical efficiency between farmerswho had access to extension services and those who didnot in a study on farmers within and outside the SasakawaGlobal 2000 project Extension workers play a central role ininformingmotivating and educating farmers about availabletechnology

5 Conclusions

The relationship between farm size and efficiency is oneof the more persistent puzzles in development economicseven more so as many potential determinants have been putforward and tested without being able to provide a fullysatisfying explanation The findings from this study suggestthat gains from improving technical efficiency exist in allfarm categories but they appear to be much higher on largethan on small farms While small farms tend to use landmore intensively in an attempt to alleviate land constraintsthe study suggests that the relatively higher level of technicalefficiency observed on small farms is largely attributable tothe adoption of traditional land saving techniques ratherthan the use of modern land saving technologies Smallscale farms are found to be more allocatively efficient than


Table 4 Tobit model estimates for different efficiency measures

Variable Technical efficiency Allocative efficiency Economic efficiencyCoefficient 119905-ratio Coefficient 119905-ratio Coefficient 119905-ratio

Farm size 000 (006) 002lowast (190) 001 (137)

Age of head minus000 (010) 000 (084) 000 (016)Gender 001 (013) minus000 (020) minus000 (020)Marital status minus005 (125) 003 (159) 000 (003)Education 004

lowastlowast (236) minus001 (151) 001lowastlowastlowast (262)

Main occupation 000 (010) minus000lowast (121) 001 (139)

Belonging to group minus001 (062) 001 (137) 000 (038)Distance to extension service minus000

lowast (177) minus000 (146) minus000lowastlowast (226)

Distance to certified seed seller minus000 (095) minus000 (006) 000 (095)Tenure minus000 (020) minus000 (031) 000 (005)Seed source minus001 (081) minus000 (025) minus000 (016)Constant 090

lowastlowastlowast (1145) 095lowastlowastlowast (2638) 087

lowastlowastlowast (3690)Observations 129 129 129Absolute value of 119905 statistics in parentheses lowastsignificant at 10 lowastlowastsignificant at 5 lowastlowastlowastsignificant at 1

the larger farms Nevertheless gains from improving alloca-tive efficiency exist in more than 90 of the sample house-holds Accordinglymeasures aimed at reducing labor conges-tion on the farms relaxing liquidity constraints and improv-ing the functioning of land rental markets can significantlyimprove productive efficiencyWhile self-sufficiency inwheatremains a stated goal of the government it has remainedelusive over the years With current yields self-sufficiencywill be accomplished only if area under wheat is increasedsubstantially or through intensification leading to higheryields

Efforts should also be made to improve extension ser-vices access to high yielding seed varieties and propercop husbandry methods Opening up more areas in thepotential wheat areas in the country mostly in the marginalareas through irrigation could assist in increasing outputsubstantially faster than simply targeting policy interventionstowards increased input use The existing small scale wheatfarmers should be supported in lowering their costs ofproduction to ensure that they remain in production sincetheir production will remain critical to the governmentrsquosstrategies on food security poverty reduction and increasedrural employment

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors are grateful to CMAAE (Collaborative Mastersin Applied Agricultural Economics) program for providingthe financial assistance and to the paper reviewers for theirobjective comments on the earlier drafts

References

[1] J J Assuncao and M Ghatak ldquoCan unobserved heterogeneityin farmer ability explain the inverse relationship between farmsize and productivityrdquo Economics Letters vol 80 no 2 pp 189ndash194 2003

[2] S Dercon and P Krishnan ldquoIncome portfolios in rural Ethiopiaand Tanzania choices and constraintsrdquo Journal of DevelopmentStudies vol 32 no 6 pp 850ndash875 1996

[3] C B Barrett ldquoOn price risk and the inverse farm size-productivity relationshiprdquo Journal of Development Economicsvol 51 no 2 pp 193ndash215 1996

[4] J J Assuncao and L H B Braido ldquoTesting household-specificexplanations for the inverse productivity relationshiprdquo TheAmerican Journal of Agricultural Economics vol 89 no 4 pp980ndash990 2007

[5] M Lipton ldquoFrom policy aims and small-farm characteristicsto farm science needsrdquo World Development vol 38 no 10 pp1399ndash1412 2010

[6] C B Barrett M F Bellemare and J Y Hou ldquoReconsideringconventional explanations of the inverse productivity-size rela-tionshiprdquoWorld Development vol 38 no 1 pp 88ndash97 2010

[7] F Byiringiro and T Reardon ldquoFarm productivity in Rwandaeffects of farm size erosion and soil conservation investmentsrdquoAgricultural Economics vol 15 no 2 pp 127ndash136 1996

[8] R L Lamb ldquoInverse productivity land quality labor marketsand measurement errorrdquo Journal of Development Economicsvol 71 no 1 pp 71ndash95 2003

[9] P Collier and S Dercon ldquoAfrican agriculture in 50 yearssmallholders in a rapidly changing worldrdquo in Paper Presentedat the 2009 Food and Agriculture Organization Expert Meetingon How to Feed the World in 2050 2009

[10] J Nyoro M Muyanga and I Komo ldquoWheat and wheat prod-ucts trade in Kenyardquo Tech Rep Cereal Growers AssociationCereal Millers Association and Tegemeo Institute 2005

[11] G A Obare D O Nyagaka W Nguyo and S M MwakuboldquoAre Kenyan smallholders allocatively efficient Evidence from


Irish potato producers in Nyandarua North districtrdquo Journal ofDevelopment and Agricultural Economics vol 2 no 3 pp 078ndash085 2010

[12] R Mulwa A Emrouznejad and L Muhammad ldquoEconomicefficiency of smallholder maize producers in Western Kenyaa DEA meta-frontier analysisrdquo International Journal of Opera-tional Research vol 4 no 3 pp 250ndash267 2009

[13] B Abate F Machel and A Gezahegn ldquoEffect of Farm Size onTechnical Efficiency of Teff Production A case Study of theMoretina Jiru District Central Ethiopiardquo 2006

[14] K Ogundari and S Ojo ldquoEconomic Efficiency of small scalefood cropproduction inNigeria a stochastic frontier approachrdquoJournal of Social Sciences vol 14 no 2 pp 123ndash130 2007

[15] R J Kopp and W E Diewert ldquoThe decomposition of frontiercost function deviations into measures of technical and alloca-tive efficiencyrdquo Journal of Econometrics vol 19 no 2-3 pp 319ndash331 1982

[16] M J Farrell ldquoThe measurement of productive efficiencyrdquoJournal of the Royal Statistical Society Series A vol 120 pp 253ndash290 1957

[17] T J Coelli A Guide to FRONTIER Version 41 A ComputerProgram for Stochastic Frontier Production and Cost FunctionEstimation Department of econometrics University of NewEngland Armidale Australia 1994

[18] B E Bravo-Ureta and R E Evenson ldquoEfficiency in agriculturalproduction the case of peasant farmers in eastern ParaguayrdquoAgricultural Economics vol 10 no 1 pp 27ndash37 1994

[19] B E Bravo-Ureta and L Rieger ldquoDairy farm efficiency mea-surement using stochastic frontiers and neoclassical dualityrdquoAmerican Journal of Agricultural Economic vol 73 no 2 pp421ndash428 1997

[20] P Drysdale K P Kalirajan and S Zahao ldquoThe impact of eco-nomic reform on production growth in Chinese agriculturerdquoAmerican Journal of Agricultural Economics vol 73 no 2 pp266ndash275 1995

[21] G E Battese and G S Corra ldquoEstimation of a productionfrontier model with application to the Pastoral Zone of EasternAustraliardquo Australian Journal of Agricultural Economics vol 21no 3 pp 169ndash179 1977

[22] K P Kalirajan ldquoThe importance of efficient use in the adoptionof technology a micro panel data analysisrdquo Journal of Produc-tivity Analysis vol 2 no 2 pp 113ndash126 1991

[23] S C Ray ldquoData envelopment analysis nondiscretionary inputsand efficiency an alternative interpretationrdquo Socio-EconomicPlanning Sciences vol 22 no 4 pp 167ndash176 1988

[24] K R Sharma P Leung andHMZaleski ldquoTechnical allocativeand economic efficiencies in swine production in Hawaii acomparison of parametric and nonparametric approachesrdquoJournal of Agricultural Economics vol 20 no 1 pp 23ndash35 1999

[25] B R Dhungana P L Nuthall and G V Nartea ldquoMeasuringthe economic inefficiency of Nepalese rice farms using dataenvelopment analysisrdquo The Australian Journal of Agriculturaland Resource Economics vol 48 no 2 pp 347ndash369 2004

[26] R V Krejcie and D W Morgan ldquoDetermining sample size forresearch activitiesrdquo Education and Psychological Measurementvol 30 pp 607ndash610 1970

[27] R W Uaiene and C Arndt ldquoFarm household technical effi-ciency in Mozambiquerdquo in Contributed Paper for Presentationat the IAAE Conference Beijing China August 2009

[28] M Bozoglu and V Ceyhan ldquoMeasuring the technical efficiencyand exploring the inefficiency determinants of vegetable farms

in Samsun province Turkeyrdquo Agricultural Systems vol 94 no3 pp 649ndash656 2007

[29] A Abdulai and R Eberlin ldquoTechnical efficiency during eco-nomic reform in Nicaragua evidence from farm householdsurvey datardquo Economic Systems vol 25 no 2 pp 113ndash125 2001

[30] M J Seyoum G E Battese and E M Fleming ldquoTechnicalefficiency and productivity of maize producers in easternEthiopia a study of farmers within and outside the Sasakawa-Global 2000 projectrdquo Agricultural Economics vol 19 no 3 pp341ndash348 1998

Submit your manuscripts athttpwwwhindawicom

Child Development Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Education Research International


Biomedical EducationJournal of



Psychiatry Journal

ArchaeologyJournal of



AnthropologyJournal of


Research and TreatmentSchizophrenia


Urban Studies Research

Population ResearchInternational Journal of


CriminologyJournal of


Aging ResearchJournal of



NursingResearch and Practice

Current Gerontologyamp Geriatrics Research

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

Sleep DisordersHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

AddictionJournal of


Depression Research and TreatmentHindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Geography Journal


Research and TreatmentAutism


Economics Research International


declines Lipton [5] used differentiation in farmmanagementskills as an explanatory variable of farm productivity usingpanel data which allows for household-specific fixed effectsHowever the evidence does not suggest thatmanagerial skillsexplain land productivity

A third explanation of the land productivity is relatedto methodological issues As one of the unsettled issuesLipton [5] mentions that large farms cannot be consideredlinear replicas of small ones Incentives to use inputs varywith production scale that is larger farms use differenttechnologies than small farms Most empirical studies onthe land productivity are based on cross-sectional data andeconometric models can fail to capture nonlinearities andoften impose a common specification (parameters) for thewhole sample Moreover the scale ranges that are allowed inthe models may be too small to measure scale effects [9]

11 Background of the Study Wheat is the second mostimportant crop after maize in Kenya with regard to bothproduction and consumptionUntil the early 1970sKenyawasa net exporter of wheat but currently the country importsabout 60 of the total domestic demand Wheat is grown inthe cooler andmedium-rainfall regions covering the NakuruUasin Gishu Trans-Nzoia and Narok districts and is mostlyrain-fed Production is carried out by small medium andlarge scale farmers numbering about 9000 The industrysupported by about 20 millers contributes 14 and 30 tooverall and cereal GDP respectively The small scale farmersare the majority of the producers but their productionaccounts for only one-quarter of the total wheat producedThe domestic demand for wheat is growing at the rate of 7per year even though production is increasing marginallyWheat and its by-products have gained importance in thehouseholdsrsquo consumption patterns in the last decade In2005 wheat and its by-products accounted for 44 of totalexpenditure of main staples in urban areas up from 35in 1999 [10] Kenya is a high cost wheat producer and forthis reason the country requested the Common Marketfor Eastern and Southern Africa (COMESA) for safeguardmeasures to allow the country to address weaknesses incompetitiveness of the subsector

The increasing domestic demand for wheat is drivenlargely by the rapidly growing population increased urban-ization rising incomes and a change in food preferencesfrom traditional cereals towards wheat and wheat productsThough the country has the potential of increasing theproduction of wheat the sector is faced by several challengesnotably expensive inputs (chemicals seeds and fertilizers)insufficient farm machineries high fuel prices unstableproducer prices and subdivision of large scale farms intosmaller units The small scale farmers are the majorityof the producers but they differ significantly in the useof inputs agronomic practices and productivity from thelarge scale farmers [10] The actual levels of efficiency andsources of inefficiencies among the different size categoriesare however unknown Measuring economic efficiency inwheat production is important for a number of reasonsthe significance of the subsector in terms of farm incomes

to the rural economy regional integration (more openborders especially under COMESA and the East AfricanCooperation) is spawning higher levels of competition thatrequire increased production and distribution efficiency andthe importance of the subsector to the countryrsquos strategiesrelating to achievement of broad food self-sufficiency ruralemployment creation and poverty reduction

Following the experiences of the 200708 global foodcrisis when many food net-importing countries especiallythose in sub-Saharan Africa were unable to secure suppliesfrom the international market the country has embarkedon an aggressive plan to boost its domestic food productionunder the auspices of the Agriculture Sector DevelopmentStrategy (ASDS) This is essentially an import substitutionstrategy that requires increased investments to the agriculturesector reformation of the agricultural research and informa-tion dissemination systems and improving access to creditin order to increase technological innovation particularlyamong the growers of the major cereal grains (maize wheatand rice)

12 Objectives of the Study The analysis of the link betweeneconomic efficiency and farm size in Kenya is partly moti-vated by the increasing pressure on agricultural land thatarises from increasing population and the persistence of highrural populations despite increasing urbanization Agricul-tural land is also under pressure from other sources climatechange that aggravates the already diminished fallow periodsdue to fragmentation in the more populous and high rainfallpotential regions declining soil fertility and the need forequity in land ownership that brings the large wheat farmsinto high prominence The study therefore addresses animportant question of whether or not there are significanteconomic efficiency differences between large scale farms andsmallholder units that are the most likely to predominatein the future as the different pressures mount on the landresource

The general objective of this study is to examine theeffect of farm size on economic efficiency among wheatproducers in Nakuru District and to suggest ways to improvewheat production in the country The specific objectives areto estimate the levels of technical allocative and economicefficiencies among the large and small scale wheat producersto assess the effect of farm size on technical allocative andeconomic efficiency and to determine socioeconomic factorsinfluencing efficiency among small and large scale wheatproducers The following null hypotheses will be tested

H0 farm size has no effect on economic efficiency

H0 none of the identified socioeconomic factors influ-ences efficiency

2 Farm Size and Efficiency

Several studies have investigated the levels of technicaland allocative efficiencies on various farm enterprises withdifferent findings Obare et al [11] applied a dual stochasticefficiency technique and a two-limit Tobit model to analyzeresource allocative efficiency in Irish potato production in











119884119894= 119891 (119883

119894 120573) + 119890

119894 (1)




119890119894= (119881119894minus 119880119894) (2)






2 The 119894th farm




119894from



YTE

CTECOB

CEEO X1

X2

DC

A

B


X1

lowast

X2

lowast





related thus

1205902= 1205902

V + 1205902

119906 (3)

The ratio 120574 = 1205902




119884lowast

119894= 119910119894minus V119894= 119891 (119883

119894 120573) minus 119880

119894 (4)







119894is




119862119894= 119891 (119875

119894 120572 119884lowast

119894 120572) (5)




119883119890



120597119862119894

120597119875119894

= 119883119890

119894(119875119894119884lowast

119894 120573) 119894 = 1 2 119898 inputs (6)



1198751015840

119894119883119905

119894 and 119875

1015840

119894119883119890



TE119894=1198751015840

119894119883119905

119894

1198751015840

119894119883119894

(7a)

EE119894=1198751015840

119894119883119905

119894

1198751015840

119894119883119894

(7b)


AE119894=1198751015840

119894119883119890

119894

1198751015840

119894119883119905

119894

(8)


119894119883119894minus 1198751015840

119894119883119890


119894119883119894minus

1198751015840

119894119883119905

119894) and allocative (1198751015840

119894119883119905

119894minus 1198751015840

119894119883119890

119894) components





119884 = (119871119870) = 119860119871119886119870119887 (9)





ln119884119894= 1205730+ 1205731ln fert

1+ 1205732ln seed

2

+ 1205733ln chem

3+ 1205734ln foliar

4+ 1205735ln hlab

5

+ 1205736ln flab

6+ 119881119894minus 119880119894

(10)




3




119894=


119894= parameters






119862119894= 119891 (119875

119894 120572 119884lowast

119894+ 119880119894) 119894 = 1 2 3 119873 (11)










2

+ 1205723ln pseed

3+ 1205724ln119901chem


5

+ 1205726ln phlab

6+ 1205727pflab7+ 119880119894

(12)


1



3=price of seeds


5= price


7=





119884lowast

119896= 119883119896120573 + 119880

119896 (13)











119878 =1205942119873119875 (1 minus 119875)

1198892 (119873 minus 1)+ 1205942119875 (1 minus 119875) (14)











ln119884119894= 45 + 048 ln seed

119894+ 011 ln fert

119894


119894


119894

(15)






lowast






lowast



119894=







ln119862119894= minus 1507 + 0267 (pseed

119894) + 0010 (pfert

119894)

+ 0012 (pfoliar119894) + 0223 (pchem

119894)


119894)

(16)


119894



119894= the price


119894=
























for purchased seed



5 Conclusions





Farm size 000 (006) 002lowast (190) 001 (137)













Acknowledgments


References










































Psychiatry Journal



















Volume 2014


AddictionJournal of




Geography Journal















119884119894= 119891 (119883

119894 120573) + 119890

119894 (1)




119890119894= (119881119894minus 119880119894) (2)






2 The 119894th farm




119894from



YTE

CTECOB

CEEO X1

X2

DC

A

B


X1

lowast

X2

lowast





related thus

1205902= 1205902

V + 1205902

119906 (3)

The ratio 120574 = 1205902




119884lowast

119894= 119910119894minus V119894= 119891 (119883

119894 120573) minus 119880

119894 (4)







119894is




119862119894= 119891 (119875

119894 120572 119884lowast

119894 120572) (5)




119883119890



120597119862119894

120597119875119894

= 119883119890

119894(119875119894119884lowast

119894 120573) 119894 = 1 2 119898 inputs (6)



1198751015840

119894119883119905

119894 and 119875

1015840

119894119883119890



TE119894=1198751015840

119894119883119905

119894

1198751015840

119894119883119894

(7a)

EE119894=1198751015840

119894119883119905

119894

1198751015840

119894119883119894

(7b)


AE119894=1198751015840

119894119883119890

119894

1198751015840

119894119883119905

119894

(8)


119894119883119894minus 1198751015840

119894119883119890


119894119883119894minus

1198751015840

119894119883119905

119894) and allocative (1198751015840

119894119883119905

119894minus 1198751015840

119894119883119890

119894) components





119884 = (119871119870) = 119860119871119886119870119887 (9)





ln119884119894= 1205730+ 1205731ln fert

1+ 1205732ln seed

2

+ 1205733ln chem

3+ 1205734ln foliar

4+ 1205735ln hlab

5

+ 1205736ln flab

6+ 119881119894minus 119880119894

(10)




3




119894=


119894= parameters






119862119894= 119891 (119875

119894 120572 119884lowast

119894+ 119880119894) 119894 = 1 2 3 119873 (11)










2

+ 1205723ln pseed

3+ 1205724ln119901chem


5

+ 1205726ln phlab

6+ 1205727pflab7+ 119880119894

(12)


1



3=price of seeds


5= price


7=





119884lowast

119896= 119883119896120573 + 119880

119896 (13)











119878 =1205942119873119875 (1 minus 119875)

1198892 (119873 minus 1)+ 1205942119875 (1 minus 119875) (14)











ln119884119894= 45 + 048 ln seed

119894+ 011 ln fert

119894


119894


119894

(15)






lowast






lowast



119894=







ln119862119894= minus 1507 + 0267 (pseed

119894) + 0010 (pfert

119894)

+ 0012 (pfoliar119894) + 0223 (pchem

119894)


119894)

(16)


119894



119894= the price


119894=
























for purchased seed



5 Conclusions





Farm size 000 (006) 002lowast (190) 001 (137)













Acknowledgments


References










































Psychiatry Journal



















Volume 2014


AddictionJournal of




Geography Journal






YTE

CTECOB

CEEO X1

X2

DC

A

B


X1

lowast

X2

lowast





related thus

1205902= 1205902

V + 1205902

119906 (3)

The ratio 120574 = 1205902




119884lowast

119894= 119910119894minus V119894= 119891 (119883

119894 120573) minus 119880

119894 (4)







119894is




119862119894= 119891 (119875

119894 120572 119884lowast

119894 120572) (5)




119883119890



120597119862119894

120597119875119894

= 119883119890

119894(119875119894119884lowast

119894 120573) 119894 = 1 2 119898 inputs (6)



1198751015840

119894119883119905

119894 and 119875

1015840

119894119883119890



TE119894=1198751015840

119894119883119905

119894

1198751015840

119894119883119894

(7a)

EE119894=1198751015840

119894119883119905

119894

1198751015840

119894119883119894

(7b)


AE119894=1198751015840

119894119883119890

119894

1198751015840

119894119883119905

119894

(8)


119894119883119894minus 1198751015840

119894119883119890


119894119883119894minus

1198751015840

119894119883119905

119894) and allocative (1198751015840

119894119883119905

119894minus 1198751015840

119894119883119890

119894) components





119884 = (119871119870) = 119860119871119886119870119887 (9)





ln119884119894= 1205730+ 1205731ln fert

1+ 1205732ln seed

2

+ 1205733ln chem

3+ 1205734ln foliar

4+ 1205735ln hlab

5

+ 1205736ln flab

6+ 119881119894minus 119880119894

(10)




3




119894=


119894= parameters






119862119894= 119891 (119875

119894 120572 119884lowast

119894+ 119880119894) 119894 = 1 2 3 119873 (11)










2

+ 1205723ln pseed

3+ 1205724ln119901chem


5

+ 1205726ln phlab

6+ 1205727pflab7+ 119880119894

(12)


1



3=price of seeds


5= price


7=





119884lowast

119896= 119883119896120573 + 119880

119896 (13)











119878 =1205942119873119875 (1 minus 119875)

1198892 (119873 minus 1)+ 1205942119875 (1 minus 119875) (14)











ln119884119894= 45 + 048 ln seed

119894+ 011 ln fert

119894


119894


119894

(15)






lowast






lowast



119894=







ln119862119894= minus 1507 + 0267 (pseed

119894) + 0010 (pfert

119894)

+ 0012 (pfoliar119894) + 0223 (pchem

119894)


119894)

(16)


119894



119894= the price


119894=
























for purchased seed



5 Conclusions





Farm size 000 (006) 002lowast (190) 001 (137)













Acknowledgments


References










































Psychiatry Journal



















Volume 2014


AddictionJournal of




Geography Journal







ln119884119894= 1205730+ 1205731ln fert

1+ 1205732ln seed

2

+ 1205733ln chem

3+ 1205734ln foliar

4+ 1205735ln hlab

5

+ 1205736ln flab

6+ 119881119894minus 119880119894

(10)




3




119894=


119894= parameters






119862119894= 119891 (119875

119894 120572 119884lowast

119894+ 119880119894) 119894 = 1 2 3 119873 (11)










2

+ 1205723ln pseed

3+ 1205724ln119901chem


5

+ 1205726ln phlab

6+ 1205727pflab7+ 119880119894

(12)


1



3=price of seeds


5= price


7=





119884lowast

119896= 119883119896120573 + 119880

119896 (13)











119878 =1205942119873119875 (1 minus 119875)

1198892 (119873 minus 1)+ 1205942119875 (1 minus 119875) (14)











ln119884119894= 45 + 048 ln seed

119894+ 011 ln fert

119894


119894


119894

(15)






lowast






lowast



119894=







ln119862119894= minus 1507 + 0267 (pseed

119894) + 0010 (pfert

119894)

+ 0012 (pfoliar119894) + 0223 (pchem

119894)


119894)

(16)


119894



119894= the price


119894=
























for purchased seed



5 Conclusions





Farm size 000 (006) 002lowast (190) 001 (137)













Acknowledgments


References










































Psychiatry Journal



















Volume 2014


AddictionJournal of




Geography Journal








119878 =1205942119873119875 (1 minus 119875)

1198892 (119873 minus 1)+ 1205942119875 (1 minus 119875) (14)











ln119884119894= 45 + 048 ln seed

119894+ 011 ln fert

119894


119894


119894

(15)






lowast






lowast



119894=







ln119862119894= minus 1507 + 0267 (pseed

119894) + 0010 (pfert

119894)

+ 0012 (pfoliar119894) + 0223 (pchem

119894)


119894)

(16)


119894



119894= the price


119894=
























for purchased seed



5 Conclusions





Farm size 000 (006) 002lowast (190) 001 (137)













Acknowledgments


References










































Psychiatry Journal



















Volume 2014


AddictionJournal of




Geography Journal










lowast






lowast



119894=







ln119862119894= minus 1507 + 0267 (pseed

119894) + 0010 (pfert

119894)

+ 0012 (pfoliar119894) + 0223 (pchem

119894)


119894)

(16)


119894



119894= the price


119894=
























for purchased seed



5 Conclusions





Farm size 000 (006) 002lowast (190) 001 (137)













Acknowledgments


References










































Psychiatry Journal



















Volume 2014


AddictionJournal of




Geography Journal


















for purchased seed



5 Conclusions





Farm size 000 (006) 002lowast (190) 001 (137)













Acknowledgments


References










































Psychiatry Journal



















Volume 2014


AddictionJournal of




Geography Journal








Farm size 000 (006) 002lowast (190) 001 (137)













Acknowledgments


References










































Psychiatry Journal



















Volume 2014


AddictionJournal of




Geography Journal



































Psychiatry Journal



















Volume 2014


AddictionJournal of




Geography Journal













Psychiatry Journal



















Volume 2014


AddictionJournal of




Geography Journal





Documents

Research Article Analysis of Economic Efficiency and Farm ...downloads.hindawi.com/archive/2014/802706.pdf · Research Article Analysis of Economic Efficiency and Farm Size: A Case