This study examined the relationship between farm size and technical efficiency in small holder cassava production in Ideato LGA of Imo state using data from a 2008 farm-level survey of 90 rural households. The study showed a strong inverse relationship between farm size and technical efficiency. Smaller farms are found to be more technically efficient, than larger farms. These results favour land redistribution policies targeted towards giving lands to the small-holder farmers. Policies of de-emphasizing cassava production in the estate sector while encouraging it in smallholdings will foster equity and efficiency

Agbaeze, C.C

Aniedu, O.C

Asumugha, G.N

Mbanaso, E.N.A

Okoye, B.C

Munich Personal RePEc Archive

MPRA
Munich Personal RePEc Archive
Small is Beautiful: Empirical Evidence of
an Inverse Relationship between Farm
Size and Productive Efficiency in
Small-Holder Cassava Production in
Ideato North LGA of Imo State
B.C Okoye and C.C Agbaeze and G.N Asumugha and O.C
Aniedu and E.N.A Mbanaso
National Root Crops Research Institute, Umudike, Abia State
2009
Online at http://mpra.ub.uni-muenchen.de/17418/
MPRA Paper No. 17418, posted 26. September 2009 06:46 UTC
Small is Beautiful: Empirical Evidence of an Inverse Relationship between  Farm 
Size and Productive Efficiency in Small-Holder Cassava Production in Ideato North 
LGA of Imo State. 
 
Okoye, B.C1., Agbaeze, C.C2., Asumugha, G.N1., Aniedu, O.C1 and Mbanaso, E.N.A1 
 
1National Root Crops Research Institute, Umudike, Abia State. okoyebenjamen@yahoo 
2 Dept. of Agricultural Economics, Micheal Okpara University of Agriculture, Umudike.  
 
Abstract 
This study examined the relationship between farm size and technical efficiency in small 
holder cassava production in Ideato LGA of Imo state using data from a 2008 farm-level 
survey of 90 rural households. The study showed a strong inverse relationship between 
farm size and technical efficiency. Smaller farms are found to be more technically 
efficient, than larger farms. These results favour land redistribution policies targeted 
towards giving lands to the small-holder farmers. Policies of de-emphasizing cassava 
production in the estate sector while encouraging it in smallholdings will foster equity 
and efficiency. 
 
Keywords: Farm Size, Productivity and Technical Efficiency 
. 
 
Introduction 
Cassava is a staple food crop in South-Eastern Nigeria. It contributes about 15% of the 
daily dietary energy intake of most Nigerians and supplies about 70% of the total calories 
intake of about 60 million people in Nigeria (Ezulike et al., 2006). Nigeria is the world’s 
largest producer of cassava, with about 45.75 million metric tones and ranks 2nd after yam 
in extent of production among the root and tuber crops of economic value in Nigeria 
(FAO, 2007). Planting of high yielding and improved varieties has resulted in higher cash 
income, especially in areas with access to improved processing technology and market 
(RMRDC, 2004) 
 
One of the important economic arguments in favor of the equitable distribution of 
farmland is that smaller farms are more productive (Masterson, 2007). The majority of 
studies of agricultural productivity in developing countries support the view that there is 
an inverse relationship between productivity and farm size (Berry and Cline, 1979; 
Barrett, 1996; Heltberg, 1998; Hazarika and Alwang, 2003; Masterson, 2007; Gul Unal, 
2008; Okoye et al., 2007, 2008a and 2008b). Land reform could contribute to improving 
both equity and efficiency in agriculture. One of the most common characteristics of 
developing countries is the large share of agriculture in their economies. This feature 
produces the widely observed inverse size-yield relationship (IR) (Gul Unal, 2008). 
 
Due to its policy implications for employment, efficiency, equity, and sustainability, IR 
has been one of the most important and hotly debated topics in agricultural economics for 
more than 40 years. (Heltberg, 1998 and Gul Unal, 2008). One critique leveled at the 
literature on the productivity-farm size relationship is that the measure used, land 
 2 
productivity, is inappropriate. Because it only compares total output to the size of the 
farm, ignoring other factors of production and inputs, land productivity is said to be, at 
best, an incomplete measure of efficiency (Masterson, 2007). This study will address this 
issue. Small farms have both higher land productivity and equal or better technical 
efficiency. This is true even when controlling for many of the factors literature suggests 
as possible explanations for the inverse relationship (ibid, 2007). 
 
Following the classical definition of Farrell (1957), a firm is considered to be technically 
efficient if it obtains the maximum attainable output given the amount of inputs and the 
technology used. Since technical efficiency is unobservable, it has to be estimated 
somehow. In the parametric approach the typical way to do this is to model inefficiency 
as part of the random term (Aigner et al., 1977). By examining the relationship between 
farm size and technical efficiency in cassava production, this paper aims to discover 
whether smallholder cultivation has increased efficiency. This paper explores the 
relationship between farm size and technical efficiency in small-holder cassava 
production in Ideato LGA of Imo State. 
 
Methodology 
Analytical Procedures 
a. Stochastic Frontier Model 
In our analysis of the data we use the Cobb-Douglas stochastic frontier production 
function. Since the basic stochastic frontier model was first proposed by Aigner et al. 
(1977) and Meeusen and van den Broeck (1977), various other models have been 
suggested and applied in the analysis of cross-sectional and panel data on producers. 
Some models have been proposed in which the technical inefficiency effects in the 
stochastic frontier models are also modeled in terms of other observable explanatory 
variables (Seyoum et al., 1996). The stochastic frontier model is defined thus; 
lnYi = f (lnXi;β) exp (Vi-Ui),     i = 1,2….n ……………..…….(1) 
where the subscript, i, indicates the ith farmer in the sample (I =1, 2, …., 90); ln 
represents the natural logarithm (i.e., logarithm to base e); Y represents the productivity 
of cassava (kg/ha); Xi is the vector of input quantities used by the i-th farm, β is a vector 
of unknown parameters to be estimated, f( ) represents an appropriate function (e.g Cobb- 
Douglas, translog etc).  The Vi’s are assumed to be independent and identically 
distributed random errors having N(o, σv2)  distribution; and the Ui’s are non-negative 
random variables, called technical inefficiency effects, which are assumed to be 
independently distributed such that Ui is defined by the truncation (at zero) of the 
N(o,σu2) distribution (i.e. half-normal distribution) or have exponential distribution. The 
maximum-likelihood estimates for all the parameters of the stochastic frontier and 
inefficiency model, defined by Eq. (1), are simultaneously obtained by using the 
program, FRONTIER Version 4.1 (Coelli, 1996). The technical efficiency of production 
of the ith farmer in the appropriate data set, given the levels of his inputs, is defined by 
Technical efficiency (TE) = Yi/Yi*  
= f (Xi;β) exp (Vi-Ui) / f (Xi,β) exp (Vi) = exp (-Ui) ………………………..………... (2) 
Where Yi is the observed productivity and Yi* is the frontier productivity. The technical 
efficiency of a farmer is between 0 and 1 and is inversely related to the level of the 
technical inefficiency effect. The technical efficiencies can be predicted using the 
 3 
FRONTIER program which calculates the maximum-likelihood estimator of the predictor 
for Eq. (2) that is based on its conditional expectation (Battese and Coelli, 1988).  
 
b. Empirical Model 
The stochastic frontier model for farmers is defined by the the Cobb-Douglas type 
defined as follows: 
In Yi = β0 + β1 In X1 + β2 In X2 + β3 In X3 + β4 In X4 + β5 In X5  + Vi-Ui …........……..(3) 
Where Y is productivity of cassava in kg/ha., X1 is farm size in hectares, X2 is labour 
input in mandays, X3 is fertilizer input in kg, X4 is planting material in bundles and X5 is 
capital input in naira made up of depreciation charges on farm tools and equipment, 
interest on borrowed capital and rent on land. β0-β5 are regression parameters to be 
estimated while Vi and Ui are as defined earlier.  
 
Determinants of Technical Efficiency 
In order to determine factors contributing to the observed technical efficiency in cocoyam 
production, the following model was formulated and estimated jointly with the stochastic 
frontier model in a single stage maximum likelihood estimation procedure using the 
computer software Frontier Version 4.1 (Coelli, 1996). 
TEi:=  ao+a1Z1+a2Z2+a3Z3+a4Z4+a5Z5+a6Z6  …… ………………………………...…...(4) 
Where TEi, is the technical efficiency of the i-th farmer; Z1 is farmers age in years; Z2 is 
farmers level of education in years; Z3 is no of extension contacts; Z4 is household size; 
Z5 is farm size in hectares and Z6 is square of farm size in hectares while a1-a6 are 
parameter estimates. 
 
Data 
The study was carried out in Ideato North L.G.A. of Imo State using a two-stage 
randomized sampling technique. At the first stage, three circles were randomly selected 
from the LGA. At the second stage, 30 farmers were randomly selected form each circle 
using the community list of farmers from the ADP for detailed study. This gave a total of 
90 farming households. Data were collected by means of well structured questionnaires 
on their production activities in terms of inputs, output, and socio-economic 
characteristics for the year 2008. 
 
Results and Discussion 
Average Statistics of Cocoyam Farmers: The average statistics of the sampled cassava 
farmers are presented in Table 1. On the average, a typical cassava farmer in the LGA is 
48 years old, with 10 years of education. The average cassava farmer cultivated 1.47 ha, 
made an average of 1 extension contact in the year, used about 257.08kg of fertilizer and 
68 bundles of cassava stems, spent about N 1542.12 on capital inputs, employed 145 
mandays of labour and produced an output of 4635kg of cassava. The results of the 
analysis show that individual farm level technical efficiency was 75%.  
  
Table 1: Average Statistics of Cassava Farmers in Ideato LGA of Imo State, 
Nigeria. 
S/N Variables Mean Maximum   Minimum 
Value 
 4 
o    Value Value  
1 Farm size (ha) 1.4695 2.60 0.25 
2 Labour (mandays) 144.8167 251.00 39.00 
3 Fertilizer input (kg) 257.0833         96.40 0.00 
4 Cocoyam setts (kg)                250.25               500.00             50.00 
5 Capital input (N) 1542.119 11200.00 355.00 
6 Age (yrs) 48.40 65.00                     32.00 
7 Education (yrs)                  10.2667                 18.00                     4.00 
8 Extension contact 1.43 4.00 0.00 
9 Planting materials 
(bundles) 
68.00 20.00 135.00 
10 Output (kg)                          4635.92             9200.00                      1195.00 
11 Technical Efficiency(%) 75.00 91.00 35.00 
Source: Survey data, 2008 
Table 2 presents weighted maximum-likelihood estimates of the stochastic production 
frontier. The productivity of cassava significantly increases at 1% level in the value of 
output per hectare, with increase in labour and fertilizer. Productivity, however, appears 
to decrease with farm size and was significant at 1%. The coefficients for depreciation in 
capital inputs and planting materials had a negative and positive relationship with 
productivity but were not significant. The elasticity of production of farmers was 
estimated to be less than one (0.53). Decreasing returns to scale would explain the inverse 
relationship (Masterson, 2007). This is perhaps not surprising, given that the mean farm 
size for cassava in the area is 1.4ha. 
 
The estimated variance (σ2) is statistically significant at 1% indicating goodness of fit and 
the correctness of the specified distribution assumptions of the composite error term. 
Gamma (γ) is estimated at 0.962 and is statistically significant at 1% indicating that 
96.2% of the total variation in cassava output is due to technical inefficiency. 
 
Table 1: Estimated Cobb-Douglas Stochastic Frontier Production Function for  
              Cassava Farmers in Ideato LGA of Imo State 
Variables Parameters Coefficients Standard 
Error 
t-value 
Production 
factors 
    
Constant term βo 5.1554 0.8496 6.0674*** 
Farm size β1 -0.2016 -0.0322 -6.2433*** 
Labour β2 0.5811 0.1642 3.5382*** 
Fertilizer β3 0.1875 0.0341 5.4670*** 
Planting 
Materials 
β4 0.2694 0.2412 1.1169 
Depreciation β5 -0.3050 0.5620 -0.5437 
Elasticity  0.5314   
 5 
Efficiency 
factors 
    
Constant term a0 3.8444 1.6839 2.2830** 
Age a1 -0.2827 0.0451 -6.2673*** 
Levels of 
Education 
a2 -0.1214 0.1472 0.8248 
Extension 
Contact 
a3 0.9775 1.5198 0.6431 
Experience a4 0.1774 0.3359 0.5281 
Farm size  a5 -6.1462 1.4591 -4.2122*** 
Farm size2 a6 -2.6657 0.0548 -4.8672*** 
Diagnostic 
statistics 
    
Total Variance 
(Sigma 
squared) 
σ
2
 0.1973 0.0259 7.589*** 
VarianceRatio 
(Gamma)) 
γ 0.9620 0.0463 20.7807*** 
LR Test  22.9902   
Log 
Likelihood 
Function 
 -45.3918   
 Source:  Computed from frontier 4.1 MLE results/Surveys data, 2008, *** 
and ** are significant levels at 1.0% and 5.0%. 
 
Sources of Technical Efficiency 
 
The estimated determinants of technical efficiency in cassava production as presented in 
Table 2 shows that age, farm size and farm size interaction had a negative and significant 
effect on efficiency at 1% level of probability. We expect age to have a positive 
relationship since age is used as a proxy for experience. However, old age might pose 
disadvantages in agriculture because most of the work is physically demanding and also 
because older household heads might be too conservative to try new, more efficient 
techniques. This is in line with the findings of Ajibefun and Daramola (2003); Ajibefun 
and Aderionla (2004); Okoye, 2007; 2008a and 2008b). 
 
One reason why small farms produce more value per hectare is because land utilization is 
much higher on smaller farms since large farms cultivate less land in proportion to their 
size, i.e., larger farms have more idle land. Thus, even if small and large farms produce 
equal value of output per hectare cultivated, this does not disprove the “IR puzzle.” (Gul 
Unal, 2008). Doubling the farm size also results in decreased technical efficiency. 
Research in developing countries has centered round the ‘inverse hypothesis’ that smaller 
farms are more productive because land is used more intensively (Bharadwaj, 1974 and 
Cornia, 1985). 
 
Conclusion 
Given the inverse productivity/efficiency-size relationship in agriculture, what is needed 
for increased productivity and efficiency in agriculture and overall growth is land 
redistribution supported by technical and financial assistance for farmers. Policy 
conclusion to be drawn from these results is that policies favorable to large-scale farms 
 6 
may foment overall growth in the agricultural sector, but they will do less than nothing to 
combat the problem of rural poverty. They will contribute neither to the well being of 
small farmers nor to employment opportunities for landless peasants, since the larger 
farms are so capital intensive. It is no stretch to say that the argument for redistribution of 
land is bolstered by this study. Giving land to smaller farms will increase overall 
productivity and efficiency, as well as improve the welfare of the small and landless 
peasantry. The questions of how to achieve this goal is outside the scope of this study. 
The results also call for policies aimed at encouraging new entrants especially the youths 
to cultivate cassava. 
 
 
References 
Aigner, D., Lovell, C., Schmidt, P., (1977). Formulation and estimation of stochastic 
frontier production function models. J. Econometrics 6:21–37. 
Ajibefun, I. A and Daramola, A.G. (2003) Efficiency of Micro Enterprises in the 
Nigerian Economy. AERC Research paper 134. African Economic Research 
Consortium, Nairobi 
Ajibefun, I.A and Aderinola, E.A (2004) Determinants of Technical Efficiency and 
Policy Implication in Traditional Agricultural Production: Empirical Study of 
Nigerian Food Crop Farmers. Final Report Presentation at Bi-annual Research 
Workshop of African Economic Research Consortium. Nairobi, Kenya. 
Barret, C.B. 1996. “On Price Risk and the Inverse Farm Size-Productivity Relationship.” 
Journal of Development Economics 51(369): 193–215. 
Battese, G.E., Coelli, T.J., (1988). Prediction of firm-level technical efficiencies with 
generalised frontier production function and panel data. Journal of Econometrics 
38:387-399. 
Berry, A., and W. Cline. (1979). Agrarian Structure and Productivity in Developing 
Countries. Baltimore: Johns Hopkins University. 
Bharadwaj, K. (1974). Production Conditions in Indian Agriculture: A Study Based on 
Farm Management Surveys. Cambridge, UK: Cambridge University Press. 
Coelli, V.J (1996) Guide to Frontier Version 4.1: A Computer Program for Stochastic 
Frontier Production and Cost Function Estimation. Department of Economics, 
University of New England, Armidale, Australia. 
Cornia, G.A. 1985. “Farm Size, Land Yields, and the Agricultural Production Function: 
An Analysis for Fifteen Developing Countries.” World Development 13(4): 513–
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Ezulike, T. O., Nwosu, K. I., Udealor, A. and Eke- Okoro, O. N. (2006). Guide to 
Cassava Production in Nigeria. Extension Guide No. 16. National Root Crops 
Research Institute, Umudike, Nigeria. 10 pp. 
FAO (2007). Food and Agriculture Organisation, Database Results. 
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Statistics Society. Series A General Vol: 120, Part III. 
Gul Unal, F (2008). Small Is Beautiful: Evidence of an Inverse Relationship between 
Farm Size and Yield in Turkey. Working Paper No. 551, The Levy Economics 
Institute P.O. Box 5000 Annandale-on-Hudson, NY 12504-5000. 
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Hazarika, G and Alwang, J. (2003) Access to credit, plot size and cost inefficiency 
among smallholder tobacco cultivators in Malawi. Agricultural Economics 29:99-
109 
Heltberg, R. 1998. “Rural Market Imperfections and the Farm Size-Productivity 
Relationship: Evidence from Pakistan.” World Development 26(10): 1807–26. 
Masterson, T (2007) “Productivity, Technical Efficiency, and Farm Size in Paraguayan 
Agriculture”. The Levy Economics Institute of Bard College. Working Paper No. 
490, Feb. 2007. 
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prodduction function with composite error. International Economic Review , Vol 
18(2) pp: 123-134.  
Okoye, B.C, Onyenweaku, C.E and Asumugha, G.N. (2007). Allocative Efficiency of 
Small-Holder Cocoyam Farmers in Anambra State, Nigeria. The Nigerian 
Agricultural Journal. Vol.38 (2007). Pp. 70-81 
Okoye, B.C., C. E. Onyenweaku, O. O. Ukoha, G. N. Asumugha and O. C. Aniedu 
(2008). Determinants of Labour Productivity on Small-Holder Cocoyam farms in 
Anambra State, Nigeria. Academic Journals Scientific Research and Essay. Vol 
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Holder Cocoyam Farmers in Anambra State, Nigeria: Implications for 
Agricultural Extension Policy. Paper presented at the 13th Annual Conference of 
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Micheal Okpara University of Agriculture, Umudike. April, 8-11, 2008 
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Small is Beautiful: Empirical Evidence of an Inverse Relationship between Farm Size and Productive Efficiency in Small-Holder Cassava Production in Ideato North LGA of Imo State

Munich RePEc Personal Archive

MPRAMunich Personal RePEc ArchiveSmall is Beautiful: Empirical Evidence ofan Inverse Relationship between FarmSize and Productive Efficiency inSmall-Holder Cassava Production inIdeato North LGA of Imo StateB.C Okoye and C.C Agbaeze and G.N Asumugha and O.CAniedu and E.N.A MbanasoNational Root Crops Research Institute, Umudike, Abia State2009Online at http://mpra.ub.uni-muenchen.de/17418/MPRA Paper No. 17418, posted 26. September 2009 06:46 UTCSmall is Beautiful: Empirical Evidence of an Inverse Relationship between  Farm Size and Productive Efficiency in Small-Holder Cassava Production in Ideato North LGA of Imo State.  Okoye, B.C1., Agbaeze, C.C2., Asumugha, G.N1., Aniedu, O.C1 and Mbanaso, E.N.A1  1National Root Crops Research Institute, Umudike, Abia State. okoyebenjamen@yahoo 2 Dept. of Agricultural Economics, Micheal Okpara University of Agriculture, Umudike.   Abstract This study examined the relationship between farm size and technical efficiency in small holder cassava production in Ideato LGA of Imo state using data from a 2008 farm-level survey of 90 rural households. The study showed a strong inverse relationship between farm size and technical efficiency. Smaller farms are found to be more technically efficient, than larger farms. These results favour land redistribution policies targeted towards giving lands to the small-holder farmers. Policies of de-emphasizing cassava production in the estate sector while encouraging it in smallholdings will foster equity and efficiency.  Keywords: Farm Size, Productivity and Technical Efficiency .  Introduction Cassava is a staple food crop in South-Eastern Nigeria. It contributes about 15% of the daily dietary energy intake of most Nigerians and supplies about 70% of the total calories intake of about 60 million people in Nigeria (Ezulike et al., 2006). Nigeria is the world’s largest producer of cassava, with about 45.75 million metric tones and ranks 2nd after yam in extent of production among the root and tuber crops of economic value in Nigeria (FAO, 2007). Planting of high yielding and improved varieties has resulted in higher cash income, especially in areas with access to improved processing technology and market (RMRDC, 2004)  One of the important economic arguments in favor of the equitable distribution of farmland is that smaller farms are more productive (Masterson, 2007). The majority of studies of agricultural productivity in developing countries support the view that there is an inverse relationship between productivity and farm size (Berry and Cline, 1979; Barrett, 1996; Heltberg, 1998; Hazarika and Alwang, 2003; Masterson, 2007; Gul Unal, 2008; Okoye et al., 2007, 2008a and 2008b). Land reform could contribute to improving both equity and efficiency in agriculture. One of the most common characteristics of developing countries is the large share of agriculture in their economies. This feature produces the widely observed inverse size-yield relationship (IR) (Gul Unal, 2008).  Due to its policy implications for employment, efficiency, equity, and sustainability, IR has been one of the most important and hotly debated topics in agricultural economics for more than 40 years. (Heltberg, 1998 and Gul Unal, 2008). One critique leveled at the literature on the productivity-farm size relationship is that the measure used, land  2 productivity, is inappropriate. Because it only compares total output to the size of the farm, ignoring other factors of production and inputs, land productivity is said to be, at best, an incomplete measure of efficiency (Masterson, 2007). This study will address this issue. Small farms have both higher land productivity and equal or better technical efficiency. This is true even when controlling for many of the factors literature suggests as possible explanations for the inverse relationship (ibid, 2007).  Following the classical definition of Farrell (1957), a firm is considered to be technically efficient if it obtains the maximum attainable output given the amount of inputs and the technology used. Since technical efficiency is unobservable, it has to be estimated somehow. In the parametric approach the typical way to do this is to model inefficiency as part of the random term (Aigner et al., 1977). By examining the relationship between farm size and technical efficiency in cassava production, this paper aims to discover whether smallholder cultivation has increased efficiency. This paper explores the relationship between farm size and technical efficiency in small-holder cassava production in Ideato LGA of Imo State.  Methodology Analytical Procedures a. Stochastic Frontier Model In our analysis of the data we use the Cobb-Douglas stochastic frontier production function. Since the basic stochastic frontier model was first proposed by Aigner et al. (1977) and Meeusen and van den Broeck (1977), various other models have been suggested and applied in the analysis of cross-sectional and panel data on producers. Some models have been proposed in which the technical inefficiency effects in the stochastic frontier models are also modeled in terms of other observable explanatory variables (Seyoum et al., 1996). The stochastic frontier model is defined thus; lnYi = f (lnXi;β) exp (Vi-Ui),     i = 1,2….n ……………..…….(1) where the subscript, i, indicates the ith farmer in the sample (I =1, 2, …., 90); ln represents the natural logarithm (i.e., logarithm to base e); Y represents the productivity of cassava (kg/ha); Xi is the vector of input quantities used by the i-th farm, β is a vector of unknown parameters to be estimated, f( ) represents an appropriate function (e.g Cobb- Douglas, translog etc).  The Vi’s are assumed to be independent and identically distributed random errors having N(o, σv2)  distribution; and the Ui’s are non-negative random variables, called technical inefficiency effects, which are assumed to be independently distributed such that Ui is defined by the truncation (at zero) of the N(o,σu2) distribution (i.e. half-normal distribution) or have exponential distribution. The maximum-likelihood estimates for all the parameters of the stochastic frontier and inefficiency model, defined by Eq. (1), are simultaneously obtained by using the program, FRONTIER Version 4.1 (Coelli, 1996). The technical efficiency of production of the ith farmer in the appropriate data set, given the levels of his inputs, is defined by Technical efficiency (TE) = Yi/Yi*  = f (Xi;β) exp (Vi-Ui) / f (Xi,β) exp (Vi) = exp (-Ui) ………………………..………... (2) Where Yi is the observed productivity and Yi* is the frontier productivity. The technical efficiency of a farmer is between 0 and 1 and is inversely related to the level of the technical inefficiency effect. The technical efficiencies can be predicted using the  3 FRONTIER program which calculates the maximum-likelihood estimator of the predictor for Eq. (2) that is based on its conditional expectation (Battese and Coelli, 1988).   b. Empirical Model The stochastic frontier model for farmers is defined by the the Cobb-Douglas type defined as follows: In Yi = β0 + β1 In X1 + β2 In X2 + β3 In X3 + β4 In X4 + β5 In X5  + Vi-Ui …........……..(3) Where Y is productivity of cassava in kg/ha., X1 is farm size in hectares, X2 is labour input in mandays, X3 is fertilizer input in kg, X4 is planting material in bundles and X5 is capital input in naira made up of depreciation charges on farm tools and equipment, interest on borrowed capital and rent on land. β0-β5 are regression parameters to be estimated while Vi and Ui are as defined earlier.   Determinants of Technical Efficiency In order to determine factors contributing to the observed technical efficiency in cocoyam production, the following model was formulated and estimated jointly with the stochastic frontier model in a single stage maximum likelihood estimation procedure using the computer software Frontier Version 4.1 (Coelli, 1996). TEi:=  ao+a1Z1+a2Z2+a3Z3+a4Z4+a5Z5+a6Z6  …… ………………………………...…...(4) Where TEi, is the technical efficiency of the i-th farmer; Z1 is farmers age in years; Z2 is farmers level of education in years; Z3 is no of extension contacts; Z4 is household size; Z5 is farm size in hectares and Z6 is square of farm size in hectares while a1-a6 are parameter estimates.  Data The study was carried out in Ideato North L.G.A. of Imo State using a two-stage randomized sampling technique. At the first stage, three circles were randomly selected from the LGA. At the second stage, 30 farmers were randomly selected form each circle using the community list of farmers from the ADP for detailed study. This gave a total of 90 farming households. Data were collected by means of well structured questionnaires on their production activities in terms of inputs, output, and socio-economic characteristics for the year 2008.  Results and Discussion Average Statistics of Cocoyam Farmers: The average statistics of the sampled cassava farmers are presented in Table 1. On the average, a typical cassava farmer in the LGA is 48 years old, with 10 years of education. The average cassava farmer cultivated 1.47 ha, made an average of 1 extension contact in the year, used about 257.08kg of fertilizer and 68 bundles of cassava stems, spent about N 1542.12 on capital inputs, employed 145 mandays of labour and produced an output of 4635kg of cassava. The results of the analysis show that individual farm level technical efficiency was 75%.    Table 1: Average Statistics of Cassava Farmers in Ideato LGA of Imo State, Nigeria. S/N Variables Mean Maximum   Minimum Value  4 o    Value Value  1 Farm size (ha) 1.4695 2.60 0.25 2 Labour (mandays) 144.8167 251.00 39.00 3 Fertilizer input (kg) 257.0833         96.40 0.00 4 Cocoyam setts (kg)                250.25               500.00             50.00 5 Capital input (N) 1542.119 11200.00 355.00 6 Age (yrs) 48.40 65.00                     32.00 7 Education (yrs)                  10.2667                 18.00                     4.00 8 Extension contact 1.43 4.00 0.00 9 Planting materials (bundles) 68.00 20.00 135.00 10 Output (kg)                          4635.92             9200.00                      1195.00 11 Technical Efficiency(%) 75.00 91.00 35.00 Source: Survey data, 2008 Table 2 presents weighted maximum-likelihood estimates of the stochastic production frontier. The productivity of cassava significantly increases at 1% level in the value of output per hectare, with increase in labour and fertilizer. Productivity, however, appears to decrease with farm size and was significant at 1%. The coefficients for depreciation in capital inputs and planting materials had a negative and positive relationship with productivity but were not significant. The elasticity of production of farmers was estimated to be less than one (0.53). Decreasing returns to scale would explain the inverse relationship (Masterson, 2007). This is perhaps not surprising, given that the mean farm size for cassava in the area is 1.4ha.  The estimated variance (σ2) is statistically significant at 1% indicating goodness of fit and the correctness of the specified distribution assumptions of the composite error term. Gamma (γ) is estimated at 0.962 and is statistically significant at 1% indicating that 96.2% of the total variation in cassava output is due to technical inefficiency.  Table 1: Estimated Cobb-Douglas Stochastic Frontier Production Function for                Cassava Farmers in Ideato LGA of Imo State Variables Parameters Coefficients Standard Error t-value Production factors     Constant term βo 5.1554 0.8496 6.0674*** Farm size β1 -0.2016 -0.0322 -6.2433*** Labour β2 0.5811 0.1642 3.5382*** Fertilizer β3 0.1875 0.0341 5.4670*** Planting Materials β4 0.2694 0.2412 1.1169 Depreciation β5 -0.3050 0.5620 -0.5437 Elasticity  0.5314    5 Efficiency factors     Constant term a0 3.8444 1.6839 2.2830** Age a1 -0.2827 0.0451 -6.2673*** Levels of Education a2 -0.1214 0.1472 0.8248 Extension Contact a3 0.9775 1.5198 0.6431 Experience a4 0.1774 0.3359 0.5281 Farm size  a5 -6.1462 1.4591 -4.2122*** Farm size2 a6 -2.6657 0.0548 -4.8672*** Diagnostic statistics     Total Variance (Sigma squared) σ2 0.1973 0.0259 7.589*** VarianceRatio (Gamma)) γ 0.9620 0.0463 20.7807*** LR Test  22.9902   Log Likelihood Function  -45.3918    Source:  Computed from frontier 4.1 MLE results/Surveys data, 2008, *** and ** are significant levels at 1.0% and 5.0%.  Sources of Technical Efficiency  The estimated determinants of technical efficiency in cassava production as presented in Table 2 shows that age, farm size and farm size interaction had a negative and significant effect on efficiency at 1% level of probability. We expect age to have a positive relationship since age is used as a proxy for experience. However, old age might pose disadvantages in agriculture because most of the work is physically demanding and also because older household heads might be too conservative to try new, more efficient techniques. This is in line with the findings of Ajibefun and Daramola (2003); Ajibefun and Aderionla (2004); Okoye, 2007; 2008a and 2008b).  One reason why small farms produce more value per hectare is because land utilization is much higher on smaller farms since large farms cultivate less land in proportion to their size, i.e., larger farms have more idle land. Thus, even if small and large farms produce equal value of output per hectare cultivated, this does not disprove the “IR puzzle.” (Gul Unal, 2008). Doubling the farm size also results in decreased technical efficiency. Research in developing countries has centered round the ‘inverse hypothesis’ that smaller farms are more productive because land is used more intensively (Bharadwaj, 1974 and Cornia, 1985).  Conclusion Given the inverse productivity/efficiency-size relationship in agriculture, what is needed for increased productivity and efficiency in agriculture and overall growth is land redistribution supported by technical and financial assistance for farmers. Policy conclusion to be drawn from these results is that policies favorable to large-scale farms  6 may foment overall growth in the agricultural sector, but they will do less than nothing to combat the problem of rural poverty. They will contribute neither to the well being of small farmers nor to employment opportunities for landless peasants, since the larger farms are so capital intensive. It is no stretch to say that the argument for redistribution of land is bolstered by this study. Giving land to smaller farms will increase overall productivity and efficiency, as well as improve the welfare of the small and landless peasantry. The questions of how to achieve this goal is outside the scope of this study. The results also call for policies aimed at encouraging new entrants especially the youths to cultivate cassava.   References Aigner, D., Lovell, C., Schmidt, P., (1977). Formulation and estimation of stochastic frontier production function models. J. Econometrics 6:21–37. Ajibefun, I. A and Daramola, A.G. (2003) Efficiency of Micro Enterprises in the Nigerian Economy. AERC Research paper 134. 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Coelli, V.J (1996) Guide to Frontier Version 4.1: A Computer Program for Stochastic Frontier Production and Cost Function Estimation. Department of Economics, University of New England, Armidale, Australia. Cornia, G.A. 1985. “Farm Size, Land Yields, and the Agricultural Production Function: An Analysis for Fifteen Developing Countries.” World Development 13(4): 513–34 Ezulike, T. O., Nwosu, K. I., Udealor, A. and Eke- Okoro, O. N. (2006). Guide to Cassava Production in Nigeria. Extension Guide No. 16. National Root Crops Research Institute, Umudike, Nigeria. 10 pp. FAO (2007). Food and Agriculture Organisation, Database Results. Farrel, J.M (1957) The Measurement of Production Efficiency. Journal of Royal Statistics Society. Series A General Vol: 120, Part III. Gul Unal, F (2008). Small Is Beautiful: Evidence of an Inverse Relationship between Farm Size and Yield in Turkey. Working Paper No. 551, The Levy Economics Institute P.O. 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Small is Beautiful: Empirical Evidence of an Inverse Relationship between Farm Size and Productive Efficiency in Small-Holder Cassava Production in Ideato North LGA of Imo State

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