Dyson Ligomba Dissertation

TECHNICALEFFICIENCY OF SOY BEAN PRODUCTION IN SELECTED DISTRICTS OF
CENTRALMALAWI
BY
DYSON LIGOMBA
Cell: 0882541656/0996375994
Email: ligombadyson@gmail.com
A RESEARCH PROJECT REPORT SUBMITTED TO THE FACULTY OF DEVELOPMENTAL
STUDIES IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR A BACHELOR OF
SCIENCE DEGREE IN AGRICULTURAL ECONOMICS
LILONGWE UNIVERSITY OF AGRICULTURE AND NATURALRESOURCES
DEPARTMENT OF AGRICULTURALAND APPLIED ECONOMICS
BUNDA CAMPUS
LILONGWE
MAY, 2015

i
Declaration
I hereby declare that the text of this dissertation is my own work and has never been
submitted by anyone for an academic award.
SIGNATURE:
___________________________________________________
DATE:
_________________________________________________

ii
Certificate of approval
We certify that this dissertation has been submitted to Lilongwe University of Agriculture
and Natural Resources with our approval as a fulfillment required for the degree of Bachelor
of Science degree in Agricultural Economics.
SUPERVISOR : MR A MAGANGA
SIGNATURE : __________________________________________
DATE : ___________________________________________
HEAD OF DEPARTMENT : DR MAR PHIRI
SIGNATURE : ___________________________________________
DATE : ___________________________________________
DEAN OF FACULTY : DR B MAONGA
SIGNATURE : ___________________________________________
DATE : ___________________________________________

iii
Dedication
I dedicate this piece of work to my dear mother and young brother Ruth and Charles
respectively, for your entire support throughout my rigorous academic years, wishing you a
long life.

iv
Acknowledgements
Firstly I wish to thank the almighty God for giving me life. He has been so generous to me; I
will never be able to thank him enough. The preparation of this important document would not
also have been possible without the support from others. Worth mention is the commitment
and dedication of my Project Supervisor Mr. Assa Maganga whose help, stimulating
suggestions and encouragement have always been at my disposal. I wish you continual success.
I would like to express my gratitude to the entire staff of the Department of Agricultural and
Applied Economics at Lilongwe University of Agriculture and Natural Resources for their
constructive advice and technical support in the production of this work.
Lastly, I should also acknowledge all authors whose works I have appropriately recognized in
this paper. It would not have been easy without your work.

v
Abstract
Agriculture remains the corner stone of most African economies, including Malawi. There has
been specific focus by government in Malawi on promotion of legumes regarding the high
demand prevailing on both domestic and international market as raw materials in oil
producing industries. The aim of this study was to explore the socio-economic and institutional
factors influencing technical efficiency of soy bean (glycine max) production in some selected
districts of central Malawi.
The study used both stratified and simple random sampling to come up with the required
sample size. To determine sample size of each stratum, proportion probability sampling (PPS)
was employed and simple random sampling (SRS) was used to come up with the 300 farmers
from all the four EPAs. The data was collected during the 2013/14 cropping season, both a
Translog stochastic frontier model and a multiple linear regression model were fitted in the
estimation of technical efficiency levels as well as the determinants of technical efficiency
levels.
The study found that individual farm level technical efficiency ranged between 21.28% and
96.40% with an average of 78.91%. This implies that farmers in the study area have a shortfall
of 21.09%, suggesting that there is still room for further increase in soy bean output under the
same technology level and without increasing the level of inputs used.
The study identified socio-economic and institutional factors resulting to technical efficiency
differentials, these were gender, farmer club membership, credit access, education, use of
modern soy bean seed and extension contacts. These factors were found to improve farm level
efficiency with female farmers being more efficient than male farmers. This entails that by
enhancing farmer’s access to credit, extension, and modern seed technical efficiency of soy
bean farmer is more likely to improve.
The study went further to estimate returns to scale (RTS) experienced by farmers in the study
area. Farmers in the study area were found to experience increasing returns to scale with the
use of available land, seed and labour under the same technology level. This implies that with
the enhancement of socio-economic and institutional factors any increase in the use land,
labour and seed will double soy bean output.
Key words: Soy bean, Production, Technical efficiency, Translog stochastic frontier model
Returns to scale.

vi
List of abbreviations and acronyms
AEDOs : Agricultural Extension Development Offices
ASWAP : Agricultural Sector Wide Approach
DEA : Data Envelopment Analysis
EPA : Extension Planning Area
GDP : Gross Domestic Product
IITA : International Institute of Tropical Agriculture
ICRISAT : International Crops Research Institute for the Semi-Arid Tropics
MoAFS : Ministry of Agriculture and Food Security
MoFDP : Ministry of Finance Development Planning
NASFAM : National Small Farmers Association of Malawi
TSFM : Translog Stochastic Frontier Model
RTS : Returns to scale
PPS : Probability Proportion Sampling
SRS : Simple Random Sampling
VIF : Variance Inflation Factor

vii
Table of Contents
Declaration...............................................................................................................................................i
Certificate of approval ............................................................................................................................ii
Dedication..............................................................................................................................................iii
Acknowledgements................................................................................................................................iv
Abstract...................................................................................................................................................v
List of abbreviations and acronyms .......................................................................................................vi
List of figures.......................................................................................................................................viii
List of tables...........................................................................................................................................ix
1.0 Introduction.................................................................................................................................1
1.1 Background Information...............................................................................................................1
1.2 Statement of the problem..................................................................................................................2
1.2.1 Justification of the study ................................................................................................................2
1.3 Study objectives............................................................................................................................4
1.3.1 Underlying Objective.............................................................................................................4
1.3.2 Specific Objectives ....................................................................................................................4
1.4 Hypothesis.....................................................................................................................................4
2.0 Literature review...............................................................................................................................5
2.1 Definition of technical efficiency .................................................................................................5
2.1 Stochastic frontier analysis approach of estimating technical efficiency .....................................5
2.3 Related studies on efficiency estimation using parametric methods.............................................6
2.4 Related studies on efficiency estimation using non parametric methods......................................7
2.5 Previous Econometric models on efficiency analysis...................................................................8
3.0 Methodology...................................................................................................................................10
3.1 Study Area ..................................................................................................................................10
3.2 Sampling procedure and data collection .....................................................................................10
3.3 Data analysis...............................................................................................................................11
3.3.1 Analytical framework ..........................................................................................................11
3.3.2 Empirical model specification .............................................................................................12
4.1 Characteristics of soy bean farmers ............................................................................................13
4.3 The determinants of soy bean output ..........................................................................................15
4.4 Socio-economic and institutional determinants of technical efficiency......................................17
4.5 Hypotheses testing ......................................................................................................................19
4.6 Model diagnostic tests.................................................................................................................19
4.7 Technical efficiency levels of soy bean farmers.........................................................................20
5.0 Conclusion ......................................................................................................................................26
6.0 Policy recommendations.................................................................................................................26
References.............................................................................................................................................28

viii
List of figures
Figure 1: Average technical efficiency and modern seed adoption
Source: Computed from field survey data, 2014 .....................................................................22
Figure 2: Average technical efficiency and gender of the farmer
Figure 3: Average technical efficiency and education level of the farmer
Figure 4: Average technical efficiency and land allocated to soy bean production
Figure 5: Average technical efficiency and extension contact
Figure 6: Average technical efficiency and household size

ix
List of tables
Table 1: Number of soy bean farmers sampled per EPA.........................................................10
Table 2: Descriptive Statistics of soy bean farmers.................................................................14
Table 3: Frequency of Soy bean farmer characteristics...........................................................14
Table 4: Maximum Likelihood estimates of the Translog Stochastic Frontier Model............16
Table 5: Determinants of technical efficiency of Soy bean farmers........................................17
Table 6: Tests of Hypothesis....................................................................................................19
Table 7: Technical efficiency levels of farmers.......................................................................20
Table 8: Technical efficiency levels with respect to EPAs......................................................21

1
1.0 Introduction
1.1 Background Information
Soya beans (Glycine max) is one of the more important grain legume crops in the world. It has
a very high protein content, reasonable oil content, and potential to fix nitrogen well in excess
of its own requirements. It thus can assist in soil improvement leading to a higher level of
sustainable agriculture, with minimum inputs (Siregar, Wen Sumaryanto, 2003). There is
increasing demand for the crop both domestically and on the international market. In Malawi,
the industry sector demands more soy bean but supply is still very low to meet demand, the
prominent companies demanding more soy bean in the country include Rab processors limited
and Tambala food products etc. (ICRISAT, 2013).
Soybean yields in the country still remain low as farmers obtain 40 percent less (800 kg/ha) on
average than the potential yield of 2000-2500 kg/ha (ICRISAT, 2013). Smallholder farmers
allocate small portions of land to soy bean production which is even sometimes intercropped
with cereals.
The Malawi government through the Agricultural Sector Wide Approach strategizes to
improve agricultural productivity in order to enhance food self-sufficiency and combat
malnutrition problems particularly in the rural areas of the country. Among other things
emphasis is on crop diversification which includes production of various legumes in particular
soy bean which is an important and affordable protein source. Soy bean is predominantly grown
at the country’s central region mostly by smallholder farmers.
In the main soy bean producing districts of Lilongwe and Dowa, the study found that
smallholder farmers on average cultivate soy bean 0.52 acres, farmers commonly recycle seed
from the previous growing seasons which are among other soy bean problems. Following low
productivity of soybean production in the country it is therefore necessary to understand the
level of technical efficiency of soy bean farmers and other factors contributing to their state of
inefficiency.
Technical efficiency is a component of production efficiency and is derived from the
production function. Production efficiency consists of technical efficiency and allocative
efficiency. Production efficiency represents the efficient resource input mix for any given
output that minimizes the cost of producing that level of output or equivalently, the
combination of inputs that for a given monetary outlay maximizes the level of production

2
(Forsund et al., 1980). Technical efficiency reflects the ability of the firm to maximize output
for a given set of resource inputs while allocative efficiency reflects the ability of the firm to
use the inputs in optimal proportions given their respective prices and the production
technology (Chirwa, 2007).
It is therefore the principal aim of this study to establish the technical efficiency levels and
sources of inefficiency of soy bean farmers in central Malawi by employing the Translog
stochastic production frontier model so as useful policy instruments can be derived to modify
the current situation and improve productivity among soy bean farmers in the country.
1.2 Statement of the problem
Research results show that soybeans are well adapted for production in all agro-ecological
zones of Malawi (NASFAM, 2013). However, Soybean yields are still low as farmers obtain
40 percent less (800 kg/ha) on average than the potential yield of 2000-2500 kg/ha. Increased
production through area expansion may not be possible in most parts of the country because of
population pressure on the land. On average Soybean yield increased from 961kg/ha in 2010
to 982kg/ha in 2011 and then decreased to 970kg/ha in 2012. This implies that there are
production problems locking the sector (ICRISAT, 2013). The available inputs are not
productive enough to carter for home consumption and to sale in order to access farm inputs
and other basic needs (Shively, 2001).
Therefore, given a situation where smallholder farmers have inadequate, infertile prime land
with increasing population size that even primarily depends on small-scale farming
characterized by inadequate farm inputs, there is therefore need for soybean smallholder
farmers to improve on technical efficiency in their production in order to maximize
productivity of the available input resources.
1.2.1 Justification of the study
According to the Malawi Growth Development Strategy (MGDS II), the agricultural sector
faces a number challenges including over dependence on rain-fed farming, low adoption of
improved technologies, weak private sector participation, and lack of investment in
mechanization. Evidence from past studies also suggests that levels of technical efficiency
among the majority of Malawian smallholder farmers are low to moderate (Chirwa, 2007).
The government of Malawi implemented a soybean seed subsidy program to promote
production since the 2007/08 season. There has been a presidential initiative on the promotion

3
of grain legumes (soybean, groundnuts, pigeon pea and beans) production and marketing aimed
at doubling legume production to generate income for farmers and foreign exchange for the
country. Additionally, Malawi has intentions to implement the “Greenbelt Initiative” with the
aim of increasing production and productivity of agricultural crops through the development
of small-scale and large-scale irrigation (MoAFS, 2012). However, these are policies targeting
agricultural production at national level. On the other hand, smallholder soybean farmers
continue to experience low yields regardless of farm inputs and technology levels being used.
Therefore this study was conducted to establish major constraints causing efficiency
differentials in smallholder farmers’ soy bean production as well as providing
recommendations for policy makers to come up with effective policies which will enhance
soybean production and boost productivity which will in turn make soybean production move
from subsistence to commercial production and enhance both domestic and international trade
through exports.

4
1.3 Study objectives
1.3.1 Underlying Objective
The study aimed primarily to assess the technical efficiency of soybean production among
smallholder farmers.
1.3.2 Specific Objectives
1. To estimate the efficiency level of soybean production in the study area
2. To determine socio-economic and institutional factors causing efficiency differentials
among smallholder soybean farmers.
3. To determine the effect of socio-economic and institutional factors on technical efficiency
of soybean smallholder farmers in the study area.
4. To provide policy implications of socio-economic and institutional factors on technical
efficiency of soybean smallholder farmers.
1.4 Hypothesis
The following hypotheses were formulated for this research:
1. Smallholder soy bean farmers are technically efficient and their socio-economic as well
as institutional factors do not influence technical efficiency of soy bean production.
2. The Cobb-Douglas specification is an adequate representation of the stochastic frontier
model.
3. Soy bean farmers have constant returns to scale.

5
2.0 Literature review
A considerable number of studies have been conducted to estimate technical efficiency levels
in the agricultural and other sectors of the economy. This section discusses a review of literature
related to this study.
2.1 Definition of technical efficiency
According to literature, technical efficiency is derived from the production function.
Production efficiency consists of technical efficiency and allocative or factor price efficiency.
Production efficiency represents the efficient resource input mix for any given output that
minimizes the cost of producing that level of output or, equivalently, the combination of inputs
that for a given monetary outlay maximizes the level of production (Chirwa, 2007). Allocative
efficiency reflects the ability of the firm to use the inputs in optimal proportions given their
respective prices and the production technology while technical efficiency of an individual
farm is defined in terms of the ratio of the observed output to the corresponding frontier
output, conditioned on the level of inputs used by the farm. Technical inefficiency is
therefore defined as the amount by which the level of production for the farm is less
than the frontier output (Ingosi, 2005).
2.1 Stochastic frontier analysis approach of estimating technical efficiency
The literature identifies alternative approaches to measuring technical efficiency which are
categorized into non-parametric frontiers and parametric frontiers. Non-parametric frontiers do
not specify a functional form on the production frontiers and do not make assumptions about
the error term. While others have used linear programming approaches; the commonly used
non-parametric approach has been the data envelopment analysis (DEA), however they do not
provide a general relationship relating output and input. Parametric frontier approaches specify
a functional form on the production function and make assumptions about the data. The most
common functional forms include the Cobb–Douglas, constant elasticity of substitution and
Translog production functions.
The other distinction is between deterministic and stochastic frontiers. Deterministic frontiers
assume that all the deviations from the frontier are a result of firms’ inefficiency, on the other
hand, a research conducted by Maganga (2012) reported that the stochastic production frontier
is significantly different from the deterministic frontier in that the stochastic frontier approach,
unlike the other parametric frontier measures, makes allowance for stochastic errors arising
from random effects and measurement errors.

6
The stochastic frontier model decomposes the error term into a two sided random error that
captures the random effects outside the control of the farm and the one sided efficiency
component. Therefore, in real world situations technical efficiency of production is subjected
to both random effects and other measurable factors and as such the stochastic frontier is
usually a preferred measure of frontier analysis compared to the deterministic approaches.
2.3 Related studies on efficiency estimation using parametric methods
Various studies have been conducted on technical efficiency using the stochastic frontier
approach. For example Siregar and Sumaryanto (2003) determined technical efficiency in
Brantas river basin in Indonesia. Their study showed that technical efficiency of soybeans
production in the sites was high around 83 percent. However, analysis failed to identify
determinants of technical efficiency because none of the parameters in the study was
significant.
Amos (2007) conducted a study on the production and technical efficiency of smallholder
cocoa farmers in Nigeria. Farmers were observed to be experiencing increasing returns to scale.
The efficiency levels ranged between 0.11 and 0.91 with a mean of 0.72. This indicated that
there is plenty of room for farmers to improve on their efficiency levels. The major contributing
factors to efficiency were age of farmers, level of the education of household head and family
size.
Chirwa (2007) studied the sources of technical efficiency among smallholder maize farmers in
southern Malawi, results showed that many smallholder maize farmers are technically
inefficient, with mean technical efficiency scores of 46 percent and technical efficiency scores
as low as 8 percent. The mean efficiency levels were lower but comparable to those obtained
in other African countries whose means range from 55 percent to 79 percent. The results also
support the hypotheses that technical efficiency increases with the use of hybrid seeds and club
membership. One of the variables used for capturing adoption of technology showed that the
application of fertilizers does not explain the variations in technical inefficiency. This may
imply that most farmers using these technologies use them inappropriately on small land
holdings.
In examining the technical efficiency of alternative land tenure systems among smallholder
farmers, Kuriuki et al (2008) conducted a study in Kenya to identify determinants of
inefficiency with the objective of exploring land tenure policies that would enhance efficiency
in production. The study was based on the understanding that land tenure alone was not enough

7
to indicate the levels of efficiency of individual farms. Socio economic factors such as gender,
education and farm size were expected to be important determinants of efficiency.
Other factors such as education status of household head, access to fertilizers, and group
participation were also found to significantly influence technical efficiency.
A study by Weir and Knight (2000) analyzed the impact of education externalities on
production and technical efficiency of rural farmers, and found evidence that the source of
externalities to schooling is in the adoption and spread of innovations which shift out the
production frontier. Nonetheless, one limitation of their study is that they only investigated the
levels of schooling as the only source of technical efficiency.
Adzawla et al (2000), reported that farmers tended to be less inefficient as their farm sizes
increased. Thus, farmers with larger farms were more technically efficient than their
counterparts with smaller farms. This is in contrast with the findings of Tsimpo (2010) and
Gal et al (2009), who found technical efficiency to be higher for small farms. In his study,
Adzawla, found that age, education and extension variables were insignificant. However, in
the studies by Nebal et al (2010), Gal et al (2009) and Kouser et al (2010), the age variable had
a negative significant effect on technical efficiency. Similarly, while education had a negative
significant impact on technical efficiency in Gal et al (2009), it positively influenced technical
efficiency in Kouser et al (2010). However, most of these studies did not focus much on some
important institutional factors such as the family size, access to extension services, farmer
group participation and access to capital credit which also have influence on the farm level
technical efficiency.
2.4 Related studies on efficiency estimation using non parametric methods
Non parametric methods of determining efficiency have been used in many research works.
These methods do not specify a functional form on the production frontiers and do not make
assumptions about the error term. The commonly used methods include the linear programming
approaches and the data envelopment analysis (DEA). A study conducted by Helfand and
Levine (2000) explored the determinants of technical efficiency and the relationship between
farm size and efficiency, in the Centre-West of Brazil. The efficiency measures were regressed
on a set of explanatory variables which included farm size, type of land tenure, composition of
output, access to institutions and indicators of technology and input usage. The relationship
between farm size and efficiency was found to be non-linear. Efficiency was first falling and
then started rising with farm size. Further, they found that the type of land tenure, access to

8
institutions and markets, and modern inputs were found to be important determinants of the
differentials in efficiency across farms.
In their study Rios and Shively (2005) also looked at the relationship between farm size
and efficiency. They focused on the efficiency of smallholder coffee farms in Vietnam by using
the two stage analysis approach. In the first step, technical and cost efficiency measures were
calculated using DEA. In the second step, Tobit regression was used to identify factors
correlated with technical and cost inefficiency. Research results indicated that small farms
were less efficient than large farms and inefficiencies observed on small farms appeared
to be related, in part, to the scale of investments in irrigation infrastructure.
While the non-parametric approaches have the advantage of determining efficiency in
multiple input-multiple output scenarios and no requirement of the explicit mathematical form
for the production function, on the other hand they are weak in that efficiency differentials due
to randomness is neglected in their application.
A study by Ray (2001), used linear programming to measure efficiency for a sample of 63 West
Bengal farms. The efficiency measures were decomposed into technical efficiency and
informational efficiency. The latter was defined as the ratio between optimal output given the
existing technology and optimal output when additional technology information is available.
Univariate and multivariate statistical tests were conducted to compare the performance of
three farm groups classified according to size. The results revealed that, although there was no
significant difference in technical efficiency across farm size groups, informational efficiency
was very low for the small farms. The author suggested that marked improvements could be
attained by the diffusion of information about the standard crop production technology.
2.5 Previous Econometric models on efficiency analysis
A variety of econometric models for measuring efficiency have been used extensively in
research. Bettese and Coelli (1995), Tijani (2005), Kibaara (2005), Amaza and Maurice (2005)
applied the Translog stochastic frontier model to estimate technical efficiency using input
approach, where output is the dependent variable expressed as function of production inputs
and some composite error term. In their application of the stochastic approach a Cobb Douglas
logarithmic function was adopted resulting in estimation of the technical inefficiency equation.
The estimated Cobb-Douglas stochastic frontier production function was assumed to specify
the technology of the farmers.

9
Basnayake and Gunaratne (2002) used both the Cobb-Douglas and the Translogarithmic
models in the estimation of technical efficiency and it’s determinants in the tea small holding
sector in the Mid Country Wet Zone of Sri Lanka. The study reported that the specified
econometric models have the ability to represent a technology frontier in a simple mathematical
form and also assume non-constant returns to scale.
Caracota, (2010) conducted an econometric analysis of Indian manufacturing sector, in her
study she discovered that the Cobb Douglas specification is nested in the Translog model,
therefore, the Translog functional specification with two inputs labour and capital was used.
Greene (2007) analysed the different econometric approaches in estimating technical
efficiency, he observed that the Ordinary Least Square approach was not the best approach for
frontier analysis due to the duality in the random error term of the stochastic frontier models.
He therefore, recommended the maximum likelihood Estimation approach which assumes
random error term to be exponentially, half-normally and gamma distributed. Eventually, the
stochastic error term was well accounted for by the maximum likelihood estimation method.

10
3.0 Methodology
3.1 Study Area
The study was conducted in four EPAs; Chitekwere and Nyanja of Lilongwe district;
Nachisaka and Madisi of Dowa district. These areas were chosen purposively because of their
popularity in soybean production where most farmers grow soybean under farmer group
supervision. The farmer groups either access inputs through credits or purchase them by
themselves, the groups are just responsible for monitoring production, attainment of bargaining
power on input and output prices and they are a good medium used by extension officers to
reach the majority of the farmers in the areas. However, all the crop husbandry practices are
carried out by individual farmers at farm level.
3.2 Sampling procedure and data collection
Cross-sectional data was collected from 300 soybean farmers during the 2013/14 cropping
season through administration of a pre-tested structured questionnaire. The data collected
included the plot level output of soybeans produced, inputs used in the production process
(land, seed, labour) on each plot, socio economic characteristics of the farmers as well as plot
specific characteristics.
Both stratified and simple random sampling were employed to come up with the required
sample size. To determine sample size of each stratum PPS was used and simple random
sampling was used to come up with the 300 individual farms from all the strata. Table 1 below
summarizes the sample sizes obtained from each EPA in the two sampled districts.
Table 1: Number of soy bean farmers sampled per EPA
District EPA SAMPLE PER EPA PERCENTAGE (%)
Lilongwe Chitekwere 90 30
Nyanja 62 20.67
Dowa
Nachisaka 90 30
Madisi 58 19.33
TOTAL 300 100

11
3.3 Data analysis
The data obtained were analyzed using both descriptive and inferential statistics. Means,
standard deviations, percentages, graphs and frequency counts were used in analyzing socio-
economic characteristics of the farmers, input and output variables and the distribution of
efficiency levels.
3.3.1 Analytical framework
The analytical framework used to test the above hypotheses is based on efficiency measures
according to Tsimpo (2010) the fundamental idea underlying all efficiency measures is that the
output of goods and services per unit input must be attained without waste. There are two basic
method of measuring technical efficiency: the classical and the frontier approach. There are
controversies and dissatisfaction as well as some short comings with the classical approach.
This has led to the development of the advanced econometric and statistical techniques by some
other economists for the analysis of efficiency related issues. Both techniques have in common
the concept of frontier which is regarded as the measure of efficiency as such this study adopted
the frontier approach.
A stochastic frontier model is theoretically defined as:
𝑌𝑖 = 𝑓 (𝑋𝑖
′
; Ϣ) + 𝑣𝑖 − 𝑢𝑖 , 𝑖 = 1,2, … 𝑛
Where;
𝑌𝑖 ; Soybean output level of the ith
farmer (in natural logarithm).
𝑋𝑖 ; is a (1 x w) vector of farm inputs (in natural logarithm).
Ϣ ; is a (w x 1) vector of parameters to be estimated.
𝑽𝒊 − 𝑼𝒊 = 𝜺𝒊 ; is a composite error term
𝑽𝒊; measures the random variation in output (𝒀𝒊) due to factors outside the control of the farm
such as weather and 𝑼𝒊 ; on the other hand measures the factors (within the control of the
farmer) responsible for that farmer’s inefficiency.
According to Bettese and Coelli (1995) the technical efficiency of a given firm (at a given time
period) is defined by the ratio of its mean production (conditional on its level of factor inputs
and farm-effects) to the corresponding mean production if the farm utilizes its levels of inputs
most efficiently.

12
This gives;
𝑇𝐸𝑖 =
𝑦 𝑖
𝑦𝑖
∗ =
𝑓(𝑋 𝑖;Ϣ)exp(𝑉𝑖−𝑈 𝑖)
𝑓(𝑋 𝑖;Ϣ)𝑒𝑥𝑝𝑉𝑖
= exp(−𝑢𝑖),
𝑌𝑖
∗
= exp(𝑌𝑖)
Where the numerator is the soybean output of the ith
farmer and the denominator is the potential
or average soybean output of the efficient farmers in the soybean production.
The technical efficiency index (TEi) is bound between 0 and 1, such that 0 < TEi ≤ 1 (Cabrera
et al., 2010). When technical efficiency is equal to one (TEi = 1), it indicates that a farmer is
producing on the frontier with the available resources and technology as such the farmer is said
to be technically efficient. If TEi is less than the frontier (TEi < 1), it implies that the farmer is
not producing on the production frontier for a given technology and resources. Such a farmer
is said to be technically inefficient. Aigner et al. (1977) suggested that the maximum-likelihood
estimates of the parameters of the model be obtained in terms of the parameterization,
𝜎2
= 𝜎𝑣
2
+ 𝜎 𝑢
2
and the estimate of the ratio of the standard deviation of the inefﬁciency
component to the standard deviation of the idiosyncratic component, λ=
𝜎 𝑢
𝜎𝑣
⁄ .
On the other hand, Battese and Corra (1977) proposed the parameter, 𝛾 =
𝜎 𝑢
2
𝜎𝑠
2⁄ to be used,
because it has values between zero and one, whereas the λ parameter could be any non-negative
value. The parameter, 𝛾 is associated with the variance of the inefficiency effects. When close
to one it can be concluded that there are technical inefficiency effects associated with the
production process of the farmer.
3.3.2 Empirical model specification
The collected data were analysed using the stochastic frontier approach as it provides estimates
of the efficiency level of each farmer and the various variables associated with the farmer’s
efficiency. The Translog stochastic production frontier model was used to estimate the
production function, considering its flexibility as opposed to the Cobb-Douglas specification.
The empirical Translog stochastic frontier model is defined as follows:
ln 𝑌𝑖 = Ϣ0 ∑ Ϣ𝑖
𝑛
𝑖=1 ln 𝑋𝑖𝑗 + ∑ Ϣ𝑖
𝑛
𝑖=1 ln 𝑋𝑖𝑗
2
+
1
2
∑ ∑ Ϣ𝑖ln 𝑋𝑖𝑗 ∗ ln𝑛
𝑖=1
𝑛
𝑖=1 𝑋𝑖𝑗 + 𝜀𝑖

13
Where X1 is farm size (acres), X2 is labour (man days), X3 is seed quantity (kilograms),
Ϣ0 … Ϣ 𝑛 are estimated parameters and 𝜀𝑖 is composite error term that measures the random
variation in output due to factors beyond farmer’s control and the variation due to farmer’s own
inefficiency.
A multiple linear regression model was used to determine the farm level factors contributing
to inefficiency of a soy bean farmer. The model can be expressed as;
𝑈𝑖 = 𝛺0 + ∑ 𝛺 𝑘
8
𝑘=1
𝑋𝑖𝑘 + 𝑒𝑖
Where 𝑈𝑖 represents technical inefficiency level of the ith
farmer, 𝛺0 … 𝛺 𝑘 are estimated
parameters of the multiple regression model, 𝑋𝑖𝑘 represents a vector of socio-economic and
institutional explanatory variables which include; Age measured in number of years, Education
in number of years in formal education, Experience in number of years a farmer is into soy
bean production, Extension in number of extension visits, land in acres, household size in
number of individuals whereas Gender, seed type and credit access are dummy variables in the
model in which case seed type represents the use of modern seed or not by the farmer.
4.0 Results and discussion
4.1 Characteristics of soy bean farmers
The descriptive statistics of the sampled farmers are summarized in Table 2. On the average, a
typical soy bean farmer in the study area is 45 years old, with an average of 5 years in formal
education. There is a range of 11 in the number of members of the farmers’ family given an
average household size of 5. Soy bean farmers in the area cultivated the crop for an average of
5 years with a land holding size of 0.52 acres in the 2013/14 cropping season. This farm size
produced an average output of 114.56kg of soy bean using 10.18kg of seeds and 24 man days
of labour. Finally, on average the farmers were visited five times by extension agents during
the farming season.
Table 3 summarizes other basic characteristics of the farmer, it was observed that 48.67 percent
represented female soy bean farmers regardless of whether they were married or not, this was
based on the person actively taking care of soy bean production operations. Among all the
sampled farmers 45.67 percent were affiliates of farmer clubs that had a special focus on soy

14
bean production. It was however, encouraging to observe that 59 percent of farmers were
adopters of hybrid or modern soy bean seed varieties, this was enhanced by the farmers’ access
to credit in form of seed and cash through farmer clubs which were supported by both the
government under the presidential initiative on the promotion of grain legumes and ICRISAT
in which case 46 percent of farmers in the study area accessed the credit.
Table 2: Descriptive Statistics of soy bean farmers
Table 3: Frequency of Soy bean farmer characteristics
Variable Frequency Percentage (%)
Club Membership
(a) Member 137 45.67
(b) Non member 163 53.33
Gender
(a) Male 154 51.33
(b) Female 146 48.67
Modern seed Adoption
(a) Adopter 177 59
(b) Non Adopter 123 41
Credit Access
(a) Got credit 138 46
(b) No credit 162 54
Variable Units Mean Standard
deviation
Minimum Maximum
Age Years 45.81 14.88 18 76
Household
size
No. of persons 5.15 2.16 1 12
Education Years 5.19 3.54 0 16
Experience Years 10.81 3.67 4 25
Extension No. of visits 5.22 2.06 0 13
Farm size Acres 0.52 0.44 0.1 2.97
Labour Man days 23.58 17.17 9 35
Seed kgs 10.18 16.84 3.87 22
Output kgs 114.56 147.14 15.72 1350

15
4.3 The determinants of soy bean output
Table 4 presents the maximum likelihood estimation results of the Translog stochastic frontier
model. It can be observed that the estimated coefficients of all the first order terms were
significant. Also, while labour and seed had the expected positive sign, farm size had a negative
sign. In the case of the squared variables, there is a different scenario, as both farm size and
seed squared maintain a negative sign, labour squared had a positive sign. In general, the
squared terms show the relationship between the factors with output on their continuous usage.
Thus, in the case of farm size it can be said that in the initial stages of its use, less of it must be
employed if output is to be increased while in the continuous use of seed more of it tends to
decrease output. The opposite is true with labour where both in the initial and later stages of
production more of it increased output.
The interaction terms entail the substitutability or complementarity of the factors, whereby a
significant positive coefficient of an interaction term means that the two inputs are
complements, whereas substitutes would have a negative term.
From the table, the interaction between farm size and seed is significant and positive implying
that both inputs must be increased in order to increase output. A similar explanation applies to
the interaction between farm size and labour. To the contrary, the negative interaction between
seed and labour is negative, which suggests that while one must be increased, the other must
be decreased in order to increase output.
It is observed in table 4 that the Maximum Likelihood (ML) estimate of γ is 0.724 with
estimated standard error of 0.120. The value of γ is greater than 0 and less than 1 in which case
it entails that other factors beyond farmer’s control are contributing to variations observed in
soy bean output in the study area. In addition, the γ estimate implies that 72 percent of the
variation in output comes from farmer’s technical inefficiency with only 28 percent from the
stochastic random shocks.

16
Table 4: Maximum Likelihood estimates of the Translog Stochastic Frontier Model
Variable Parameter Coefficient Standard error T-ratio
Production factors
Constant Ϣ0 -5.645** 0.586 -9.64
Lnland Ϣ1 -4.003** 0.270 -14.81
Lnseed Ϣ2 5.970** 0.345 17.29
lnlabour Ϣ3 2.403** 0.216 11.12
½(lnland)2
Ϣ4 -0.485** 0.039 -12.41
½(lnseed)2
Ϣ5 -0.433** 0.087 -4.99
½(lnlabour)2
Ϣ6 0.166** 0.044 3.77
lnland*lnseed Ϣ7 2.343** 0.185 12.65
lnland*lnlabour Ϣ8 .9182** 0.124 7.40
lnseed*lnlabour Ϣ9 -2.186** 0.208 -10.48
Variance Parameters
Sigma-squared (𝝈 𝒗
𝟐
+ 𝝈 𝒖
𝟐
) σ2
0.153*** 0.031 2.03
Gamma (𝝈 𝒖
𝟐
/(𝝈 𝒗
𝟐
+ 𝝈 𝒖
𝟐
)) Γ 0.724* 0.120 2.53
Log-likelihood -47.651
Number of observations N 300
*, **, *** imply significance at 1%, 5% and 10% level respectively.
Source: Survey data, 2014

17
4.4 Socio-economic and institutional determinants of technical efficiency
In Table 5 socio-economic and institutional variables responsible for farmer’s technical
inefficiency are presented. The variables with negative coefficients have negative relation with
technical inefficiency but positive relation with technical efficiency and vice versa.
Table 5: Determinants of technical efficiency of Soy bean farmers
Variable Units parameter Coefficient Standard error
Constant 𝛺0 0.314** 0.1074
Farm size Acres 𝛺1 0.032** 0.0083
Age Years 𝛺2 -0.124 0.0324
Education Years 𝛺3 -0.004** 0.0016
Experience Years 𝛺4 0.002** 0.0007
Gender 1=male, 0=female 𝛺5 0.018** 0.0081
Household size no. of persons 𝛺6 -0.012 0.0021
Extension No. of visits 𝛺7 -0.013** 0.0019
Modern seed 1=Adopter,0=non adopter 𝛺8 -0.018 ** 0.0092
Farmer club 1=member,0=non
member
𝛺9 -0.006** 0.0088
Credit access (1=access, 0=no access) 𝛺10 -0.003*** 0.0068
R-squared 0.6619
F-value 56.59**
Observations n 300
*, **, *** imply significance at 1%, 5% and 10% respectively
(source: survey data, 2014)
The model F value is significant at 5% implying that the overall model is significant and the
coefficient of multiple determination (R2
= 0.6619) implies that approximately 66.19 percent
of the total variation observed in technical inefficiency can be attributed to the socio-economic
and institutional factors in the model.

18
The coefficient of farm size (total land cultivated in the season) was positive and significant at
5% showing that an increase in farm size for soy bean cultivation increased levels of technical
inefficiency holding other factors constant. The significant positive relationship implies that
optimal combination of factors of production is achieved on smaller plots than on larger plots.
In addition, large plots proved difficult in terms of management of husbandry practices by most
of the smallholder farmers as they also shared their time with other income generating
activities.
The coefficient of education is negative and statistically significant at 5% implying that the
more years a farmer stayed in formal school the more technically efficient he/she was in soy
bean production, other factors constant. This could be because education enhances the
acquisition and utilization of information on improved technologies such as modern seed
varieties. The coefficients of both age and household size showed a negative relation with
inefficiency, however, being an old farmer with a large family was not enough to significantly
contribute to efficiency as their coefficients were not statistically significant.
An unexpected case was noted where a statistical positive relationship existed between
experience and inefficiency, this indicated that technical inefficiency increases with
experience, holding other factors constant. This can be explained by most of the experienced
farmers used to recycle soy bean seed and they tend to ignore advice given by extension agents.
The farmers who adopted modern soy bean seed were found to be more efficient as evidenced
by the statistical significant negative relationship of the seed adoption variable. The coefficient
of extension was statistically significant and had the expected negative relationship with
inefficiency implying that frequent visits by extension agents increased the farmers’ levels of
technical efficiency.
The coefficient of gender was significant with a positive sign implying that female farmers are
more technically efficient in production, holding other factors constant. This can be explained
by the tendency of most male farmers ignoring taking part in farmer clubs where females
registered more than males, this denies most male farmers access to extension services as the
extension agents normally deliver their services to organized farmer groups in the area.
The study also found that farmer club membership negatively contributed to inefficiency, this
can be explained by normal delivery of extension services to farmer groups from which only
affiliates have access hence, enabling them to be more productive in soy bean production. A

19
positive statistical significant coefficient of credit access showed that efficiency increased for
those farmers that received credit in form of seed and cash from the efforts of government
under the presidential initiative on the promotion of grain legume as well ICRISAT.
4.5 Hypotheses testing
In the study three main hypotheses were tested. The first was that soy bean farmers in the study
area are technically efficient in their production and any variation is due to random effects (H0=
γ = Ω1 +…+ Ω10 = 0), in other ways there are no inefficiency effects in the model which implies
that all the inefficiencies were due to factors outside the control of the farmers. This was
rejected since the estimated likelihood-ratio X2
test statistic (17.05) was significantly different
from zero at all significance levels. This entails that socio-economic and institutional factors
were also responsible for the inefficiencies.
The second hypothesis was that the Cobb-Douglas representation is an adequate representation
of the stochastic production frontier model. This was also rejected under an overall test in which
showed significant results and as such the Translog Stochastic frontier model was used to
estimate the technical efficiency of the farmers.
The final null hypothesis was that soy bean farmers in the study have constant returns to scale,
this hypothesis was tested and rejected at 5% alpha level when actually the study found soy
bean farmers experiencing increasing returns to scale in the study area.
Table 6: Tests of Hypothesis
Null Hypothesis Test statistic (X2) F-test Decision
H0 : γ = Ω1 +…+ Ω10 = 0 17.05** Rejected
H0: Ϣ4 +…+ Ϣ9 = 0 242.40** Rejected
Returns to scale
Estimation
Coefficient T-value Decision
H0: Ϣ1 +… + Ϣ3 =1 3.370 8.73** Rejected
** Hypothesis rejected at 5% significance level
Therefore, the study revealed that soy bean farmers in the study area are experiencing
increasing returns to scale, this follows a post estimation analysis conducted where the null
hypothesis that soy bean farmers are producing at constant returns to scale was rejected (Table
6).
4.6 Model diagnostic tests
The adoption of a multiple linear regression model called for some diagnostic tests in order to
ensure that there are no problems of non-constant error variance (heteroskedasticity) and

20
multicollinearity. These are common problems associated with Ordinary Least Square method
whereas maximum likelihood estimation is robust to heteroskedasticity and not
multicollinearity problem. The Breusch-Pagan / Cook-Weisberg test for heteroskedasticity was
ran and proved the absence of heteroskedasticity in the multiple regression model following a
chi-square value of 2.46 and a p-value of 0.1166, indicating a constant error variance, hence
absence heteroskedasticity in the model.
On the other hand, variance inflation factor was post estimated in which an average factor of
0.93 showed that multicollinearity problem did not affect the model
4.7 Technical efficiency levels of soy bean farmers
The study also aimed at finding out the efficiency levels of the soy bean farmers in the study
area. It can be observed in table 7 that on average a typical soy bean farmer was 78.91%
technically efficient in the 2013/14 cropping season, this entails that on average 78.91% of soy
bean output was obtained from the given mix of production inputs by the farmers. This is an
indication that soy bean output had fallen by 21.09%, otherwise, there is a potential of
increasing output by 21.09%. through the adoption of efficient farming practices. However,
the study found that majority of farmers (56%) have technical efficiency levels ranging from
81 to 96.40 percent.
Table 7: Technical efficiency levels of farmers
Variable Mean (%) Standard deviation Minimum Maximum
Efficiency 78.91 9.81 21.28 96.40
Range (%) Frequency (n) Percentage (%)
20 - 40 4 1.3
41 - 60 10 3.3
61 - 80 118 39.3
81 above 168 56.0
Total 300 100

21
Technical efficiency levels were also estimated for respective EPAs in the study area, from
Table 8, it can be observed that among all the sampled EPAs technical efficiency level was
found to be high in Nyanja EPA where soy bean farmers were 80.83% followed by Nachisaka
EPA with farmers at 79.52% while Chitekwere EPA came third with 77.98% technical
efficiency and finally Madisi EPA had the lowest estimated technical efficiency level of
77.36%.
Table 8: Technical efficiency levels with respect to EPAs
EPA Mean Technical Efficiency (%)
Chitekwere 77.98
Madisi 77.36
Nachisaka 79.52
Nyanja 80.83
The figures (1-6) complement the relationship between average technical efficiency and the
socio-economic factors of the farmers. It can be observed that farmers who adopted modern
soy bean seed had an average technical efficiency level of 84% while those who used local or
recycled varieties their efficiency level was at 72%. This suggests that modern seed varieties
made a contribution towards technical efficiency of the farmers.

22
Figure 1: Average technical efficiency and modern seed adoption
Source: Computed from field survey data, 2014
From figure 2, it is evident that among soy bean farmers female farmers are more technically
efficient having an average of 84% efficiency than male farmers who are 74% efficient. This
could be due to the fact that males are usually engaged in other non-farm income generating
activities with more others growing tobacco as their main cash crop while females have special
interest in growing soy bean as evidenced by their increased membership in farmer groups with
particular focus on legume production.
Figure 2: Average technical efficiency and gender of the farmer
Figure 3, depicts the relationship between average efficiency and farmer’s years spent in formal
education. It is evident that the more year a farmer spent in formal education the higher the

23
efficiency level. This is true as seen earlier, the education variable in the econometric model
was significant.
Figure 3: Average technical efficiency and education level of the farmer
Figure 4 confirms the estimation results that farmers who had relatively large farms (1.96 acres
above) had lower efficiency (74%) than those who had smaller farms (0.07 – 1.95 acres); the
average technical efficiency of the latter being 79%. This could be because most farmers with
relatively larger farms had used most of their land to grow tobacco during the season therefore,
even though they grew soy bean but much focus was given to the husbandry of the cash crop.
This finding is contrary to that found by Adzawla in his efficiency study of cotton production
in Yendi municipality, northern Ghana who found efficiency levels increasing with farm size.
Those with smaller landholding sizes had high efficiency levels, this might be the result of a
well-focused attention in terms of allocation of labor and timely completion of husbandry
practices in their small landholdings.

24
Figure 4: Average technical efficiency and land allocated to soy bean production
As depicted in Figure 5 below, farmers who received between 11 and 13 extension visits during
the growing season were more technically efficient (92%) as compared to those who made
extension contacts between 6 to 10 and had an efficiency level of 85% followed by those with
virtually no contact to only 5 contacts and having an efficiency level of 75%.
Figure 5: Average technical efficiency and extension contact
Finally, Figure 6 indicates that technical efficiency reduced with increasing household size.
Farmers with family size of between 1 and 4 had the highest average technical efficiency level
of 85%, followed by those with between 5 and 8 (77%) and then those with size between 9 and
12 (64%). However, household size was not significant enough to influence farmer’s technical
efficiency (Table 5)

25
Figure 6: Average technical efficiency and household size

26
5.0 Conclusion
The main objective of this study was to assess the technical efficiency of soy bean producers
in the central region of Malawi, (Dowa and Lilongwe) with a link to farm and farmer
characteristics. According to results from Translog stochastic frontier model, technical
efficiency levels of farmers in the area were found to be relatively high with an overall average
efficiency level of 78.91% and 56% of farmers being between 81 and 96.40% technically
efficient. However, an average technical efficiency level of 78.91% means that farmers in the
study area have a shortfall of 21.09%. This suggests that there is still room for further increase
in soy bean output under the same technology level and without increasing the level of inputs
used.
Secondly, the study found that farm size and experience of the farmers were among the socio-
economic factors that negatively influenced technical efficiency whereas age, education,
extension contacts, use of modern seed, farmer club membership and credit access had
positively influenced technical efficiency. It was also found that female farmers were more
technically efficient than their male counterparts. In essence, increasing farmer club
membership, extension contacts and credit access to farmers will significantly increase
farmers’ technical efficiency in soy bean production.
The presence of socio-economic factors responsible for technical efficiency differentials in this
study entails that variation in technical efficiency was not only due to random shocks alone but
also farm and farmer’s level characteristics.
The study also went further to estimate returns to scale experienced by soy bean farmers in the
study area. It was found that farmers in the study area experienced increasing returns to scale
in their production.
Lastly, the study focused on three main inputs such as farm size, seed and labour. Basically,
these were the main inputs used by the farmers in the growing of soy beans, utilization of the
three inputs by farmers gave rise increasing returns to scale.
6.0 Policy recommendations
The study showed that an increase in the extension contacts, farmer club membership, credit
access, and modern seed adoption had improved technical efficiency of farmers in the study
area. Therefore, the study recommends that farmers’ access to extension services and credit be
enhanced through the provision of modern soy bean seed on credit and strengthening the
capacity of extension services through the deployment of extension field staff with relevant
information pertaining to soy bean production. In addition, the already existing presidential

27
initiative on legume promotion may be one of the ways to enhance farmers’ soy bean
productivity in the area.
Secondly, extension workers should emphasize the need for soy bean farmers to work in groups
or associations, in order to ensure effective spread of extension messages to most farmers and
enhance uptake of new technologies such as modern seed adoption.
The study narrowed its focus to only technical efficiency of soy bean farmers in the study area.
However, being technically efficient is just a necessary condition but not sufficient enough to
make a soy bean farmer excel in production. Therefore, there is a need for another study
investigating economic efficiency of soy bean farmers in the study area.

28
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