UNIVERSITY OF GHANA
DETERMINANTS OF TECHNICAL EFFICIENCY OF SMALL-
HOLDER PINEAPPLE PRODUCERS IN THE AKUAPEM SOUTH
MUNICIPALITY
BY
ABEASI HARRY AHWIRENG
(10395260)
THIS THESIS IS SUBMITTED TO THE UNIVERSITY OF GHANA, LEGON
IN PARTIAL FULFILLMENT OF THE REQUIREMENT FOR THE AWARD
OF A MPHIL ECONOMICS DEGREE
DEPARTMENT OF ECONOMICS
SCHOOL OF SOCIAL STUDIES
JUNE, 2014
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DECLARATION
I, Abeasi Harry Ahwireng, the author of this thesis titled “DETERMINANTS OF
TECHNICAL EFFICIENCY OF SMALL-HOLDER PINEAPPLE
PRODUCERS IN THE AKUAPEM SOUTH MUNICIPALITY, hereby declare
that, this work was done entirely by me under supervision at the Department of
Economics, University of Ghana, Legon from August 2013 to June 2014.
This work has never been presented either in whole or in part for any other degree at
this University or elsewhere, except for past and present literature, which have been
duly cited.
..............................………………………..
……….……………
ABEASI HARRY AHWIRENG DATE
(10395260)
..............................………………………..
……….……………
PROF. PETER QUARTEY DATE
SUPERVISOR
..............................………………………..
……….……………
DR. ALFRED BARIMAH DATE
SUPERVISOR
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ABSTRACT
The efficiency of resource-use is of major concern in agricultural production since
farmers’ productivity and profitability depends on them. The study thus assesses the
efficient use of production resource among small-holder pineapple farmers’ in the
Akuapem South Municipality. The study area was selected since it has one of the
largest numbers of small-holder pineapple producers in the country. The objective of
the study was to determine and estimate the levels of resource efficiency of small-
holder farmers. A cross-sectional secondary data of 150 small-holder pineapple
farmers’ was used. Socio-economic factors that influence small-holder farmers’
efficiency were identified using a stochastic frontier model and the results revealed
that farmers’ experience, levels of education, access to credit and age was negatively
related to inefficiency. Results from the Maximum Likelihood Estimation (MLE)
also showed that the estimated coefficients of the production inputs were positively
related to production with the exception of capital use. Farms size, labour and
fertilizer use was the most significant production inputs that affected output of the
farmers’. Results on the efficiency of resource-use indicated that farm size; labour and
fertilizer which were found as being the most productive inputs were underutilized
implying that an increase in these factors will affect outputs positively. The study also
found that farmers exhibited increasing returns-to-scale and that in the long run output
levels can be improved if farm inputs are efficiently combined. The findings of the
study establishes that farmers’ efficient use of resource and productivity improvement
are interlinked with their socio-economic characteristic, and thus to improve
efficiency it is essential to improve the factors that affects the overall efficiencies of
farmers’ such education and access to credit. Based on the findings, the study
recommends among other things that government and policy-makers in the pineapple
sector intensify their efforts at providing affordable credit facilities and adequate
education (formal and non-formal) to small-holder farmers’ to boost their outputs. It
is also recommended that planting materials be provided on a subsidized rate to
farmers so as to boost the desire of younger farmers into pineapple production.
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DEDICATION
This thesis is dedicated to my parents, Mr. Samuel Kwaku Ahwireng and Mrs.
Margaret Appiah for their love and support they have shown throughout my
education.
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ACKNOWLEDGEMENT
I am most grateful to Jehovah God for his many blessings and grace during my study.
I owe Jehovah God all the praise. I extend a heartfelt appreciation to the Department
of Economics, University of Ghana, Legon for offering me this opportunity to pursue
a master’s degree in economics and deepening my knowledge in this field.
My warmest appreciation goes to my supervisors, Prof. Peter Quartey and Dr. Alfred
Barimah, for their kind assistance and challenging questions that helped shaped the
course of this thesis. It is their guidance and comments that gave shape and meaning
to this work. To Dr Michael Danquah, of the Department of Economics, who was
always been available to offer extra lessons on the use of the stochastic frontier
approach. I must confess his seminars on the use of the methodology developed my
interest in this field. I acknowledge the warm friendship and times we spent together
on this thesis.
I also appreciate the efforts of my wonderful course mates who were available to
assist anytime I called on them. Though numerous, special mention goes to Mr. Aloka
Innocent, Frank Bredu, Betty-Ann Anane, Sampson Senahey, Nyamadi Godfred,
Salomey Kotin and Gloria Quarshie. I thank these people for all the love they showed
during my time of study. To my wonderful parents Mr. Samuel Ahwireng and Mrs.
Margaret Appiah, my siblings Linda, Hilda, Nana, Frank, Pat and Gifty; I thank them
all for their love, patience and support. Finally to my dear Dorcas Owusu Ankamah
for her unflinching support and understanding when I had little time for her. I thank
you for all the love.
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TABLE OF CONTENTS
DECLARATION ................................................................................................................. i
ABSTRACT ........................................................................................................................ ii
DEDICATION ................................................................................................................... iii
ACKNOWLEDGEMENT ................................................................................................. iv
TABLE OF CONTENTS .................................................................................................... v
LIST OF TABLES ............................................................................................................. ix
LIST OF APPENDICES ..................................................................................................... x
LIST OF ABBREVIATIONS ............................................................................................ xi
CHAPTER ONE ................................................................................................................. 1
INTRODUCTION .............................................................................................................. 1
1.1 Background ............................................................................................................... 1
1.2 Problem Statement .................................................................................................... 6
1.3 Objectives ................................................................................................................ 11
1.4 Hypothesis of the Study .......................................................................................... 12
1.5 Significance of the study ......................................................................................... 12
1.6 Organization of the study ........................................................................................ 13
CHAPTER TWO .............................................................................................................. 14
OVERVIEW AND DEVELOPMENT OF GHANA’S PINEAPPLE INDUSTRY......... 14
2.1 Introduction ............................................................................................................. 14
2.2 Production of Pineapples in Ghana ......................................................................... 14
2.3 Marketing of Ghana’s pineapples ........................................................................... 19
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2.4 Challenges of the Industry....................................................................................... 21
2.4.1 Land .................................................................................................................. 22
2.4.2 Finance.............................................................................................................. 23
2.5 Governmental Interventions .................................................................................... 25
2.6 Conclusion. .............................................................................................................. 26
CHAPTER THREE .......................................................................................................... 28
LITERATURE REVIEW ................................................................................................. 28
3.1 Introduction ............................................................................................................. 28
3.2 Efficiency ................................................................................................................ 28
3.3 Techniques and approaches to efficiency measurements ........................................ 34
3.4 Econometric approach to efficiency measurement ................................................. 38
3.5 Review of efficiency measurement in agriculture................................................... 44
3.6 Chapter summary .................................................................................................... 52
CHAPTER FOUR ............................................................................................................. 53
THEORETICAL FRAMEWORK AND METHODOLOGY .......................................... 53
4.1 Introduction ............................................................................................................. 53
4.2 The concept of Production ...................................................................................... 53
4.2.1 Production Possibility Set ................................................................................. 53
4.2.2 The production frontier ..................................................................................... 55
4.3 Theoretical framework ............................................................................................ 58
4.4 Conceptual framework of efficiency measurement ................................................ 61
4.5 Assumptions underlying the study .......................................................................... 65
4.6 Cross-sectional production frontier models ............................................................ 65
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4.6.1 Corrected Ordinary Least Squares (COLS) ...................................................... 66
4.6.2 Modified Ordinary Least Squares (MOLS) ...................................................... 67
4.6.3 Stochastic frontier production functions ........................................................... 68
4.7 Empirical frontier models specified for the study ................................................... 73
4.7.1 Definition of variables and expected signs ....................................................... 76
4.7.2 Measuring resource efficiency, elasticities and returns to scale of
production. ................................................................................................................. 77
4.8 Determinants of inefficiency ................................................................................... 79
4.9 Source of Data ......................................................................................................... 82
CHAPTER FIVE .............................................................................................................. 84
DATA ANALYSIS AND DISCUSSIONS ...................................................................... 84
5.1 Introduction ............................................................................................................. 84
5.2 Farmers Socio-economic Characteristics ................................................................ 84
5.3 Summary statistics of the production variables....................................................... 88
5.4 Estimation of production frontier function using Ordinary Least Square ............... 89
5.5 Stochastic frontier production function estimation using Maximum Likelihood ... 91
5.6 Determinants of inefficiency in production ............................................................ 96
5.7 Diagnostic statistics ................................................................................................. 98
5.8 Correlation matrix of technical inefficiency and its determinants ........................ 104
5.9 Elasticity of production variables and returns to scale .......................................... 105
5.10 Measuring resource-use efficiency of pineapple farmers ................................... 106
CHAPTER SIX ............................................................................................................... 109
SUMMARY, CONCLUSION AND RECOMMENDATIONS ..................................... 109
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6.1 Introduction ........................................................................................................... 109
6.2 Summary and conclusion of the study .................................................................. 109
6.3 Recommendations for policy implementation and further studies........................ 113
REFERENCES ............................................................................................................... 115
APPENDICES ................................................................................................................ 122
APPENDIX 1 .................................................................................................................. 122
ORDINARY LEAST SQUARE RESULTS ................................................................... 122
APPENDIX 2 .................................................................................................................. 122
APPENDIX 3 .................................................................................................................. 123
APPENDIX 4 .................................................................................................................. 123
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LIST OF TABLES
Table
Page
Definition of variables in the production frontier ............................................................. 77
Variables in the inefficiency model and expected signs ................................................... 82
Age distribution of pineapple farmers .............................................................................. 86
Sex distributions of pineapple farmers ............................................................................. 87
Farmers’ access to credit ................................................................................................... 88
Summary statistics of production variables ...................................................................... 89
Ordinary Least Squares Estimation (OLS) of the Cobb-Douglas production function .... 91
Summary statistics of the production variables ................................................................ 92
Maximum Likelihood estimation of the Cobb-Douglas production function. ................. 93
Ordinary Least Square Estimates for technical inefficiency effects ................................. 99
Correlation matrix of the technical inefficiency effects ................................................. 104
Resource-use efficiency of input variables in the frontier production function ............. 107
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LIST OF APPENDICES
Appendix 1 Ordinary Least Squares Results
Appendix 2 Maximum Likelihood Estimation of Production Function
Appendix 3 Diagnostic Statistics
Appendix 4 Validation of Test Hypothesis
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LIST OF ABBREVIATIONS
BoG Bank of Ghana
CSIR Council for Scientific and Industrial Research
DANIDA Danish International Development Agency
DEA Data Envelopment Analysis
DMB Deposit Money Banks
EDAIF Export Development and Agricultural Investment Fund
EMQAP Export Marketing and Quality Awareness Project
EU European Union
FAO Food and Agricultural Organization
FBO Farmer Based Organizations
GAEC Ghana Atomic Energy Commission
GDP Gross Domestic Product
GEPA Ghana Export Promotion Authority
GSGDA Ghana Shared Growth and Development Agenda
IFPRI International Food Policy Research Institute
ISSER Institute for Statistical Social and Economic Research
MCP Millennium Challenge Programme
MOFA Ministry of Food and Agriculture
MOTI Ministry of Trade and Industry
MT Metric Tonnes
NTE Non Traditional Export
SAP Structural Adjustment Programme
SFA Stochastic Frontier Approach
SPEG Sea-freight Pineapple Exporters of Ghana.
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SSA Sub-Saharan Africa
UNCTAD United Nations Conference on Trade and Development
UNEP United Nations Environment Programme
USAID United States Agency for International Development
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CHAPTER ONE
INTRODUCTION
1.1 Background
The global demand for fresh pineapples has been increasing steadily and currently
hovers around a production volume of between 17.2 million metric tonnes (MTs) and
18 million MTs annually (FAO, 2013). The world market for pineapples has however
shifted towards exports of the produce. UNCTAD (2012) states that of the high
volumes of fresh pineapple produced globally, more than 70% are consumed
domestically within the countries of production. Danielou and Ravry (2005) states the
global production and exports of pineapples is largely divided between Latin America
and Sub-Saharan African countries. UNCTAD (2012) however estimates that Costa
Rica leads globally as the major producer and exporter of fresh pineapples with an
annual output volume of 1.5 million MTs worth about $ 604 million.
The production and exports of pineapples in Ghana is recorded to have reached its
peak of about 71,000 MTs in the early 90’s when there was a huge demand globally
for the produce. However in 2008, the annual volume of pineapples produced reduced
to a low of about 35,000 MTs (GEPC, 2008). The decline in production and export in
2008 is as a result of the halt in the production and export of the Smooth Cayenne
(SC) variety which was cultivated locally. The conversion from SC to the MD2
variety is also partly responsible for the declines in production since most local
producers found it difficult to switch to the production of the new variety of
pineapples which are now in demand globally. This rigidity in changing to the new
and improved variety has accounted for the low production and export of Ghanaian
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pineapples on the world market. The difference between which variety to produce and
the variety demanded by processors have also accounted for low profitability and
productivity of the industry.
Ghana, as a developing country relies heavily on agricultural exports as a source of
government revenue and foreign exchange for the economy. It is therefore not
surprising that the agricultural sector is seen as a key to national development. The
growth and development of the agricultural sector is very important due to its
immense contribution to the national economy. The Ghanaian economy like other
developing economies in Sub-Saharan Africa is relatively dependent on the
agricultural sector primarily for its contribution to the gross domestic product (GDP),
and in terms of the amount of employment it generates.
However, in recent times, the sector has been experiencing declines in its output and
contribution to the gross domestic product (GDP). Available estimates on the growth
of agriculture and its contribution to GDP over the past few years have showed a
decline in productivity. MOFA (2010) reported that the growth of output of
agriculture in the country declined from 7.5% in 2004 to -1.7% in 2007 with GDP
shares of 40.3% to 29.1% respectively. The sector however recorded an increase in
growth in 2008 which was estimated as 7.4% and a GDP of 31.0%. This trend has
however taken a downward turn from 2009-2012. In 2010, the sector recorded a
growth of 2.8 % against a target of 5.3% (2012, Budget statement).
In 2011, the sector contributed about 25% to the nation’s GDP, but recorded a decline
in 2012. The 2012 estimates of the sector indicated a reduction in its contribution to
GDP from 25% in 2011 to 22.7% in 2012 with food crops contributing about 17% to
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GDP (BOG, 2012). The continuous decline in the growth rates and patterns of the
agriculture sector has been a major concern to planners and policy-makers who view
the growth of the sector as the main engine essential for the growth and development
of the Ghanaian economy.
MOFA (2007) states that agricultural production in Ghana is predominantly
smallholder, constituting about 80% of total crop production. Crop production is
mainly on subsistence basis, though there are few large scale farmers who cultivate
large hectares of land primarily for exports (MOFA, 2007). Though, large-scale
agricultural production exists, food production in Ghana continues to be dominated by
smallholder farmers. Smallholder farmers in Ghana continue to produce mainly on
small hectares of land with the use of traditional implements (MOFA, 2007). The
crops produced forms the main staples of the population and include yams, rice,
cassava, corn, millet, sorghum and beans. Fruits and vegetables are also produced
with the dominant products being tomatoes, pepper, onions, garden eggs, and a few
others. These crops are mainly produced for domestic consumption and onward sale
of the excesses.
Cocoa, coffee, timber and oil palm forms the major cash crops of Ghana. The
production of tree plants such as shea, rubber, and kola which also forms part of
exports has been stepped up over the years. These plants are often cultivated on large
scales and are mainly for commercial exports and domestic consumption. Pineapples,
mangoes, bananas, and pawpaw constitute the bulk of horticultural crops produced
domestically. The production of horticultural crops is largely dominated by small-
holder farmers (Afari-Sefa, undated). In spite of the increase in the production of
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agricultural products, exports of the country have mainly been primary products
which are exported either unprocessed (raw) or in a partly processed state. These
developments in the exports of primary unprocessed products deprives and hinders
the economy from obtaining the much needed foreign exchange and revenue from the
exports of these commodities.
Agricultural exports in Ghana are categorized mainly into two distinct groups. The
traditional (primary exports) or non-traditional exports. The traditional exports mainly
comprises of the major cash crops and the available natural resources of the country
which includes but not limited to gold, diamond, bauxite, manganese, timber, cocoa,
coffee, rubber, and oil palm which forms the bulk of the nations export earnings. The
non-traditional exports on the other hand are mainly composed of horticultural crops
which include pineapples, cashew nuts, and pepper, pawpaw and mango fruits among
others which also generate enough exports revenue to the country.
The contribution of the agricultural sector towards the growth and development of the
Ghanaian economy cannot be overlooked. The sector despite recording reductions in
its productivity and growth over the few years still remains relevant towards the
socio-economic development of the economy through the provision of food crops for
sustained and continual food security in the country. The significance and relevance
of agriculture towards the growth of the Ghanaian economy pertains to the large
numbers of people who are engaged in agricultural activities directly or indirectly for
their livelihoods. The World Bank (2002) estimates that agricultural activities in
Ghana accounts for about 40% of employment with a majority of these farmers being
women who produce on small holder and subsistence basis. This proportion of the
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population who are engaged in agriculture re-echoes the importance of the sector
towards the national development agenda of reducing poverty and continual job
creation for sustainable growth.
The importance of agriculture towards the nation’s development has thus drawn the
attention of policy makers who have often viewed the sectors as major tool for
generating revenue through exports, thus reducing the dependence on foreign imports,
stable and sustained job creation for reducing poverty and food security as a means of
curtailing malnutrition and environmental sustainability. In Ghana, the linkage
between the growth of agriculture and poverty reduction have been widely studied.
Coulombe and Wodon (2007) estimated that national poverty rate fell from 51.7% in
1991/92 to 39.5% in 1998/99, and a further drop to 28.5% in 2005/06. It has been
argued that, due to the essential role agriculture plays in the Ghanaian economy, any
distortions in production and productivity would affect the country considerably. For
instance, Killict (1978) and Bequele (1983) have stated that the decline in the
economy in the 1970’s was mainly as a result of the declines in agricultural
productivity of the country within and during that period (Killict, 1978; Bequele,
1983).
Agricultural production is essential for three core reasons: the production and
consumption of food crops, raw materials for industrial improvements and revenues
from exports. These core objectives if maximized ensure a stable development of the
economy by promoting improved livelihoods through quality nutrition and
employment, industrial growth and essentially foreign exchange from trade. For the
past years, the nations export earnings from the traditional exports has been declining
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steadily. Earnings from the country’s main exports such as gold and cocoa have
experienced all time lows in their market prices on the international market. The
reductions in prices of the country’s major exports commodities on the international
market has a down turn effect on the export earnings since they constitute the
majority of the nation’s revenues from exports. The reasons for the declines in prices
of the country’s exports may be associated with the volatility and instability of the
prices of these commodities on the global market, and the decrease in the demand for
the commodities from the major trading partners as a result of the global economic
slow-down.
The revenues from the non traditional exports tend to augment for any short fall in
earnings from the traditional products. Fortunately, however, earnings from the non
traditional exports (NTE’s) show a positive outlook. The horticultural industry of the
NTE’s shows a positive outlook with the production and exports of pineapple being
the highest. In 2004 pineapple exports was estimated to contribute about 60% of the
total value of Ghana’s NTE’s generating more than 20,000 direct employments
(Ghana Fresh Pineapple Intelligence Report, 2005).
1.2 Problem Statement
Recent concerns on food security in Ghana have generally been centred on measures
that are aimed at improving the efficiency and productivity of the agricultural sector.
This has arisen based on the growing demands for food domestically and changes in
climatic conditions as a result of global warming. Population increases also tends to
put a further push on the demand for food crops. The rise in population and changing
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climatic conditions thus requires efficient means of increasing agricultural outputs to
meet the rise in demand for food both locally and globally.
The agricultural sector despite its challenges continues to be a significant contributor
to the nations GDP; however the sector has not received the appropriate institutional
support that it requires to become a major contributor to the growth process of the
economy. Despite being the third largest contributor to GDP after services and
industry, the sector recorded the lowest growth of 2.6% in 2012 and 0.8% in 2011
(GSS, 2012). The continual decline in the productivity of the sector is a major cause
of worry, since a vast majority of the populace are engaged in agriculture. This
signifies that the performance of the agricultural sector is paramount to national
development in relation to the creation of jobs, poverty reduction and food security.
ISSER (2003) ranked pineapple production and exports as Ghana’s most significant
NTE as it contributed about 24% to the total volume of horticultural exports in the
country. Obeng (1994) states that, the increase in pineapple exports in Ghana is partly
associated with a number of liberalization policies which were adopted under the
Structural Adjustment Programme (SAP). These policies relaxed the restrictions
placed on NTE’s and helped soar the increase in exports as a result of the gradual
removal of foreign exchange controls and income tax rebate. In addition, all non
traditional exports (NTE’s) were exempted from export duty.
Though the pineapple industry seems to be faring relatively well, the sector is saddled
with numerous challenges that hinders it progress. These challenges are so varied and
diverse in nature, such that pragmatic and concerted efforts need to be taken in order
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to address these bottlenecks within the agricultural sector. Available evidence
suggests that Ghana has a high and positive potential to develop its pineapple industry
to meet up the high demand for fresh pineapples globally and increase its export
earnings (Kleemann, 2011).
The industry though being vibrant as it seems, is faced with huge institutional
setbacks that hinder the productivity and viability of the sector. The availability of
fertile lands and the favourable climatic conditions gives the country a comparative
advantage in the production of the crop to maximise its earnings. Ghana has a huge
potential to develop its agricultural sector and in particularly the horticultural industry
in order to supplement for the decline in export earnings from the traditional exports.
The pineapple industry is one area that can contribute significantly to revenue
mobilization and the creation of sustained and stable employment.
Though a viable venture for creating employment and reducing rural poverty, the
industry has received very limited attention in the nation’s agricultural development
agenda. The contribution of the pineapple industry cannot therefore be overlooked,
but the industry is constrained with huge challenges that hinder its development and
productivity. These challenges are so diverse in nature such that a collaborative effort
would be required to reduce these drawbacks on the industry. Major challenges faced
by the industry include the supply chain management of the products, meeting the
global demand for organic pineapples (MD2 variety) and increased productivity and
profitability.
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The Ghana Export Promotion Authority states that “pineapples have been the major
driver of the performance of the horticultural sector”. This therefore re-echoes the
significance of pineapple production to the Ghanaian economy. The global demand
for fresh pineapples has been growing rapidly over the past years. Like most other
tropical crops, pineapples are mostly cultivated in developing countries, where two
thirds of rural people live on small-scale farms of less than two hectares (IFPRI,
2005). This increase in demand for fresh pineapples requires a concerted effort at
increasing the productivity of pineapple farmers in Ghana. Sadly, however, pineapple
farmers in Ghana are often unable to meet the high demands for their produce as
compared to their counterparts from Costa Rica and other African countries that are in
the production of pineapples. In Ghana, pineapple farmers are often characterised by
small-holders cultivating an average of two to three acres of arable land. The
cultivation of the fruit in Ghana is mainly predominant the Greater Accra, Central,
Western, Volta and Eastern regions (Kuwornu et al, 2013).
The Akuapem plains have one of the largest numbers of pineapple growers in the
Eastern region with a few growers scattered around the Yilo- Krobo area. The
Akuapem south municipality is one area that has a vast majority of pineapple growers
in the country. However, majority of these farmers are unable to achieve their desired
objective of maximum productivity and profitability. The failure of farmers to achieve
their desired levels of output can be attributed to diverse and varied factors which may
inadequate credit, low levels of technology, poor storage, land tenure system and
marketing facilities among others which affect their profitability and productivity
levels severely.
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These factors tend to reduce the relative efficiency of the farmers and make them less
productive and profitable. Pineapple farmers are often inefficient in the use of both
technology and the available resources efficiently for the realization of maximum
output. The difficulties on the part of the farmers to apply improved farming methods
and appropriate technologies results in lower crop yields and profits. It is therefore
essential that in an effort to raise the productivity of pineapple production in Ghana,
a more pragmatic approach is adopted and carried out to ascertain and measure the
relative efficiencies of resource use among smallholder pineapple farmers. In every
agricultural activity, efficiency is often a measure of productivity growth. Thus,
farmers’ ability to adapt to new and modern methods of farming and the rapid
utilization of the factors of production can greatly accelerate production levels. The
strategic nature of pineapples towards the growth of the Ghanaian economy has over
the years drawn the attention of policy makers who view promoting the domestic
production of pineapples as a means of reducing dependency on imports, lowering the
pressure on foreign currency reserves, ensuring stable and low-priced sources of food
for people, generating employment and income for pineapple growers.
In agricultural production, the measurement of the productive efficiency has always
been an important issue from the standpoint of agricultural development in
developing countries since they provide the necessary information that are required
for making sound management decisions, in the allocation of resources and the
formulation of useful agricultural policies. It is for this reason that an assessment of
the productivity of pineapple farmers is carried out to give a clearer focus of the
nature and dynamics of industry. As government strides in its drive to increase the
productivity of pineapple farmers, aimed at ensuring food security in the country, and
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improving the nutritional requirements of the people, it is worthy that the efficiency of
pineapple production is inculcated as a matter of national policy so as to meet the
much anticipated boost from the pineapple sub-sector of the economy.
It is only through this that the expected growth and stability can be achieved. In trying
to measure the levels of resource use efficiency of pineapple farmers, several key
questions arises. These questions are:
1. To what extent are pineapple farmers efficient in the use of the available
resources for production?
2. Are farmers technically, allocative and economically efficient in the use of
these resources for production?
3. And to what extent do their inefficiencies impact on the socio-economic
development of the local pineapple farmer.
1.3 Objectives
The general objective of this study would be to evaluate and analyse farm-specific
levels of efficiency (technical and allocative) and resource-use among small-holder
pineapple farmers in the Akuapem south Municipality. The specific objectives of the
study would seek to;
1. Estimate the levels of efficiency of resource-use among small-holder
pineapple farmers
2. Estimate the determinants of inefficiency among small-holder pineapple
farmers and its relationship with farmers’ socio-economic characteristics.
3. To provide policy recommendations based on efficiency estimates on ways at
improving the profitability and productivity of the pineapple industry.
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1.4 Hypothesis of the Study
In meeting the objectives of the study, the study hypothesis includes:
i. Pineapples farmers are not efficient in the use of resources.
ii. Education, farmers access to credit, farmers experience, age, and farm size
have no direct impact on the levels of technical efficiencies among farmers.
1.5 Significance of the study
Several studies on agricultural productivity in Ghana have often centred on major
products such as rice, yams, and tomatoes, cocoa and fish farming. Studies on
horticultural plants have also mainly considered the marketing challenges of the
industry. However, the marketing of the commodities is paramount but must not
necessarily supersede the productivity and efficiency of the industry. Fruits and
vegetable production plays an important role in the economy of Ghana. The
nutritional and aesthetic values of fruits and vegetables towards human development
have been known for several years.
Over the years, the production of fruits and vegetables particularly horticultural plants
of which pineapples are included have been increasing. It is estimated that between
the periods 1996 and 2004, the production and exports of pineapple increased
reaching a high of 71,858 metric tonnes in 2004 (Kuwornu et al, 2013). The role
therefore of the Ghanaian pineapple industry towards the development of the
economy cannot be disregarded. The study would therefore take its premise from the
point of efficiency and productivity of the pineapple sector. It is considered that an
increase in the productivity of the pineapple industry would provide the needed boost
in revenue earnings through the exports of the produce.
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A considerable increase in the productive efficiency of the industry would thus
provide an abundance of the produce so as to provide the needed materials for fruit
processing and exports. As the country continues to be challenged with high and
rising unemployment rates, the pineapple industry can thus serve as a profitable
venture that can generate the needed employment.
The significance of the study would be to broaden the discussion on measures aimed
at improving the profitability of Ghana’s pineapple industry. Results and findings of
the study will be beneficial to government and development agencies who are
interested in improving the livelihoods of rural pineapple growers. The findings of the
study will also be of great use to creating the needed awareness on the potential of
pineapple farming in the country.
1.6 Organization of the study
This study is organized into six chapters. It is outlined as follows, chapter one
provides background information on the thesis area. Chapter two presents an
overview and the development of the pineapple industry in Ghana. Reviews of
relevant literature on the stochastic frontier approach and its use in the estimation of
production as well as empirical studies that applies the stochastic frontier
methodology in agriculture are presented in chapter three. Chapter four discusses the
methodology applied, variables used and data sources. The results and discussions of
the study are presented in Chapter five. Chapter six outlines the summary, conclusions
and recommendations derived from the study.
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CHAPTER TWO
OVERVIEW AND DEVELOPMENT OF GHANA’S PINEAPPLE
INDUSTRY
2.1 Introduction
This chapter takes a central overview of the pineapple industry in Ghana. It examines
market potential of the sector and key challenges that affects the development of the
industry. Issues relating to the use of land and finance for the sector are also
discussed. Finally, the role of government and donor agencies in promoting pineapple
production and exports is highlighted further. The chapter concludes with the
prospects and potential of the Ghanaian pineapple industry.
2.2 Production of Pineapples in Ghana
Agricultural production continues to be a significant sector for the development of
most countries in Sub-Saharan Africa (SSA). The role of agriculture in Africa is
multi-diverse, as the sector forms the backbone of most developing economies in
SSA. Food insecurity in Africa tends to be severe with a large number of the
population being malnourished. World Bank (2000) estimates that agriculture account
for about 35 percent of the GNP of SSA countries, 40 percent of exports and 70
percent employment. However, severe food insecurity exists in most SSA countries
and this is largely due to the fact that agriculture production is mainly rain-fed. UNEP
(2002) also estimate that more than 40 percent of the population in SSA countries live
below the poverty line. With the high levels of unemployment and chronic food
insecurity in most African countries, the role and contribution of agricultural
production in Africa seems significant. Ghana, like most developing countries in SSA
continues to rely on agriculture for development and growth. Agricultural production
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and productivity in Ghana has been a cause of major concern to most governments in
the country who view the sector as a major growth engine for the nation’s
development. The Ghana Shared Growth and Development Agenda (GSGDA, 2010)
places agriculture and agricultural mechanization as a necessary tool essential for the
nation’s development and economic transformation. This hence places agricultural
production on the pinnacle as a significant contributor to growth. The sector in spite
of its benefits is characterized by low productivity, low incomes for farmers and
inadequate post- production infrastructure for storage.
Despite the benefits of agriculture towards the transformation of the Ghanaian
economy as expressed in the GSGDA in terms of “job creation, increased export
earnings, improved food security and environmental sustainability”, the sector
continues to struggle with problems that militate against it in achieving these stated
objectives. Agricultural production in spite of these challenges continues to thrive in
Ghana, generally due to the availability of fertile arable lands, favourable climatic
conditions and the availability of human resources. Ghana’s agricultural industry is
largely characterized by large numbers of smallholder farmers who cultivate primarily
on subsistence basis. Chamberlin (2007) and Al-Hassan et al (2006) have identified
smallholders as the largest food crop producers in the country and yet they are the
most vulnerable in Ghana’s agricultural sector. Crop production is mainly divided into
two distinct components, the traditional cash crops (cocoa, coffee, rubber etc) and
non-traditional crops which are essentially made up of horticultural crops. Over the
past years, however, the production and export of non-traditional agricultural exports
have been rising steadily. Ampadu-Agyei (1994) states that the increase in the nations
export of non-traditional agricultural products which increased from US$ 1.9 million
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in 1984 to US$ 62 million in 1990 suggests that NTE’s have a positive role to play in
the ongoing economic transformation and development in the country. This increase
in the production and exports of high-valued agricultural products arose as a result of
the introduction of export liberalization in the 1980s which was coupled with the
increase in the demand for fresh vegetables and fruits.
The demand for fresh fruits globally has been rising with pineapples leading the pact
as the most high demand horticultural crop. Pineapple production in Ghana has been
in the ascendency for the past decades. The industry is the most structured and well
developed sector of the horticultural industry in Ghana. Pineapple production in
Ghana plays a crucial and central role in the development of the agricultural sector.
Sefa-Dedeh (n.d) estimated that horticultural exports of the country increased from
22,362 MT which was valued at US$ 9,306,000 in 1994 has grown to a total of
130,000 MT valued at US$ 60,500 in 2004. The growth of the industry is largely as a
result of the development of the pineapple sector, which accounted for about 40% of
the total export earnings.
The production and exports of pineapples in Ghana is a beneficial sector to the
domestic economy, as it provides higher incomes and new employment opportunities
to farmers than do other crops grown for the domestic market and consumption
(Barrientos et al, 2009). Goldstein and Udry (1999) states that of the total value of
pineapples produced and exported in the country, about 45 percent are based on the
production by smallholders. This thus re-echoes Chamberlin (2007) assertion that
agricultural production in Ghana is dominated by smallholder farmers.
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Pineapple production in Ghana like any agricultural activity is made up of mainly
smallholder farmers. Though there are a few large farms involved in the production of
pineapples locally, smallholder production still dominates within the sector. The
Ghana Living Standards Survey (GLSS, 2009) estimates that about 17,627 households
which comprises of an average of 2 percent of all household grow pineapples, of
which majority are not on commercial basis. A large majority of the pineapples
produced domestically are exported, with the major export destinations being the
European Union. The demand for fresh cut pineapples increased globally with the
liberalization of trade and the minimization on export restrictions on horticultural
crops from developing economies. Ghana’s pineapples became a major export
commodity in the early 1980s when demands for the much cultivated smooth cayenne
(SC) variety were in high demand.
However, with the introduction of the much sweeter and organic MD2 variety in early
2004, Ghana’s share of exports of pineapples reduced considerably. This switch in the
variety of pineapple demanded caused huge declines in revenue from the export of
pineapples as the prices also fell on the international market. Kleemann (2011) states
that about 63 percent of pineapples produced in Ghana between the periods 2003 to
2007 was largely directed at the EU markets, where demands were relatively higher.
Production of pineapples in Ghana is largely denser in the southern parts of the
country where there exist relative favourable weather conditions, fertile lands and
accessibility to larger markets. Production is mostly along the Eastern, Greater Accra,
Volta and Central regions of the country. The large concentration of farmers within
this enclave ensures that farmers have a closer proximity to major export firms who
are directly involved in the export of pineapples. This ensures that harvested produce
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of farmers are readily purchased by large multi-national export companies. A major
export firm of pineapples in Ghana is the Blue Skies Limited which exports fresh cut
pineapples into the EU and also serves as a major processor of fresh pineapple juice
domestically. McMillan (2012) emphasizes that the achievement of Blue Skies
Limited in Ghana is “a financial and economic success story”. The contribution of the
company has led to huge investments in pineapple production nationwide and within
their enclave of production.
The main focus of Blue Skies Limited is to assist farmers who previously had
difficulties in changing from the less productive SC variety into the high yielding and
much demanded MD2 variety. With such investments in pineapple production, sales
from the company have grown by an average of 28 percent per year (McMillan,
2012). Though most local producers have still not fully adapted to the newly
improved variety, production levels of pineapples continue to rise gradually with the
steady adoption of the MD2 variety. Since demand for fresh cut pineapples globally
is skewed towards the more organic variety (MD2), production levels in Ghana fell in
the later part of 2003 and have suddenly seem to rise with the intervention of
developmental organizations such as USAID, DANIDA who are given support in the
form of technical assistance to local producers to increase their capacity for
production.
Green Village Agriculture Development in one organization which is leading the way
at rejuvenating pineapple production, and is in partnership with local farmers in the
Akuapem South district to promote the production and cultivation of the high yielding
and demand-driven MD2 variety. Such partnerships are increasingly becoming
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necessary as the country gears itself to increase its exports of fresh pineapples to the
major export destinations.
2.3 Marketing of Ghana’s pineapples
In any economic activity, demand and supply are matched up when there are well
structured and conducive market where exchange of goods and services can be traded.
Likewise in every agricultural activity, the issue of marketing is paramount if
producers are to have access to ready markets. Al-Hassan et al (2006) explains that in
an “era of liberalization, and globalization small holders may find it difficultly to have
ready markets for their produce”. This holds true for most of the nation’s exports
especially in the exports of fruits and vegetables. Due to the large potential of the
horticultural sector to the Ghanaian economy, efforts are continually being made to
improve the marketing potential of the country. Evidence from Owusu and Owusu
(2010) explains that efforts must be made to distinguish organic fruits and vegetables
from conventional produce in order to achieve the maximum prices on the
international market. This they explain will help increase the earnings from exports of
horticultural products.
Market and marketing opportunities in the horticultural sector is crucial if the nation
is to reek in the needed benefits of the sector. ISSER (2002) explains that marketing
challenging remain a major setback to the growth of the horticultural industry in
Ghana. They further stress that export diversification remains the viable option for
improved and sustained growth in the horticultural industry. To this extent,
diversification has largely paid off by improving the over-dependence on traditional
exports to improvements in NTE’s. Continuously, the promotion of diversification has
increased with support from major development partners such as the World Bank and
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USAID. This has contributed significantly in opening up the avenue for the country to
increase its exports of horticultural products. Over the years, the production and
export of pineapples in Ghana have become the single most essential non-traditional
exports of the country (ISSER, 2003).
The global value chain for pineapples has increased considerable with high demand
for the crop coming largely from the European Union. Legge et al (2006), FAGE
(2007) posits that export from Ghana’s horticultural sector of which pineapples forms
the majority places fourth in terms of total volumes exported to the EU, there still
remains huge potential for increased export. With the existence of multi-nationals and
corporate organizations such as Blue Skies and Dutch Togu fruits, Ghana’s exports
for pineapples continue to rise overtime (Yeboah, 2005). It is estimated that between
the period of 1994 and 2006, total volume of horticultural exports increased from an
estimated value of US$ 9.3 million to US$ 50 million, with which volumes of
pineapples amounted to about 38 percent of exports (FAO, 2004).
Luckily, in Ghana, the Ghana Export Promotion Authority (GEPA) and the Export
Development and Agricultural Investment Fund (EDAIF) established by an act of
parliament (ACT 582), two umbrella bodies mandated by law to help promote and
increase the nations returns from exports is fast gaining grounds, though a few
challenges still lingers on. Trade negotiations and restrictions which hitherto would
have impaired the growth of the industry are gradually being removed. With such
institutional challenges being readily addressed by the government and stake holders
in the industry, horticultural exports especially pineapple exports are increasingly
becoming significant revenue sources to the economy.
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The contribution of Sea-Freight Pineapple Exporters of Ghana (SPEG) a local export
association made up of indigenous exporters has contributed in increasing the volume
and values of pineapples exports from the country. Such efforts of SPEG have opened
the country’s export to trading partners in Europe and the Middle East though there
are challenges that still pertain in the growth of the industry. As the pineapple
industry is regarded as a significant sector, it has continued to receive substantial
assistance from development agencies. In 2005, when prices for pineapples on the
international market fell, the Ministry of Food and Agriculture (MOFA) in
collaboration with the African Development Bank Export Marketing and Quality
Awareness Project (EMQAP) have made considerable investment in the sum of US$
25million into the development of infrastructure and capacity building for pineapple
growers in order to increase their capacity and export potential. The potential for
pineapple exports if fully harnessed would provide the much needed boost.
2.4 Challenges of the Industry
Ghana like most developing countries in Africa has huge potentials for developing its
industrial and agricultural sectors for sustained growth. With the availability of vast
natural resource base and low cost of labour, the continent is regarded as a beacon of
hope for development. Sadly however, there are huge gaps in terms of development
and the large endowments of resource. The development of the agricultural sector in
Africa is largely regarded as a great potential for solving the continents food
insecurity and chronic famine.
The development of the agricultural sector in Ghana is considered as a major tool for
development. For this reason, several governmental policies and programmes have
often been centred on finding ways at improving agricultural productivity and
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production in Ghana. Such programmes have often not been able to turn around the
fortunes of the agricultural sector. The horticultural industry of the agricultural sector
has often been hardly hit with institutional bottlenecks that hinder its growth and
development. Pineapple production in Ghana, like any agricultural industry is faced
with huge difficulties and challenges that often stampedes its development. The
challenges of the industry are so diverse in nature such that efforts in addressing them
must be holistic and pragmatic.
Major factors that inhibit the pineapple industry are non-exhaustive but include
limited finances, access to land, high cost of inputs, pest and diseases, limited
information and inadequate storage infrastructure. Though these factors may not be
the only inhibitors to the growth of the industry, they collectively pose a major threat
to the sustainability and development of the industry.
2.4.1 Land
The sustainability and success for agricultural production depends largely on the
availability of fertile and accessible lands. In Ghana, the issues of land acquisition
have become quite difficult and cumbersome since land titles are not well regulated.
This has often led to difficulties in accessing agricultural lands for commercial
purposes for the cultivating of the crop. For any productive agricultural activity,
access to farmlands continues to be one of the single most important components for
production.
However, land administration and land tenure systems in most parts of the country
continue to generate so much inertia, such that access to commercial lands for
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agricultural purposes remains a key developmental issue. With the implementation of
the Structural Adjustment Programme (SAP) in 1983, accesses to land for commercial
agricultural purposes have been regulated. Amanor (1999) explains that the
implementation of The Land Title Registration Law (1986), for the protection of
individual property rights has contributed to ease up the problem of land accessibility.
In this direction, farmers face little risk in their pursuit for establishing medium to
large-scale farms for increased production.
Though the Land Title Registration Law (1986) has reduced the difficulties in
accessing lands, there still remains a challenge since most farm lands have their
authorities vested in traditional rulers (chiefs) who are more willing and prefer to
release these lands for infrastructural development than agricultural production.
Besides, these difficulties, the land tenure system in most parts of the country are not
favourable for effective agricultural production. Most land tenancy agreements are
mostly on short-term basis and thus prevent these farmers (small-holders and large
farms) from recouping their investments in their farming activities.
2.4.2 Finance
The profitability of any agricultural activity depends to a larger extent on the
availability of capital. Financing for agricultural production continues to be a major
constraint affecting the productivity of agriculture in Ghana. Like most developing
countries in the sub- region, farmers generally have difficulties in accessing credit
facilities from most financial instructions for their agricultural activity. Most studies
MOFA (2007), Al-hassan (2008) and Abbam (2009) have identified inadequate credit
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and limited financial assistance as a major constraint to the development of the
agricultural industry in Ghana.
Quartey et al (2012) also states that most farm households in Ghana are often rural
thus make it quite difficult for them to access credit from financial institutions which
are mostly urban based. They however observed that due to the risky nature of most
agricultural activities in Ghana, most Deposit Money Banks (DMB’s) are often
reluctant to provide financing for these purposes. Abbam (2009) stated that
inadequate finance poses a huge risk towards the viability of Ghana’s pineapple
industry. Due to the relative importance of finance towards agriculture and rural
development, pragmatic efforts have continuously been made as a means of
improving farmers’ access to finance.
In spite of the enormous contribution that agriculture plays in the economy, the sector
has received less assistance in the form of financing from most Deposit Money Banks
(DMB). For agriculture to thrive, it requires huge capital and infrastructural
investments in the form of modernization and mechanisation. This hence requires
enough financial support of which smallholder farmers are generally unable to
provide. Baker and Holcomb (1964) observed that for farmers to increase their
production and productivity, then farm resources would be greatly improved through
the supply of finances. Inasmuch as finance provides a useful means of increasing
agricultural production through the purchase of farm inputs such as fertilizers, labour
cost and agrochemicals, smallholder pineapple farmers mostly have limited access to
such financial facilities.
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It is through financing that the much needed infrastructural development such as the
provision of storage facilities, improved roads networks and agricultural
mechanization can be realised. Aside the problem associated with smallholders
gaining access to credit, the conversion from the much cultivated SC to the MD2
variety implied huge financial commitments of which most smallholder farmers could
not readily afford. Larsen et al (2006) states that as the demand for the SC variety
were gradually being squeezed out of market in favour of the newly introduced MD2
variety, smallholder farmers were generally disadvantaged. This resulted from the
huge cost associated with the purchase of inputs and implements for cultivation of the
MD2 variety, hence required huge capital investments which smallholders were
generally unable to afford.
These difficulties thus reduced small grower’s capabilities to invest and reap the
associated benefits from the much demanded MD2. Since smallholders could not
afford the high cost of credit, it implied that large farms with enough assets could
have access to the needed credit for expansion, pushing smallholders out of business.
2.5 Governmental Interventions
The pineapple industry due to its strategic nature and contribution towards the
domestic economy has attracted a lot of attention from governments and donor
agencies alike. From infrastructural development to capacity building, governments
past and present have worked tirelessly to promote the production of pineapples.
Though governmental support in the late 1990s towards the sector declined, a lot of
attention has been given to its development from the early 2000s. Major development
agencies such as USAID and the World Bank have continuously provided support to
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the industry in areas such as export promoting and quality assurance practices.
Government and donor initiatives have also centred on the modernisation of the
agricultural sector with much focus on the horticultural industry.
The largest of such supports is the partnership between the Government of Ghana
(GoG) and the United States government through the Millennium Challenge
Programme (MCP) for the promotion and diversification of the nation’s exports. A
priority of this partnership is the modernisation of agriculture with particular
relevance to the horticulture industry and pineapples in particular (Adekunle et al,
2012). The efforts of government in promoting the production of pineapples in the
country have been in the area of research and development. With the assistance of
research institutions such as the Ghana Atomic Energy Commission (GAEC), the
Plant Research Institute of the Council for Scientific and Industrial Research (PRI-
CSIR) and the Ghana Export Promotion Authority (GEPA), studies have been carried
out to produce the MD2 pineapple variety that is much demanded globally to
producers at a lower cost. Such interventions are timely, as the country braces itself to
increase its exports of pineapples. Three major ministries, the Ministry of Finance and
Economic Planning (MOFEP), Ministry of Food and Agriculture (MOFA) and the
Ministry of Trade and Industry (MOTI) together with the Export Development and
Investment Fund (EDIF) continuously provides assistance to growers and exporters of
pineapples to educate them of quality standards and export best practices.
2.6 Conclusion.
Pineapple production continues to be a relevant industry in the agricultural sector.
Though saddled with huge challenges, it continues to inspire hope due to its prospects
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for job creation, reduction of poverty, provision of food security and as a source of
government revenue. It is envisaged that the country will take measure and formulate
appropriate policies that will help address the challenges that hinders the growth of
the industry in relation to the basic constraints such as finance, land and improved
infrastructure. Most importantly, productivity and efficiency improvement merged up
with appropriate export management and promotion would serve as a basis for
increased export earnings.
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CHAPTER THREE
LITERATURE REVIEW
3.1 Introduction
This chapter is focussed to the various approaches used in estimating production. The
two main approaches that have dominated the literature for the measurement and
estimation of production are presented. Empirical studies in relation to the use of the
stochastic frontier model for measuring efficiency of agriculture are also discussed.
3.2 Efficiency
The concept of efficiency in economics has become topical and has received a lot of
attention from both applied and theoretical economist. The current literature on
production and productivity analysis has largely been focused on the empirical
estimation of efficiency. Efficiency has often been defined in the classical
microeconomics context as an individual’s, or firms ability to produce outputs given a
set of inputs with minimum production cost. Within this basic definition of efficiency,
we would expect that the combination of inputs that yields higher levels of output can
be classified as an efficient production level. However, there may be certain factors
that may inhibit the realization of these expected higher outputs. This definition of
production efficiency has led to the development of theoretical models which are
meant to explain the differences in the frontier output “efficient levels” and the actual
outputs observed.
The principle of maximising profit and cost minimisation has become paramount and
most widely used in the measurement of efficiency of production. The study and
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analysis of production efficiency of firms dates as far as Knight (1933), Koopmans
(1951) and Debreu (1951). These studies formed the basis of empirical efficiency
estimation and provided a theoretical framework within which the definition and
measurement of efficiency could be framed. Debreu (1951) provided the first measure
of the “coefficient or resource utilisation’ of production and Koopmans (1951)
decomposed efficiency into distinct components and provided a classical definition
for technical efficiency.
Koopmans (1951) defined a firm or production unit as being technically efficient if
any increase in output required a reduction in at least one of its other outputs, and if a
reduction in any input requires an increase in at least one other input or a reduction in
at least one output. However the work of Farrell (1957) changed the focus of
efficiency studies. Farrell’s (1957) work provided a functional definition of efficiency
and its measurement took up a different dimension. His study provided a working
explanation and the basic definitions of economic efficiency as comprising of both a
technical and allocative component. Farrell (1957) explained technical efficiency
within an engineering framework of an input-output relationship which refers to a
firm’s ability to produce maximum output from a specified amount of inputs, or using
minimal inputs to produce a set of specified outputs.
Lovell (1993) also relates a firm’s efficiency to the comparisons between the frontier
or ‘efficient output’ levels and the observed outputs to inputs specified. However,
Lovell (1993) explains that if we are to define the production possibilities in terms of
optimum bounds, then the comparison that would result would measure the technical
efficiency of the firm or production unit. The basic idea in microeconomics relates a
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production unit’s decision making to the behavioural assumptions underlying
production i.e. profit maximization and cost minimization. This assumption thus
assumes that firms in making production decisions would always prefer to operate on
the efficient frontier where maximum output is achieved. However this objective of
efficient production is often not achieved due to inefficiencies that arise from
production. Hence, the existences of technical inefficiency of production units have
been at the fore of debate in current economic discussions. Muller (1974) states
however that “little is known about the role of non-physical inputs, especially
information or knowledge, which influences the firm’s ability to use its available
technology set fully”.
The assumption of efficiency assumes that firm’s operate on the outer bound of the
production function that is on the efficiency frontier. Hence firms that operate within
the bound of the production frontier are technically inefficient in combining given
level of inputs to achieve the desired objective of maximum outputs. Thus, once all
the inputs for production have been factored, the measured differences in productivity
should disappear except for the unobserved disturbances that may arise. McGuire
(1987) states and argues that a technically efficient firm is one that produces on the
isoquant or on the production possibility frontier, whereas a technically inefficient
firm would necessarily operate within or outside the production frontier. This
definition of efficiency has led to the much discussed technical and allocative
efficiencies. Typically, a firm’s production possibilities and outputs are measured
based on the premise of economic theory.
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Debreu (1951) and Farrell (1957) noted that a production unit is efficient as long as it
operates on the production frontier, but not necessarily by the Koopmans (1951)
definition of technical efficiency. Koopmans (1951) definitions of technical efficiency
have often been criticized as not been efficient, since in order to increase output
another output associated with it must necessarily be decreased. Similarly, Kalirajan
and Shand (1999) proposed that firm’s performances are measured based on their
efficiency levels which are made up of the two distinct components proposed by
Farrell (1957) namely; technical and allocative efficiency. Ellis (1988) further defines
technical efficiency as the maximum possible level of output attainable from a given
set of inputs, given a range of alternative technologies available.
The presence of technical inefficiencies in production processes have been discussed
by Bauer (1990) and Kalirajan and Shand (1999), that where technical inefficiency
exists, it will exert a negative influence on allocative efficiency with a resultant effect
on economic efficiency. Kedebe (2006) however defined “technical efficiency” in his
study as the maximum attainable level of output for a given level of production
inputs, given a range of technologies available to the farmers, and allocative
efficiency as the adjustments to inputs and outputs to reflect relative prices”. He
stressed that economic efficiency is a combination of both technical and allocative
efficiency and that technical efficiency may occur without economic efficiency
necessarily being achieved.
Related studies on efficiency which have received considerable attention and provided
functional definitions to the various forms of efficiency includes the works by
Leibenstein (1966, 1978), Corra (1977), Jondrow et al (1981), Bravo-Ureta and
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Rieger (1991), Battese and Coelli (1992) and Lovell and Kumbhakar (2000) on
production efficiency. These studies each provided a different focus to the effects of
efficiency on production. The measurement of efficiency in applied economic studies
has become crucial because it provides the first step at which production resources
can be fully utilised. The study by Farrell (1957) provided a clearer definition for the
other component of efficiency as allocative “price” efficiency. This he explained as
the maximum “optimal’ input proportions given the relative prices. Bailey et al (1989)
also defines allocative or price efficiency as a firm’s ability to effectively utilize the
cost minimizing input ratios or revenue maximizing input ratio. Allocative
inefficiency of a production unit then occurs if the ratio of marginal physical products
of two inputs does not equal the ratio of their prices, e.g., i
j
j
i
w
w
f
f
Thus, a firm’s allocative efficiency based on Farrell (1957) and Bailey et al (1989)
depends on its ability to make decisions on the optimal combination of inputs with
respect to their prices. Allocative efficiency can then be viewed as the measure of a
firm’s success in choosing a set of optimal inputs given the relative prices of the
inputs. This definition of allocative efficiency re-enforces the principle in
microeconomics in which a firm’s marginal cost of factor inputs (MFC) is equated to
the marginal value product (MVP). This component of the efficiency measure thus
reduces the effect of inefficiencies from a pure technological factor to the effects of
the prices of the factor inputs.
The productive efficiency of a firm or production unit can then be thought of as the
combination of both technical and resource-allocation efficiencies. However, these
solely may not be sufficient to achieving economic efficiency. Economic efficiency
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by definition is distinct from both allocative and technical efficiency though it is the
combination of both that results in economic efficiency. The existences of technical
and allocative efficiency have often been argued as the necessary and sufficient
conditions for economic efficiency to occur. A farm that is economically efficient
should by this definition be both technically and allocatively efficient. However, this
does not usually occur in practice as stated by Akinwumi and Djato (1997).
Akinwumi and Djato (1997) stated that it is possible for a firm to have either technical
or allocative efficiency without necessarily having economic efficiency. They explain
that the farmer concerned in this case may not be able to make efficient decisions
regarding the use of inputs for production. Thus a farmer may be unable to equate his
marginal cost of factor inputs (MFC) to the marginal values of product (MVP) to
achieve economic efficiency. Goni et.al (2007) in their study of resource use
efficiency in rice farmers in the Lake Chad area of Borno state in Nigeria, concludes
that, for economic efficiency to be derived then, the underlying assumption that the
shape of the production function (MPP) should be equal to the inverse ratio of the
input price to the output price at the profit maximization point. Khan et al. (2010) also
explained economic efficiency as the ability to combine technical and allocative
efficiencies to reflect the ability of a production unit to produce a well- specified
output at the minimum cost.
Achieving economic efficiency is essential for any production process. Then for a
firm to achieve economic efficiency, technical and allocative efficiencies are a must
have. This therefore implies that a firm can have the best amount of output in
exchange of utilisation of best priced, minimum amount of inputs, but these
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characteristics may not be enough for productive or economic efficiency. Productive
efficiency of a firm is an index that ranges from 0 to 1and can be obtained by the
multiplication of technical and allocative inefficiency indices. Färe et al (1985)
discussed the analysis of productive efficiency based on input-output measures of
scale efficiency.
Scale inefficiency for a firm is defined with respect to those firms in the sample which
operate where average and marginal products are equal (Forsund et al., 1980). Scale
efficiency is used to determine how close an observed firm is to the most productive
scale size (Forsund and Hjalmarsson, 1979; Banker and Thrall, 1992). If the firm
under study exhibits variable returns to scale, then another component of economic
efficiency which is present would be scale efficiency. A firm may however be
inefficient if it exceeds productive scale size therefore experiencing decreasing
returns-to-scale or if it is smaller than the most productive scale size. The firm under
study may also exhibit economies of scope. Scope efficiency relates to benefits
realized by firms that produce several product lines compared to specialized
enterprises. This aspect of economic efficiency is of particular interest in agriculture
since there are many debates on optimal production structure of agricultural
enterprises. An empirical measurement of farms' scope efficiency was proposed by
Chavas and Aliber (1993). They measured scope efficiency as the relative cost of
producing livestock and crops separately compared to their joint production.
3.3 Techniques and approaches to efficiency measurements
The measurement of efficiency has dominated the literature on production over the
past decade. These measures of efficiency have largely been based on the principles
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of profit maximization and cost minimization. The theoretical estimation of efficiency
has largely be centred on the measures proposed by Farrell (1957) and based on his
single input/single output measures of technical and allocative efficiency. Various
approaches has over the years been proposed and used for the empirical analysis of
efficiency in production economics. There are four major approaches which have
often been used for the estimation and measurement of production efficiency (Coelli
et al., 1998) and these are often based on the mathematical and theoretical
assumptions for their application.
Charnes et al (1978) proposed the non-parametric programming approach which tends
to lean loosely towards the mathematical programming method of profit maximization
and cost minimization. Aigner and Chu (1968), Ali and Chundry (1990) also proposed
the parametric programming approach to efficiency, the deterministic statistical
approach by Afriat (1972), Schippers (2000) and Fleming et al (2004) are also used.
The stochastic frontier approach that was jointly but independently developed by
Aigner, Lovell and Schmidt (1977), Battese and Corra (1977) and Meeusen and van
den Broeck (1977) sums the various methods for analyzing efficiency. Among these
four major approaches, two methods have often been widely used in applied research.
These are the non-parametric programming approach (DEA) of Charnes et al (1978)
and the stochastic frontier approach by Aigner et al (1977), and Meeusen and van den
Broeck (1977).
The DEA which is a non parametric approach has been made much prominent by the
works of Charnes, Cooper and Rhodes (1978). In the DEA, the relative technical
efficiency of a production unit is defined as the non-monetary ratio of its total
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weighted output to its total weighted input. This approach allows each unit to choose
its own weights of inputs and outputs in order to maximize its efficiency score. For
each production unit, DEA calculates the efficiency score; determines the relative
weights of inputs and outputs; and identifies for each unit that is not technically
efficient. Aigner and Chu (1968) proposed a deterministic frontier production
function which specified the production function as a function of several inputs. The
DEA approach which became the main focus for empirical studies on production and
efficiency provided a measure of technology that is characterized by the best-
performing firm within the industry under study.
Charnes et al (1997) noted that the performance of all the firms under consideration is
compared against a constructed frontier which provides a means of analyzing the
behaviour of firms. Previous studies of efficiency measurement specified the
production function without based on non-parametric approach without incorporating
the measure of inefficiency. These studies such as Aigner and Chu (1968), Afriat
(1972) and Richmond (1974) all discussed the problem of inefficiency in production
as being a purely random factor where all inefficiencies in the production process
where assumed to be non-stochastic. These analyses were grounded mainly in the
DEA approach which was often regarded as a mathematical programming approach
of maximizing or minimizing an objective function subject to a specified constraint.
Based on the work of Charnes et al (1978) in which they generalised the measure of
efficiency of Farrell (1957) by transforming the study from a single-output/single-
input process to incorporate multiple-output and multiple-input production
technologies. The use of the DEA is regarded as a mathematical programming
approach that is used to obtain measures of efficiency using observed data that
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provides a new way of obtaining estimates of extreme relations such as production
function and inefficiency.
A major advantage of the DEA approach in empirical estimation of production is the
fact the problem of model misspecification of functional form in most econometric
modelling is avoided, since the approach is reliant primarily on the concept of
mathematical programming (linear, non-linear etc). Charnes et al (1997) states also
that the approach can easily handle and make use of disaggregated inputs and multiple
output technologies. The use of the approach has however been criticised as not been
efficient. Lovell (1993) and Coelli (1995) have argued that the DEA does not make
any distinction between data noises and inefficiencies. This they argue makes the
results from the approach difficult to use in empirical analysis.
Another deficiency that has arisen with the use of the approach is to do with the
problem of dimensionality of the input-output variables used in the cross section.
Suhariyanto (2000) noted that the problem of dimensionality occurs if the number of
observations in the study is small relative to the number of inputs and outputs used.
Charnes and Cooper (1990), Smith (1997) and Fernandez-Cornejo (1994) have all
stated different views on the ratio between the number of observations and the
number of input and output. These views have been expressed due to the fact that the
DEA tends to overestimate or underestimate the efficient frontiers. Smith (1997) in
his study asserts that even in cases where the number of observations far exceeded the
number of inputs, the DEA still overestimated the true efficiency by 27 percent. These
opinions expressed by these authors are based on the differences they observed in
their studies. As Charnes and Cooper (1990) noted that the ratio of the number of
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observations to the number of inputs and output should at least be equal to three,
Fernandez-Cornejo (1994) differs from that proposed by Charnes and Cooper (1990)
and states that the ratio should exceed five.
It is worthy to note that the deficiencies that have resulted with the use of the DEA
have led to the development of more robust measures using the same approach as a
means of remedying the associated problems outlined above. Studies by Sengupta
(1987), Desai and Schinnar (1987) and Land et al (1990) have provided some
remedial measures to the problem of dimensionality, and the differences in the ratio of
the observed inputs and outputs used. The use of these revised models however has
their own problems. Lovell (1993) points out that these revised models of DEA suffer
from serious problems such as the empirical application of the model due to the
rigorous data requirement. He further points out that aside the rigorous data required
for the revised models, it is also important to have more information about the
variables used, its variances and covariance matrices and the probability levels of the
constraints used must all be satisfied.
3.4 Econometric approach to efficiency measurement
The use of econometric models to measure efficiency has evolved over time. From the
non-parametric approach of the DEA by Aigner and Chu (1968), Richmond (1974),
and Charnes et al (1978) more robust measures have been developed to cater for the
short-comings in the DEA. The use of econometric models for efficiency
measurement can be categorized based on the data type employed. These data can be
either cross-sectional or panel in nature. In our discussion, we assume a set of cross-
sectional data on the number of Q inputs that is used in the production of a single
output that are available to a number of N producers.
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We can model a production frontier function based on the available data where Y
represents a scalar of output produced by each producer, Xi as a vector of K inputs
used by the i-th producer and );( iXf is the specified production frontier function
which may be either a translog or Cobb-Douglas function. The β parameters of the
production function and “i” are indexes for the estimated technology parameters and
the i-th farmer in the sample to be analyzed. Econometric models of efficiency
measurement hypothesize that, production frontier functions are generally
characterized by smooth, continuous, differentiable, quasi-concave production
transformation functions (Greene, 1980).
In the econometric model of efficiency, the key measure of interest is the technical
efficiency component which captures the difference between the observed output and
the maximum feasible output (frontier output). Firms that deviate from the efficiency
frontier are assumed to be inefficient. These inefficiencies in production may be
characterised by booth technical inefficiencies or random variations that occurs in
production. Technical inefficiency of the production function would be specified as:
);(
);(
i
u
ii
Xf
eXfTE
i
where u
i eXf );( represents the observed output from the specified function and
);( iXf is the efficient frontier output. The technical inefficiency in production will
then be measured by this difference in the observed output to the frontier output.
Empirical estimation of the technically efficient frontier occurs only if TE i =1, however if
TEi < 1, then the production observation lies below the frontier and considered technical
inefficiency. Econometric and empirical models used in the study of efficiency are
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generally classified as either being a deterministic frontier or stochastic frontier based on
the underlying assumption of the inefficiency term.
Greene (1980) noted that in the deterministic frontier functions, any deviation from the
theoretical maximum is purely as a result of inefficiency in the production process of the
firm. However he notes further that those deviations from the frontier are assumed to be
determined by both the production function and the random or unexpected external
disturbances that may affect the production process. The deterministic frontier is further
assumed to cater for factors that are outside the control of the production unit, such as the
nature of the land, weather conditions and other environmental factors and so on as
inefficiency.
Battese (1991) decomposed the deterministic frontier model as:
)exp();( iii UXfY
where Yi is the possible observed production level for i-th firm, );( iXf is a
specified production function (Cobb-Douglas or translog functions), Xi as the vector
of inputs and β the parameters to be estimated. The divergence here is the introduction
of a symmetric error term Ui that is assumed to be non-negative and lies within the
range of zero and one (Battese, 1991). The Ui which is assumed to be a non-negative
random variable associated with technical inefficiency captures the firm-specific
factors which contribute to the i-th firm not attaining a maximum production level.
Battese (1991) notes further that the presence of the non-negative error term thus
defines the nature and scope of technical inefficiency of the firm and further imposes
the assumption of exp(Ui) being within the range of zero and one. This assumption
however follows that the maximum observed outputs of Yi is bounded above by the
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non-stochastic quantity );( iXf . Aigner and Chu (1968) in their specification for
the deterministic frontier specified the model with an inequality as );( ii XfY .
Their specification of the deterministic frontier model is couched in the context of a
Cobb-Douglas production function and proposed that the frontier model can be
estimated using a linear or quadratic programming approach. Aigner and Chu (1968)
suggested further that the constrained programming could be applied such that some
observed outputs could lie outside the frontier. Such estimation of the frontier
function suggested by Aigner and Chu (1968) has been criticized as the estimates of
the mathematical programming lack any economic or statistical rationale (Battese,
1991). These criticism of the parametric approach led Timmer (1971) to propose the
probabilistic frontier production functions in which small proportions of the
observations are permitted to lie outside the frontier. This feature of the deterministic
frontier was considered desirable because the model was sensitive to outliers;
however it also lacked any logical economic interpretation (Battese, 1991).
However, any error that arose with the specification of the deterministic frontier
model could easily be translated as inefficiency. A much reasonable interpretation that
can be derived is that any producer or firm faces their own production frontier
function, and that any deviations from the frontier might be a collection of random
factors that are out of the control of the producer. Since the parametric approach
failed to provide parameters with known statistical properties, Schmidt (1976)
assumed a function by adding a one-sided disturbance term to the function as
iii XfY );( . Schmidt (1976) further states that if we are to assume a
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distributional assumption for the disturbance term, the specified model can be
estimated using the maximum likelihood estimation technique.
However, if we assume that –εi follows an exponential distribution it then leads to a
linear programming approach suggested by Aigner and Chu (1968). If a half-normal
distribution is assumed a quadratic programming approach would be essential to
estimate the parameters in the model. The deficiencies encountered with the use of the
parametric approach for the empirical estimation of efficiencies led to the
development of the “so-called” stochastic frontier approach (SFA) models. Following
the short-comings of the deterministic frontiers in producing realistic estimates for
efficiency, a more robust measure was developed to correct for these short-falls in the
deterministic approach. The stochastic frontier model (SFA) independently and
simultaneously developed by Aigner, Lovell and Schmidt (ALS) (1977), Meeusen and
van den Broeck (MB) (1977) and Battese and Corra (BC) (1977) was formulated to
account for the deficiencies in using the parametric approach as a means of measuring
efficiency in production processes. The SFA follows the theoretical bases of the
deterministic model proposed by Aigner and Chu (1968), Afriat (1972) and Richmond
(1974) which assumed a production function, giving maximum feasible outputs, with
specified inputs and a level of technology. However, the major point of departure of
the SFA from the deterministic frontier functions lies in the specification of the
functional forms of both models.
As opposed to the deterministic frontier where deviations from the frontier are
assumed to be solely as a result of technical inefficiency, the SFA developed by ALS
(1977), and MB (1977) provided a new focus for efficiency estimation. Aigner et al
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(1977) and Meeusen and van den Broeck (1977) formulated their function by
incorporating a random disturbance term composed of two components. The
specifications of the stochastic frontier function in terms of a general production
function for the i-th production unit is:
iii XfY );( = ii uv
ii eXfY
);(
iii uv
In the above specified model, there is a modification to the model specified and used
by Aigner and Chu (1968). The modification in the model results from the
incorporation of a composed error term Vi and Ui which captures the effects of
random disturbances such as measurement errors, effects of weather and climatic
conditions etc which are out of control by the production firm and an inefficiency
component that takes account of technical and allocative effects. The error term Vi
represents the symmetric disturbance term and is assumed to be independently and
identically distributed as N~ ),0(2
v and takes account of the effects of the statistical
noise as stated. The error term Ui which captures the effect of inefficiencies in the
model is assumed to be non-negative and independently distributed of Vi. The error
component in the model (𝜀 = 𝑣 − 𝑢) is not symmetric, since U≥ 0. If we assume that
Vi and Ui are distributed independently of the independent parameter Xi, then ordinary
least squares (OLS) can be used to estimate the parameters which will yield consistent
estimates except for the intercept term β0. This inconsistency of the intercept arises
from the expectation of the error component as
0-E(u)E(u)-E(v))E(
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The non-positive error component Ui reflects the fact that each production units
output must lie on or below the efficient frontier denoted as [ ii vXf );( ]. This thus
assumes that any deviation is solely as a result of factors that are under the firms
control such as technical and economic inefficiency. On this assumption, the frontier
itself can be assumed to vary randomly across firms or over time for the same firm
(Greene, 1980). Greene (1980) interpretations on the random variations of the
disturbance term make the frontier function stochastic in nature.
Greene (1980) however noted that Ui can be assumed to have different distributional
assumptions such as half-normal, truncated normal, exponential and gamma
distributions. Meeusen and van den Broeck (1977) in their study however considered
the case in which Ui had an exponential distribution. The stochastic frontier model
collapses to a deterministic frontier model when δv2 = 0, and collapses to the Zellner,
Kmenta and Dréze (1966) stochastic frontier production model when δu2 = 0 (Greene,
1980). According to Aigner et al (1977), Weinstein (1964) proposed the
decomposition of the distribution function of the sum of the symmetric normal
random variable and a truncated normal random variable.
3.5 Review of efficiency measurement in agriculture
Recent studies on agricultural production and productivity over the last decade have
largely been dominated by efficiency measurement and its contribution to production
(Kumbhakar, 1989; Battese 1991; Battese and Coelli, 1995; Battese and Wan. 1992).
These studies have contributed to the development of theoretical models that are
aimed at measuring the efficiencies of production units. In agricultural production, the
possibility to empirically measure the difference between optimal (efficient)
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production levels and actual levels have led to adoption of the deterministic (DEA)
and non- deterministic (Stochastic frontier) approaches in measuring efficiency. The
stochastic frontier approach has however been the most used approach in most studies
of applied agriculture with studies such as Battese and Corra (1977), Russell and
Young (1982), Dawson et al (1991), Kumbhakar (1990), Battese (1991), Bravo-Ureta
and Rieger (1991) and a lot of other related applied works in other areas of
agriculture.
Battese and Corra (1977) are however the first to empirically apply the stochastic
frontier models to study farm-level efficiencies using agricultural data from the
Austrian Grazing Industry Survey. The study of the scope of efficiency has generally
been focused on technical, allocative and economic efficiency which has been made
prominent by the famous work of Farrell (1957). Farrell (1957) study of productive
efficiency and the decomposition of efficiency into its various components have
generated much interest largely in production of which agriculture is inclusive. In
agriculture however, two major functional forms for the study of efficiency have
dominated the literature. These are the Cobb-Douglas production function and the
transcendental logarithmic (translog) production productions. The flexibility of these
functional forms has led to its application in most recent studies on agricultural
efficiency measurements.
Kalirajan and Flinn (1983) applied the stochastic frontier model to estimate the level
of farm-specific technical efficiency of 79 rice farmers in the Philippines. The study
applied the translog stochastic frontier production function specification. Farmer-
specific characteristics such as farming experience and extension contacts were found
to impact positively on reducing production inefficiencies. Farm production inputs
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used included labour, capital and rice seedlings. These inputs and farmer-specific
characteristic were estimated to have positive effects on reducing technical
inefficiency. The average efficiency of the rice farmers was found to be 50 percent in
the study area.
Yao and Liu (1988) conducted a similar study of grain (rice, wheat and maize)
production in China. Inputs for the study included fertilizer, land, labour, irrigation
and machinery. The study applied a stochastic frontier function to estimate the effect
of these inputs on famers output. Land and labour use were found to be the most
productive and significant factors. Farmers were also found to be producing below the
efficient frontier with an average efficiency of 36 percent. This implied that farmers
had about 64 percent allowance to improve their efficiencies and increase output. The
study recommended that to improve the productivity of grain production in China,
there is the need to enhance and improve irrigation facilities, technology and pesticide
use among grain farmers.
Ajibefun and Abdulkadri (1990) also estimated the technical efficiency for food crop
production in Ondo state of Nigeria. Results of the study indicated high and wide
variations in the level of technical efficiency which ranged between 0.22 and 0.88.
Olagoke (1991) examined the efficiency of resource use in the production of rice
under two farming systems in Anambra state of Nigeria. The study found that there
exist statistically significant differences between net returns on irrigated rice farms
and non- irrigated upland rice farm lands. He finds however that, both the irrigated
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and non- irrigated farm groups underutilized resources that were available such as
land and labour.
Dawson, Lingard and Woodford (1991) studied farm-specific technical efficiency of
rice producers in Central Luzon in the Philippines. They applied the stochastic
frontier model on a set of panel data from 1970-1989. Compared to other studies on
efficiency, their study however applied both the translog and Cobb-Douglas
functional forms. The translog production function was rejected for the Cobb-Douglas
production function due to the high degrees of multicollinearity between the cross
products used. They estimated that the rice producers had a mean efficiency between
of 84 and 95 percent across the twenty two (22) farmers studied. Land, labour and
fertilizer were estimates to be the significant factors of the rice producers. They infer
that, the effect of fertilizer use though small was positively related to output
improvement. The study concludes that rice farmers had improved in their adoption of
new farming methods and improved their technological adoption between 1970 and
1984 as against a previous study by Dawson and Lingard (1989). Their study however
posits that there existed no technological lags and hence there is no rationale in
relating the very narrow spread of farm-specific inefficiencies to farm specific socio-
economic factors such as access to credit, farmer’s age, extension contact and
education and that increase in rice production can be achieved through further
technological improvement and progress.
Onyenwaku (1994) also studied the resource use efficiency between irrigated and
non-irrigated farmlands in Nigeria and concludes that irrigated farmlands were
technically efficient and had higher levels of production compared to non- irrigators.
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His finding however contradicts from that observed by Olagoke (1991) who he finds
both farm groups to be technically inefficient in the use of the resources for
production. The study concludes that both farm groups were technically inefficient
though the irrigators had a higher level of technical efficiency. He observes however
that both farm groups underutilized the available resource such as land and capital but
over utilized labour and irrigation services.
Parikh et al (1995) used a stochastic cost frontier function to study the efficiency of
agricultural production in Pakistan. The study finds that farmers’ education, credit,
working animals and extension services contributed significantly to increase the cost
efficiency of farmers. However, he finds that large farm holdings and subsistence
decreased cost efficiency significantly. Battese and Coelli (1995) analysed the
efficiency of 14 Indian paddy rice farmers using a set of panel data over a ten year
period from 1975-76 to 1984-85. The Cobb-Douglas stochastic frontier model was
used in measuring the efficiencies of these farmers. Factors such as age of farmers’,
age of schooling and year were used in the inefficiency model. The coefficients of
land and labour were found to be high and significant with elasticity’s of 0.37 and
0.85 respectively. The study observed that the variable for year included in the
inefficiency model had a small and insignificant effect over the period; farmers’ age
was found to affect efficiency positively with younger farmers being much efficient.
They however found that age of schooling impacted significantly at reducing
inefficiency.
Seyoum, Battese and Fleming (1998) studied the technical efficiencies of two groups
of maize farmers in Ethiopia. The Cobb-Douglas stochastic production function was
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used in measuring the technical efficiencies of the farmers. A cross-sectional data
from 1995-1996 was used and fitted onto the stochastic frontier. Results from the
study indicated that the project farmers had higher technical efficiencies and
productivity compared to their non-project counter parts. Average technical efficiency
for the project farmers was found to be higher than their non-project farmers. Their
average efficiencies were estimated as 97% and 79% respectively. The study
however suggested the adoption of new and improved farming technologies for maize
farmers to increase their productivity and incomes. These findings conform to that
reported by Dawson and Lingard (1989) and Dawson et al (1991) in their study of rice
producers in Philippines.
Abdulai and Huffman (1998) studied the profit inefficiency of rice farmers in Northern
Ghana. Their study applied the translog stochastic profit function on a sample of 256 rice
farmers located in four districts of the Northern region. The study results indicated that
there existed some levels of profit inefficiency in the study area estimated at 27.4 percent.
Factors that were found to positively affect farmers’ productivity and profitability were
access to credit, farmers’ education and greater specialisation. Education and credit were
however identified as significant factors that contributed to improved efficiency and
profitability. Education they emphasize enhances farmers’ ability to adapt to modernised
farming methods. Their conclusion re-enforces the proposition by Schultz (1975) who
hypothesized that education improves the productivity of farmers’ through a “modernised
environment”.
Basnayake and Gunaratne (2002) looked at the estimation of technical efficiency of
smallholder tea farmer in Sri Lanka, using both the translog and Cobb-Douglas stochastic
frontier function. Factors that affected farmers’ efficiency were found to be education,
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age and farmers’ occupation. The inefficiency model indicated that the effect of age and
education had a significant effect on the overall efficiency of farmers. The mean
efficiency was estimated to be 61.06 percent. The Cobb-Douglas production function was
also found to be the most preferred and appropriate specification for the study. This was
because there were huge differences between the mean efficiencies for the Cobb-Douglas
and translog specifications. The study concludes that older farmers are more efficient than
younger farmers since the older farmers tended to have much experience in the farming
activity. Their result on farmers’ age contradicts the findings of Al-hassan (2008), Battese
(1991) and Battese and Coelli (1995) who reported a negative relation between farmers’
age and their levels of efficiency.
Umoh (2006) adopted the stochastic frontier production function to analyse the
resource use efficiency of urban rice farmers in Uyo, south-eastern Nigeria. Results of
the study showed that farmers were operating below the efficiency frontier with an
estimated mean efficiency of 65 percent. He reports that farmers in the study region
were generally inefficient (allocative and technical), and suggest that there is the need
for farmers to increase their efficiency by adopting modern farming methods and the
efficient utilisation their of production inputs.
Amos (2007) looked at the productivity and technical efficiency of small holder 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 efficiency of
0.72. This finding indicates that there is a potential to increase the efficiency of
farmers so as to increase their output and productivity. The major contributing factors
to efficiency were age of farmers, level of the education of household head and family
size.
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The study of Chirwa (2007) on the sources of technical efficiency among small scale
maize farmers in southern Malawi, reported that maize farmers’ were generally
inefficient in their production. Further results of the study revealed that majority of
the smallholder maize were operating below their efficiency frontier with mean
technical efficiency of 46 per cent and technical scores as low as 8per cent. The mean
efficiency levels were lower but comparable to those estimated by Amos (2007).
Shehu and Mshelia (2007) used the Cobb-Douglas stochastic frontier production
function to investigate the productivity and efficiency of small-scale rice farmers in
the Adamawa state in Nigeria. Their study finds that of the factors used in rice
production, land size, labour and seed used were the most significant. The coefficient
of land was however found to be the most significant with an elasticity of 0.828. The
estimated mean efficiency was found to be 0.957 with a majority of farmers within
the range of 90 and 100 percent. They study recommends that since land size and seed
use were most efficient, efforts at increasing rice production and efficiency within the
state must be targeted at these factors.
Goni et al (2007) like Shehu and Mshelia (2007) also proceed to examine the
efficiency of resource use among smallholder rice farmers in the Lake Chad area of
Borno state in Nigeria. The study employs the Cobb-Douglas function to estimate the
resource efficiency of 100 rice farmers. They state that farmers were generally
inefficient in using all the resources efficiently and hence were operating below the
efficient frontier. The study however concludes that the inability of farmers’ to
achieve maximum yield was related directly to the high cost of inputs particularly the
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cost of fertilizer and seeds. They however recommend that increases in extension
services would greatly enhance farmers’ efficiency and productivity.
Al-hassan (2008) applied the translog stochastic production frontier methodology in
his study of farm-specific technical efficiencies of rice farmers’ in the Upper East
region of Ghana under two different cultivation system. His study was to explore
whether efficiencies differed significantly under different farming systems. The
results reports that irrigators were more technically efficient compared to non-
irrigators with a mean technical efficiency of 48 and 45 percent and that education
and access to credit helped farmers to increase their productivity levels by lowering
inefficiencies.
3.6 Chapter summary
The chapter summarizes the various definitions and measures of efficiency that has
dominated the current literature on efficiency analysis and productivity growth. The
development of the various measures of efficiency from the non-parametric approach
to the parametric approach of the stochastic frontier methods, and its use in the
empirical estimation of efficiency in agriculture is highlighted. Further discussion of
the various methodologies and assumptions underlying the use of the SFA in applied
research will be discussed in the subsequent chapter on theoretical framework and
methodology.
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CHAPTER FOUR
THEORETICAL FRAMEWORK AND METHODOLOGY
4.1 Introduction
The chapter presents the theoretical concepts and principles of production and the
development and application of the stochastic frontier model in empirical estimation
of production. The conceptual assumptions underlying the stochastic frontier
approach in efficiency measurement are also presented. This approach forms the basic
methodology used to estimate farm-specific levels of efficiency among smallholder
pineapple farmers. Factors that determine farm-specific levels of inefficiency are
discussed and these are based on the production functions specified. The functional
models used for the estimation of the efficiency frontier is clearly specified and
explained. The chapter concludes with the description of the variables used in the
study and the expected signs of the variables in both the production and inefficiency
models.
4.2 The concept of Production
4.2.1 Production Possibility Set
Classical microeconomics has generally defined the production process in terms of an
input- output process. A production generally is a process of transforming a set of
inputs into outputs with a given set of technology. Firm’s ability to combine inputs
into a set of feasible outputs is principally dependent on the available technology
referred to as technological feasibility. If we define a production function to use a
vector of given inputs which is denoted by a function X = (x1,...............,xn) for a set of
real numbers Rn, which is required to produce a set of nonnegative output which is
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denoted by the function ),,.........( 1 nyyY for a set of real numbers Rm
. Then a firm’s
production possibility is defined as the subset of the production space which is given
bynmR .
The principal of profit maximization is the dominant characteristics of most
production processes. Though economist have found other rationale for production
such as cost, prestige and market shares, the largely and well recognized goal of
production still remains profit maximization (Battese and Coelli, 1992, 1995). Since
production units (firms) are mainly concerned with the objective of profit
maximisation though cost considerations are also factored in their production
decisions, it will thus select a combination of different inputs with a level of
technology to produce a vector of output as its production plan in order to achieve its
goal of profit maximisation. A production firm’s behaviour is however not solely
guided by the principle of profit maximisation but also in the minimisation of the cost
of its inputs necessary to produce a vector of output with specified levels of
technology. The combination of technology and the vector of inputs for production of
feasible outputs define the production set of a firm.
Mas-colell, Whinston and Green (1995) describes a production set as a “set of all
production vectors that constitute feasible plans for the firm”. Lovell, Färe and
Grosskopf (1994) further explain the concept of production possibility set as the input
requirement set or the output producible set. The output producible set thus constitute
all the output vectors ),,.........( 1 nyyY that are produced from the vector of given
inputs ),........,( 1 nxxX which are subsets of real numbers.
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Varian (1992) also explains that the set of all technologically feasible production
plans is called the firms production possibility set, but the set of feasible production
plan is limited by the level of available technology. The level of technology of a firm
and the vector of inputs available will constitute the set of feasible outputs that may
be produced from the combination of technology and the available production inputs.
However a firm’s production plan may be constraint by the level of technology and
may restrict the goal of maximizing profit.
4.2.2 The production frontier
The concept of production frontiers is well espoused in most classic textbooks on
microeconomics (Varian, 1992; Gravelle and Rees, 2004). These books have often
treated production within the context of scale economies. In the illustration of the
concept of production frontier, an important assumption that arises, a firm produces a
single output y using a set of n-dimensional vector of inputs x and a specified level of
technology.
If we are to further assume that the production possibility satisfies the condition
0),( yxT , then a more general specification of the frontier technology will be given
as:
y = f (x)
Then the function f(.) is the production frontier and will give the upper boundary of T
(Varian, 1992). If we are to assume the production frontier in the form of output
maximization, then the production frontier can be expressed as:
0),(:max)( '' yxTyxf . The production frontier function then becomes the
standard to which measures of efficiency (technical and allocative) of production can
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be compared. The frontier therefore must contain only the efficient output
(observations) of the production unit.
The analysis of production frontier is crucial if we are to increase the level of
production in any production process. The analysis of frontier measurements has
largely been focussed in scale economies which form a general property of production
units. We can thus infer that as the amounts of the variable inputs used in production
are changed, the proportions in which fixed and variable inputs used are also changed.
Returns to variable proportions generally refer to how output responds in these
changes in fixed and variable inputs. In effect, the firm is free to vary all inputs, and
classifying production functions by their ‘returns to scale’ is one way of describing
how output responds to changes in inputs. Specifically, returns to scale refer to how
output responds when all inputs are varied in the same proportion. These scale
economies are the constant returns-to-scale (CRS), increasing returns-to-scale (IRS)
and decreasing returns-to-scale (DRS). The definition of scale economies in Varian
(1992) is presented as:
1. Constant returns-to-scale (CRS): A frontier technology is said to exhibit
constant returns to scale (CRS) if:
0)()( txtftxf and all values of x.
Varian (1992) however notes that there are cases in which CRS may be violated and
this occurs when we try to subdivide the production process. He argues that if it is
even possible to scale up the production process by an integer, it may not necessarily
be possible to scale the process down by the same way. Another case in which CRS
may be violated according to Varian (1992) is when we to scale up the production
process by non-integer amounts. He points out however that these two cases in which
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CRS may be violated and not satisfied are only when the scale of production is small
relative to the minimum scale output. CRS however may be satisfied according to
Varian (1992) if the following conditions are satisfied.
1.1. y in Y implies ty is in Y, for all t≥0.
1.2. X in V(y) implies tx is in V(ty) for all t≥0
1.3. The homogeneity of the production function such that:
0)()( txtftxf
Another scale economy discussed is:
2. Decreasing returns-to-scale (DRS): A frontier technology on the hand is said
to exhibit decreasing returns to scale if:
1)()( txtfxft and for all values of the vector inputs x
In the discussion of DRS Varian (1992) notes again that, the most natural case of
DRS is the case where we are unable to replicate some inputs used in the production
process. he contends further that, we should expect that the restricted production
possibility set would typically exhibit DRS. The last scale economy discussed is the
much highlighted concept in production of increasing returns to scale.
3. Increasing returns-to-scale (IRS): a production frontier technology is said to
exhibit increasing returns to scale if this assumption of the production
technology is satisfied:
)()( xtfxft and for all values of t>1
The above stated assumptions and concept of scale economies in production have
become relevant in the empirical estimation and measurement of efficiency. Their use
in efficiency measurement have been well documented in studies such as Goni et al
(2007), Banker et al (1984) and other related studies on resource and technical
efficiencies.
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4.3 Theoretical framework
Following the development of the stochastic frontier model by Aigner et al (1977) and
Meeusen and van den Broeck (1977) extensive works has been carried out to measure
the efficiency of production units in most applied economic research. Both panel and
cross-sectional data have often been used for this purpose. Studies by Al-hassan
(2007), Ambali et al (2012), Chiona (2011) and others situated their study of
measuring efficiency (technical and allocative) within the framework of cross-
sectional datasets and applied the stochastic frontier models thereof by specifying
appropriate functional forms. Considerably work in the literature also shows an
extensive use of panel data in measuring production efficiency (Schmidt and Sickles,
1984; Cornwell and Rupert, 1988; Battese and Coelli, 1992, 1995; Henderson, 2003,
Greene, 2005; Danquah et al, 2013). The advantages in the use of panel data to
measure firm level efficiency is the fact that, if inefficiency is time invariant within
the specified model, we can easily and consistently estimate the level of firm
inefficiency without distributional assumptions (Schmidt and Sickles, 1984).
However, both datasets used in the frontier analysis attempts to find estimates for
technical and resource inefficiency within a specified production function. The
estimation of technical and resource (allocative) efficiency measures within these
models largely depends on the distributional assumptions that pertain to the
inefficiency effect and the behaviour of the specified production function. Jondrow et
al (1982) explains that the distributional assumption that underlie the specification of
the stochastic frontier model is necessary if we are to separate the inefficiency effect
from the unobserved statistical noise. The use of panel data has over-time dominated
the current literature on production efficiency and these have been well documented
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in studies such as Pitt and Lee (1981), Schmidt and Sickles (1984), Battese and
Coelli (1992, 1995), Greene (2002, 2005) and Kumbhakar et al (2012).
Considerable work has also been carried out using cross-sectional data in efficiency
measurements. The study however applies the stochastic frontier approach on a set of
cross-sectional data to measure farmers’ level of efficiency. Studies by Schmidt and
Sickles (1984), Kumbhakar (1990) and Pitt and Lee (1981) provided a foundation to
the empirical estimation of efficiency using panel data instead of a cross-sectional
data. Battese and Coelli (1995) building on the foundations proposed by Pitt and Lee
(1981) specified the stochastic frontier function within a cross-sectional data
framework in the measurement of the efficiency of paddy farmers in India. Battese
and Coelli (1995) specified their function as:
iiii uvXfy );()ln(
iiii wZ
The above equations represent the stochastic frontier function and the inefficiency
model where iy is the output produced in natural logarithm of the the i-th firm, Xi is
the vector of known inputs used in the production function which are associated with
the i-th firm and is the vector of unknown parameters to be estimated given the
specified production function. The ‘composed’ error terms made up of the statistical
noise and inefficiency components were assumed to be distributed independently of
each other. Ui is assumed as the set of non-negative random variables with firm-
specific technical inefficiency of the production.
According to the Battese and Coelli (1995) specification, the inefficiency term Ui in
the production process which is assumed to be independently distributed in obtained
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by the truncation (zero) of the normal distribution with mean itZ and variance δ2. In
their specification of the inefficiency model however, Battese and Coelli (1995)
assumed there are a set of explanatory variables that affects efficiency and these may
include some parameters which are included in the specified frontier production
function provided these inefficiency effects are stochastic. In their estimation of the
time varying inefficiency effect, they proposed that if the first value of the estimated
coefficients in the inefficiency model was one and other coefficients being zero, thus
the specified model can represent the model specified by Stevenson (1980) and
Battese and Coelli (1988, 1992).
If however, all the estimated coefficients in the inefficiency model are equal to zero,
Battese and Coelli (1995) states that then technical inefficiency effects will be
unrelated to the variables specified and hence the half normal distribution specified by
Aigner et al (1977) will be obtained. Huang and Liu (1994) on their part states that if
there are any form of interaction between firm-specific parameters and input
parameters which are included in the inefficiency model, the inefficiency model
reduces to a non-neutral stochastic frontier.
Jondrow et al (1982) specified that if we are to work within the framework of the
normal-half normal stochastic frontier model of Aigner et al (1977), then the
conditional estimator of the inefficiency term iu which is the focus of the estimation
procedure for technical inefficiency model is used for the estimation of iu and it is
expressed as:
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i
i
iiii a
a
auEu
11/ˆ
2
where 21
22
uv , 2
2
v
u
,
ii Sa is the standard normal density which is
evaluated at ait and ϕ(ait) is the standard normal cumulative density function (CDF)
evaluated at ait.
From the Jondrow et al (1982) conditional estimator of the inefficiency model above,
the inefficiency frontier differs from that specified by Reifschneider and Stevenson
(1991) in that the w-random variables in the inefficiency model are not identically
distributed nor are they required to be non-negative. Battese and Coelli (1995)
however in their use of panel data for their analysis do not account for unobserved
heterogeneity in the model as observed by Greene (2002, 2005). Kumbhakar et al
(2011) however explains that the Jondrow et al (1982) estimator of inefficiency is not
consistent in cross-sectional models and that a panel data is more advantageous if
inefficiency is time invariant, then we can estimate inefficiency without necessarily
assuming a distributional assumption. The discussion of this study follows the Battese
and Coelli (1992, 1995) specification where farm-level technical inefficiency is
exogenous to the specified production function.
4.4 Conceptual framework of efficiency measurement
Several studies concerned with measuring production efficiency have tried to find an
efficient way of constructing an optimal (frontier) production output. However, since
inefficiencies occur often in most production processes, attempts have generally been
made to find levels of production that are considered as efficient output levels.
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According to Greene (1993) a firms levels of efficiency is characterized by the
relationship that exist between the level of observed production output and a
hypothesized frontier (optimal) production output. Generally, a firm’s production is
considered to be efficient if production occurs on the frontier and any deviations from
the frontier (production lying below) output are considered as inefficiencies. These
inefficiencies are normally classified as technical inefficiencies resulting from the
production process.
The principle of technical inefficiency is based on the premise of an input and output
relationships that arises from production inputs and output parameters. These
technical inefficiencies come up as a result of differences that arise when the observed
output given a specified amount of inputs is less than the maximum obtainable output.
Since firms (production units) are generally concerned with profit maximization and
cost minimization, they would choose the best input bundles that minimizes the cost
of inputs and maximizes the output producible bundle. However, since technical
inefficiencies are inherent in production, the objective of producing the efficient
output is often not attained.
Thus, for a production unit to maximize profit, it must necessarily produce the
maximum obtainable output with the level of inputs used. In such as case, the firm
will be considered as being technically efficient, by obtaining the optimal output with
its amount of inputs. We can represent technical efficiency graphically by using a
basic example of a firm using two inputs (X1, X2) to produce a single output Y. The
production process is described in the diagram below.
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Figure 4.1 Measurement of Technical, Allocative and Economic
efficiency
The figure above illustrates the definition of efficiency by Farrell (1957) in his
seminal paper. Farrell (1954) distinguished between two measures of efficiencies,
namely, technical and allocative efficiencies and explained that, while technical
efficiency (TE) reflects the ability of a firm to produce maximal output from a given
set of inputs, allocative efficiency (AE) on the other hand is a firms’ ability to use
inputs in optimal proportions to produce maximum outputs given the respective prices
of the inputs and the production technology. The combination of these two measures
of efficiency produces a measure of economic efficiency given as
EE= TE X AE.
Within the context of efficiency from the diagram above, a firm is technically
efficient if its production occurs at K where it lies on the isoquant. At M, the firm is
not efficient since it lies far away from K which represents the efficiency point. Since
X1/Y
X2/Y
●
●
●
●
M
K
L
K' I
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technical efficiency represents the distance between the observed point (M) and the
efficient point (K) at which the firms’ inputs can be reduced proportionally without
necessarily reducing output relative to the origin O. The technical efficiency of the
firm is then represented as:
OM
OKTEi
Technical efficiency measures thus lies within the range of zero and one, since it
shows the ratio of the difference between the efficient point K and M (inefficient
point) given as
OM
OKTEi 11
Technical efficiency thus lies within the range of zero and one (0<TE≤1). A technical
efficiency value of one implies that the firm is fully efficient and an efficiency of zero
implies the firm has no technical efficiency. Since allocative efficiency is concerned
with the efficient use of inputs given their prices, in the diagram specified, the input
price ratio may be represented by the slope of the straight line'II . The allocative
efficiency of the firm can also be calculated from the diagram. At point M the firms’
allocative efficiency (AE) is defined as the ratioOK
OLAEi , which represents the
distance between the points LK. These points represent the reduction in (production)
costs if production were to occur at the allocatively (and technically) efficient point
instead of the technically efficient, but allocatively inefficient point K. Economic
efficiency is thus derived from the figure as the product of the technically efficiency
points and allocative efficiency points given as:
iii xAETEEE
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OM
OL
OK
OLx
OM
OKEEi
4.5 Assumptions underlying the study
In the use of the stochastic frontier model for any empirical work, basic assumptions
that underlie their use must be adhered to. In this study however, three of these
assumptions are outlined as follow:
First, we assume that pineapple producers in the study area faced with
identical production functions.
Secondly, that all farmers under study use identical production factors in
their production activity and information relating to farmers socio-economic
characteristics are fully incorporated into the specified stochastic frontier
model
The final assumption relates to the nature of the ‘composed’ error term. This
explains that the error terms are symmetric and distributed independently of
each other.
4.6 Cross-sectional production frontier models
Generally, there are several models that are used in measuring cross-sectional frontier
models. Of these, three methods have gained popularity in the literature for the
estimation of efficiency (technical and allocative) using cross-sectional data. These
methods are the Corrected Ordinary Least Squares (COLS) (Jaforulah and
Premachendra, 2003), Modified Ordinary Least Squares (MOLS), and the Stochastic
Frontier Production Function (1977; Meeusen and van den Broeck, 1977). A
description of the above mentioned methodologies is provided below.
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4.6.1 Corrected Ordinary Least Squares (COLS)
In the use of the Corrected Ordinary Least Squares (COLS) in efficiency
measurement, the Ordinary Least Square (OLS) approach is used to first estimate the
parameters and the intercept values simultaneously. According to Greene (1980) the
use of OLS in estimating efficiency results in parameter estimates that are consistent
but less efficient due to the biased estimates for the intercept term (βo). He suggests
that, since the stochastic frontier approach is nonlinear in the parameters, a nonlinear
estimation approach such as the maximum likelihood estimates provides consistent
and unbiased parameter estimates relative to that estimated using OLS. The bias of the
intercept in the OLS estimation method is corrected such that the estimated frontier is
bounded from above. The correction of the biased intercept is shown below as:
)ˆmax(ˆˆ0
*
0 iu
where *
0 is the intercept of the COLS model, 0 and iu are intercept and the
residuals obtained from the OLS estimation method. The correction of the bias in the
model is then obtained by rewriting the residuals in the opposite direction as:
)max(ˆˆ*
iii uuu .
The measurement of technical efficiency using COLS is then obtained by the
correction of the residuals specified as:
)ˆ(*
ii ueTE
Though this approach of estimating efficiency is relatively simple to use, the
estimated parameters in natural logarithm (logs) of the production are parallel to the
OLS regression. Kuwornu et al (2013) explain that in such as a case, we may not be
able to distinguish the structure of the “best practice production technology”. The
reason for this is that the “best practice production technology” will be the same as
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the “central tendency production technology”. Winsten (1957) also explained that the
“best practice production technology” is expected to change relative to that of the
“central tendency production technology” so that the less efficient producers can be
differentiated form the “best practice production technology”. The estimation of
factors that cause inefficiency using this approach has received considerable debate in
the literature on frontier measurements. These arguments have been based on the two
stage estimation approach adopted in measuring inefficiency using the Corrected
Ordinary Least Squares (COLS).
Khem et al (1998) states that the most appropriate way to measure efficiency is to first
estimate the efficiency scores and afterwards use the predicted efficiency levels
against the firm-specific characteristics specified. Whilst Kumbhakar et al (1991),
Battese and Coelli (1995) have argued that this approach of estimating efficiency does
not produce consistent estimates of the firm-level inefficiencies. They have however
argued that the firm-specific characteristics should be included into the specification
of the production frontier and the inefficiency model since their inclusion has a
significant effect on the efficiency score. Despite the criticisms against the use of the
two step approach for measuring efficiency, Ray (1988) and Kalirajan (1991) have
argued and defended this approach based on the fact that we are able to identify and
investigate the firm-specific characteristics that affects efficiency in the production
process.
4.6.2 Modified Ordinary Least Squares (MOLS)
The use of the Modified Ordinary Least Squares (MOLS) in the measurement of
efficiency is a deterministic frontier approach that is modelled using the standard OLS
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assumptions such that the disturbance term follows a one-sided distribution such as
the half-normal and exponential distribution (Kuwornu, 2013). However, since the
estimated intercept is biased in the OLS estimation, as it occurs in COLS, the
intercept is corrected or modified by using the mean of the assumed one-sided
distribution specified. The modification of the mean in MOLS is stated below:
)ˆ(ˆ0
**
0 iuE
)ˆ(ˆˆ**
iii uEuu
Afriat (1972) and Richmond (1974) states that, the estimation of technical efficiency
using MOLS is the same as that in COLS and the estimation procedure is easy to use.
Despite being an attractive estimation approach due to its ease, it is saddled with a
few limitations. These limitations include; the possibility of obtaining technical
efficiency scores that are greater than 1. The efficiency score greater that one implies
that some firms’ production occurs beyond the efficient frontier. Moreover, the use of
MOLS causes some shift in the estimated intercept (β0) parameter such that no
production unit is technically efficient.
4.6.3 Stochastic frontier production functions
The stochastic frontier production function forms the main methodology on which the
analyses of the study are presented. A description of the frontier function is presented
below. The frontier function (translog or Cobb-Douglas) is assumed to be given as:
iii XfY );( iii uv
iV is a two sided error component which captures the effect of statistical noise in the
specified model and Ui is the nonnegative random variable that captures the effect of
technical inefficiency. Vi is assumed to be symmetric and distributed independently of
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Ui with mean zero and a constant variance [N~ ( ),02
v ]. Ui which measures the effect
of technical efficiency is assumed to be distributed independently as N+~ (0, )
2
u and
can take on any distributional assumption such as the half-normal distribution (Aigner
et al 1977), exponential distribution (Meeusen and van den Broeck, 1977). Other
proposed specifications for the distribution of Ui include the truncated normal
distribution [N~ (μ, σ2)] (Stevenson, 1980) and the normal-gamma density (Greene,
1980).
The specification of the normal-gamma distribution however provides a richer and
more flexible parameterization of the inefficiency distribution in the stochastic
frontier model than either of the specified distributional forms such as the normal-half
normal and normal-exponential distributions. Attempts however, in the use of the
normal-gamma distribution have achieved very limited success, as the log likelihood
in the distribution is possessed of a significant degree of complexity. Greene (1990)
has attempted a crude maximization procedure which failed to provide sufficient and
satisfactory parameter estimates. The challenges that arose with the interpretation of
the normal-gamma distribution have led to the specification of either the half-normal
distribution or the exponential distribution in most empirical studies.
Greene (1990) has however explained that the specification of any particular
distributional assumption about the inefficiency term (Ui) does not necessarily affect
the predicted efficiency scores. Technical efficiency can then be defined as the ratio
between the observed output and the maximum obtainable output. This is expressed
as:
iTE =
𝑦
𝑓(𝑋; 𝛽)𝑒𝑣
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In the above specified equation, the numerator represents the observed production
output and the denominator is the stochastic frontier function and consists of the
factors that are common to all the producers and 𝑒𝑣𝑖 is the firm-specific characteristics
that capture the effects of random shocks of each producer. Since the study aims at
improving the levels of efficiency of pineapple producers, the stochastic frontier
model is relied on to aid in measuring farm-specific efficiency levels that will aid in
policy formulation for the purpose of improving productivity and growth. For the
purpose of measuring the efficiency of farmers, the single stage estimation approach
proposed by (Coelli, 1995) is used to compute the relationship between the producer
and producer characteristics and the technical efficiency scores. The frontier model is
specified as
ii uv
ii eXfY
);(
where Yi is the observed output, Xi is a vector of inputs parameters, β are the vectors
of technology parameters to be estimated and e represent exponent. In the specified
model above, the error term vi is N~ ( ),02
v and captures random variation in output
due to the factors beyond the control of the farmers, such as variation in weather,
nature and type of soil, measurement errors and other statistical disturbances. The
error term Ui captures technical inefficiency in production, assumed to be farm-
specific with non-negative random variables distributed as N+ ( );
2
uiu . The
distribution specified for Ui follows the truncated normal distribution with mean μi
and variance 2
u
by (Stevenson, 1980). The μi which measures the level of
inefficiency in the frontier function is thus defined as:
iii Zu
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where, Zi is a (k×1) vector of independent parameters that is associated with the
technical inefficiency effects which could capture socio-economic farm management
features. δ is a (1×δ) vector of unknown parameter to be estimated. However, since
we are interested in measuring farm-specific efficiency between the frontier output
and observed output, we specify the difference as
iv
ii eXfY );(*
From the frontier function specified, deviations in production are assumed to be as a
result of purely random factors that are out of the control of the farmers, and not as a
result of technical inefficiencies. Conversely, since we assume that there are
inefficiencies that exist in the activities of the production unit (PU), we specify a
frontier function incorporating firm-level inefficiencies as:
ii uv
ii eXfY
);(
From the forgoing, we can examine the difference between the observed output and
the frontier output in terms of inefficiencies (technical). The technical efficiency
function is specified as
i
ii
v
i
uv
i
i
ii
eXf
eXf
Y
YTE
);(
);(*
iu
i eTE
The difference that is observed between the maximum frontier output and the actual
output is captured in u (i.e. technical efficiency of production). The estimation of Ui
depends on the distributional assumption specified though Greene (1980) has
explained that the specification of a particular distribution assumption does not impact
significantly on the estimated parameters for the inefficiency frontier. The higher the
value of Ui the higher the level technical inefficiency, however if Ui is zero (0), then
the farmer is said to be technically efficient and hence deviations from observed and
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frontier output are as a result of uncontrolled factors outside the farmers control.
According to Battese and Coelli (1995) production is technically efficient if Ui =0
thus production lies on the frontier and below the frontier if Ui > 0 (i.e. technical
inefficiency).
The Jondrow et al (1982) conditional estimator for the inefficiency term and the
specified distributional assumption about the inefficiency effect is estimated by the
maximum likelihood estimation approach and this includes the firm-specific
efficiency effects. Battese and Corra (1977) provides an estimation approach for
technical inefficiency obtained by parameterization of the variances as:
222
uv ;
)(22
2
2
2
uv
uu
;
2
2
v
u
where σ2 is the total variation from the model, σv
2 is the variation as a result of
statistical noise and σu2 the variation arising from inefficiency. The γ parameter
measures the degree of variability between the production process as to whether the
difference in production is due to technical inefficiency or wholly due to random
variations in production. If γ = 0, it implies that the variability in production is as a
result of the effects of random disturbances and not from technical inefficiencies.
However if the estimated γ=1, then this implies that differences in production arises
as a result of inefficiencies. If the variance parameter γ lies within the range of 0 and
1 (0 < γ < 1), then the difference from the frontier output is attributed to both
stochastic errors and technical inefficiency.
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4.7 Empirical frontier models specified for the study
Since the development of the stochastic frontier production model by Aigner et al
(1977) and Meeusen and van den Broeck (1977), there has been considerable
application of the methodology in the literature on production efficiency. Battese and
Corra (1977) however were the first to apply the methodology on agricultural data.
The study however adopts the approach proposed by Battese and Coelli (1995) to
study the level of efficiency among smallholder pineapple farmers. The stochastic
frontier production function assumes that firm–level technical efficiency is
exogenously determined outside the production process and that inefficiency is
directly influenced by farmers’ socio-economic factors. Given this back-drop, the
study adopts the two most commonly applied methods for efficiency studies on
production.
Generally, the choice of a functional form for any empirical work is of utmost
importance if we are to find consistent estimates for the parameter. The reason for a
consistent functional form stems from the fact that, the choice of a model can
significantly impact on the estimates derived. In most empirical study, flexible
functional forms are most preferred since they do not impose significant restrictions
on the parameters to be estimated and neither on the inputs variables used. For this
study however, we adopt both the translog production function and the Cobb-Douglas
in our estimation of farm-level technical and resource-use inefficiency. The choice of
an appropriate model will be dependent of the test statistic of the functional forms.
The specification of both functional forms is to aid in the selection of the most
appropriate model to be used for the study.
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Most studies on efficiency have employed the translog stochastic frontier production
function specification. The reasons for this specification are that the function does not
assume homogeneity, and neither separability. The function does not also impose any
restrictions on the elasticity of substitution on the specified factor input in the
function. Berndt and Christensen (1973) states that the translog function allows for
variability of the partial derivative of elasticities of substitution and for the use of
several input factors.
However this functional form has a problem of multicollinearity between the input
variables specified. Abdulai and Huffman (2000) explain that one difficulty with the
use of the translog function is that, there is a problem associated with the
interpretation of the cross terms. The translog stochastic frontier production function
is specified as:
n
i
n
i
m
j
iijiijiii uvInXInXInXInY1 1 1
02
1
5 5
1
5
1
02
1
ii j
iijiji
i
iii uvInXInXInXInY
Where Yi is the observed output produced by farmer i, Xi and Xk are the vectors of
inputs used in the production function, 𝛽˳ 𝛽j and 𝛽i are the coefficients to be
estimated. The composed error term is represented by the two sided error term, where
vi captures the effects of statistical noise and other factors such as bad weather, nature
of soil etc that are out of the control of the farmer. Ui however measures the effects of
technical inefficiency that affects the farmers’ from reaching the efficient production
point. Onumah and Acquah (2010) have also explained that the estimated coefficients
within a translog function do not have straightforward interpretations as emphasized
by Abdulai and Huffman (2000). They explain that the estimated output elasticities of
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the input variables are functions of both the first-order and second-order partial
derivatives of the input variables given as:
n
i
ijiji
ij
ij XX
YEe
1
lnln
)(ln
An alternative functional form specified for the measurement of production efficiency
is the Cobb-Douglas stochastic frontier production function. The Cobb-Douglas
function just like the translog function has been used extensively in the literature
(Idiong, 2007; Essilfie et al, 2011; Djokoto, 2011). In his study of technical
efficiency of rice farmers in Nepal, Kedebe (2001) adopts the Cobb-Douglas function
to explain for the factors that causes inefficiency. He states that the choice of
functional form is important if we are to make reasonable inferences about the
estimated parameters. Studies have shown that the Cobb-Douglas (C-D) function is
also an appropriate specification for measuring efficiency. The reason being that, the
C-D function does not impose strict restrictions on the input parameters, is flexible to
use and the interpretation of the estimated coefficients are fairly easy to make. The C-
D production function specified for the study is given as:
iii
n
i
iiii
uv
InXInY
1
0
5
1
0
i
iiiii uvInXInY
The variables specified in the C-D function are as those specified for the translog
function and are defined as:
1Y The total quantity of pineapples harvested in kilograms
1X Size of farm measured in acres.
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2X Total number of labour employed in man-days. Labour is made up of both
family and hired labour used in production.
3X The volume of fertilizer used in production. Fertilizer used is measured in
kilograms and consist of both solid and liquid fertilizer. Liquid fertilizer is measured
in milliliters (m/l).
4X Total amount of planting materials (suckers) employed in pineapple
production. Its unit of measurement is in kilograms.
4.7.1 Definition of variables and expected signs
From the specified production functions, the measurement of the productive
efficiencies of smallholder farmers depends on the input parameters and farmers’
socio-economic characteristics. Five key variables on pineapple production were
employed in the study. These were, output of pineapples produced (kgs), farm size
cultivated (acres), labour used (man/days), fertilizer use (kgs), capital (GH¢), planting
materials used (kgs). Firm-specific effects that are related to farmers' efficiencies
included in measuring efficiency were: age, farm size, experience, access to credit,
education.
All farmers are however assumed to be faced with the same production functions and
thus have identical use of production inputs. Hence the key determinants that will
account for inefficiency may result from farm practices and socio-economic factors
that are unique to each farmer. Since the stochastic frontier model is nonlinear in the
parameters, a linearization of the production parameters is carried out by taking
natural logarithms on the output and input variables. The table below indicates the
variables specified in the production functions model for measuring the efficiency of
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smallholder pineapple farmers’ in the study area. These variables are selected based
on their use in the literature to measure efficiency.
Table 1: Definition of variables in the production frontier
Variable
Definition of variable
Output
The maximum quantity of pineapples harvested by
farmer measured in kilograms
farm size
The total area of land occupied for pineapple production
in acres
Labour
The total number of labour employed. Labour use is
made up of both family and hired labour. It is measured
in man/days
Fertilizer
This refers to the total quantity of liquid and solid
fertilizer used. liquid fertilizer is measured in litres (ml)
and solid fertilizer in kilograms (kgs)
Planting materials
The total quantity of suckers used in productions in
kilograms (kgs)
Capital (GH¢)
This is the total amount of cash used. Capital use entails
the cost of inputs and labour employed
4.7.2 Measuring resource efficiency, elasticities and returns to scale of
production.
The elasticity of production which is the percentage change in output as a ratio of a
percentage change in input measures a firm's success in producing maximum output
from a set of input (Farrell, 1957). In measuring the efficiency of the production of
pineapple farmers’, the elasticities and the returns to scale of the input parameters in
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the production function are of significant importance. These elasticities of the input
variables are necessary in the estimation if we are to find the degree of responsiveness
of output to the changes in inputs. The elasticity of a factor input is given as:
5
1
lnln
)(ln
i
ijiji
ij
ij XX
YEe
On the measurement of the returns to scale of the production function, the study
applies the conventional approach used by Goni et al (2007), Onumah and Acquah
(2010) and Essilfie et al (2011), in which the returns to scale is obtained by
summarizing the estimated parameters (EP) of the specified production function.
Resource efficiency is measured as the ratio between the marginal value product and
the marginal factor cost of the input variables in the production function. A resource
is efficiently utilized if the marginal value product (MVP) equals the marginal factor
cost (MFC). The MVP of each input variable is calculated as:
MVP= yxi PMPP
where xiMPP is marginal value of the specified input variable and Py is the per unit
price the output. xiMPP is derived as:
Y
X
X
Y i
i
i .
=
X
Y
X
YMPP ixi
iX is the mean of the input variable, Y is the mean of the output and i is the output
elasticity of the variable in the production function. MVP can then be specified from
the above specification as;
y
i
xi PX
YMVP .
.
The derivation of the marginal factor cost of the variable input is given as
xiPMFC = xxi PX
YMFC .
.
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For efficiency of resource, then MVP=MFC where Px and Py are the respective unit
prices for the output and the input production variable. The ratio of MVP and MFC
provides the measure of efficiency as
MFC
MVPr
The decision rule for a resource being efficient as provided by Goni et al (2007) and
applied by Wayo et al (2013) is presented as;
If xixi MFCMVP , r >1 there is under- utilization of the input resource xi.
If xixi MFCMVP , r <1 there is over- utilization of resource xi.
If xixi MFCMVP , r =1 there is optimum utilization of resource xi
The estimation for the returns-to-scale of the input parameters in the production
function is given as the summation of the output elasticities in the function. Returns-
to-scale is formulated based on the assumptions specified, if
1EP ; the production technology exhibits constant returns to scale and implies
that doubling the factor inputs results in the doubling of the outputs.
1EP ; The production function exhibits decreasing returns to scale. This implies
that doubling the inputs results in a less than increase in output.
1EP ; implies that doubling of inputs leads to more than increase in output.
Analysis of the efficiency of the resource use in pineapple production is thus based on
these assumptions on elasticity of the input parameters and their effect on outputs. \
4.8 Determinants of inefficiency
The source of technical and allocative efficiency is of an overriding importance to the
study on efficiency analysis. Relevant studies on technical and allocative efficiency
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have generally been concerned with the role farmers’ and farms socio-economic
characteristics impact on their levels of efficiency. Mixed results have been found
between farm-specific characteristics and farm level inefficiencies. Tauer and Belbase
(1987) reports that, geographic locations have been found to have ambiguous
relationship to farm-specific technical efficiency. They also conclude that there exist
no direct relationship between farmers’ efficient utilization of input variables for
production and their levels of formal education.
In this study however we include education as a variable in measuring technical
efficiency of farmers’ since other studies on efficiency have found it to reduce the level
of inefficiency (Al-hassan, 2008; Idiong 2007; Onumah and Acquah, 2010, Kuwornu et
al 2013). The technical efficiency model for the study follows that proposed by Battese
and Coelli (1995) where the level of efficiency is associated with farmers’ socio-
economic characteristics. TE is specified as:
iiii wZu (Battese and Coelli, 1995)
where Zi are the set of exogenous variables that determine technical efficiency, δi is the
coefficient in the estimated inefficiency model and wi is a random error term. In our
present study, we specify the technical efficiency model as:
wFARMSIZECREDEXPERAGEEDUu
wZu
o
i
iiii
54321
5
1
The education variable (EDU) represents the number of years of formal education that
is achieved by the household head. The level of education of the household head
serves as a proxy for managerial know-how in the application of production inputs.
Higher formal education of farmers’ together with high levels of farming experience
is expected to lead to better managerial decisions in the use of inputs. The expected
sign for the education in the inefficiency model is negative since increasing education
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will lead to the reduction of inefficiency.
AGE of the farmer is included to assess the effect of age on the level of technical
efficiency. The age of a farmer represents his real age. The use of age as a variable is
to be made distinct from farmers’ level of experience. Since farming in the study area
is mostly traditional, we expect to have a higher number of aged farmers’. The
expected sign of the age variable is either negative or positive.
EXPER is the number of years a farmer has been actively involved in the farming
activity. The number of years of experience of a farmer is expected to impact
positively in the production decision making. It is believed that the more experienced
farmers’ are better informed in their production decisions regarding their activities
since they are able to bring their years of experience to bear on their managerial
decision making. EXPER serves as a proxy for managerial expertise in the production
process. Experience is expected to impact positively on farmers’ production
behaviour and thus reduce technical inefficiency. The expected sign of EXPER in the
inefficiency model is negative.
CRED represents the sum total of credit received by farmers either in cash or in kind.
It is measured in GH (¢). The use of credit by farmers is also believed to impact
significantly on their relative efficiencies. This arises because; farmers with sufficient
credit are able to acquire the required inputs essential for their activity. The
appropriate use of credit by farmers’ tends to improve on their productivity thereby
reducing inefficiencies. The expected sign of credit in the model is negative.
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FARM SIZE appears in both the specified production frontier function and the
inefficiency model. The inclusion of farm size in the inefficiency model is to account
for the changes in production as a result of increasing farmers’ efficiency. It serves as
a proxy for the effect on land on efficiency. This inclusion is conventional and based
on the assumption that farm size causes a shift in the frontier and further pushes the
farmer much closer to the efficient frontier. Farm size is expected to have a negative
sign on reducing production inefficiency.
The table below presents a summary of the variables specified in the inefficiency
model.
Table 2: Variables in the inefficiency model and expected signs
Variables
Expected Sign
Education (EDU)
Negative (-).
Age (AGE) Positive / Negative (+/-)
Experience (EXPER) Negative (-)
Farm size (FARM SIZE)
Negative (-)
4.9 Source of Data
A cross-sectional household survey data on crop production is used for the study. The
data is collected from the FBO dataset (ISSER, 2014), which includes a wide range of
data regarding production of various crops. Farm level data on households includes
the nature and composition of households, crop production activities, land use, credit
availability, output levels, off-farm activities and labour use. Data specific to the study
area in relation to farmers’ production activities are used. One hundred and fifty (150)
farm households are selected from the pool of dataset and these selections were based
on their cultivation of pineapples. In addition to the data on farm households, farmers’
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socio-demographic characteristics such as age, marital status, educational level and
household size are also included.
In this study, we define a household as defined by Ellis (1993), in which a household
is characterized by a group of social unit sharing the same residence. Thus household
members are assumed to share the same resources which include land use and
income. Data relating to study is sampled from the cross-sectional dataset. These
consist of other farmers’ who cultivate different food crops other than pineapples.
However, data pertaining only to households cultivating pineapples is selected and
used for the analysis.
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CHAPTER FIVE
DATA ANALYSIS AND DISCUSSIONS
5.1 Introduction
This chapter presents the findings of the study. The chapter begins with the
discussions of farmers’ socio-economic factors such as age, sex and educational
distribution. Summary statistics of the production inputs and socio-economic factors
affecting the farmers are presented. The Ordinary Least Square (OLS) approach is
used in the estimation of the production parameters. Estimation of the parameters in
the frontier function is obtained by the use of the maximum likelihood estimation
(MLE) approach from the Cobb-Douglas stochastic frontier production function. The
econometric results from both the OLS and stochastic frontier functions are discussed
and this is followed by the discussion of the estimates obtained from the
specifications. The results on returns-to-scale of the production inputs and the
efficiency of resource-use are also presented discussed.
5.2 Farmers Socio-economic Characteristics
The socio-economic characteristic of pineapple farmers’ are key determinants and
plays a crucial role in measuring efficiencies. The study presents some farm specific
socio-economic characteristics and examines the effect that arises as these
determinants changes and their effects on farmers’ technical and allocative
efficiencies. Tables 3 and 4 present the age and sex distributions of the selected
pineapple farmers in the study area. The results on farmers age distribution indicates
that about 34.67% of farmers were aged between 21 and 30 years. 27.33% of the
farmers were found to be between the age of 31 and 40 years. This indicates that more
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than 50% of the farmers who were actively engaged in pineapple production within
the area were aged between 21 and 40 years.
The higher percentage, of about 64% of farmers within these age groups indicated that
much younger farmers are fully engaged in pineapple cultivation.
The reason for this higher number may be attributed to the higher profitability of the
farming activity. The result also shows that more youth are into pineapple farming
which is an encouraging statistic. The higher of younger farmers’ engaged in
pineapple farming may be probably be as a result of the lower labour and less the
capital required, and the associated higher profitability of pineapple farming. Of the
sampled farmers’, less than 20% fell within the age groups of 51 and 70 years. This
result indicates a lower proportion of farmers were ageing. The rationale for
analyzing the effects of age on inefficiencies is based on the fact that farmers’ age
largely affects their level of efficiency and productivity.
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Table 3: Age distribution of pineapple farmers
AGE GROUPS
FREQUENCY
PERCENTAGE (%)
21-30
52
34.67
31-40
41
27.33
41-50
25
16.67
51-60
21
14.00
61-70
5
3.33
70+
TOTAL
6
150
4.00
100.00
Source: authors’ computation based on Household Database ISSER, 2014.
Table 4 shows the proportion of male-female pineapple farmers in the study area. Of
the total number of farmers selected for the study, it can be shown that pineapple
farming is a male-dominating activity with ninety-three (93) farmers representing
sixty-two percent (62%) of the total farmers. The remaining number fifty-seven
representing thirty-eight percent (38%) of the farmers’ were found to be females.
Though male farmers’ dominated in the selected sample for the study, women were
also found to be actively involved in the activity. The significance of women farmers
indicates that, more women are gradually entering into pineapple production.
The role that women farmers play in poverty reduction and malnutrition is crucial and
thus having a significant number of women farmers’ in pineapple production shows a
positive sign for domestic growth and development. Even though the study does not
explore the differences that exist between the efficiencies of male and female farmers,
the knowledge of the number of female farmers’ who are into pineapple production is
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of key policy relevance. This insight thus provides further information as a means of
encouraging and increasing the number of women farmers in agriculture and
particularly into pineapple production.
Table 4: Sex distributions of pineapple farmers
SEX
FREQUENCY
PERCENTAGE (%)
Female
57
38.00
Male
Total
93
150
62.00
100.00
Source: Author’s computation using Stata 13.0
Table 5 below shows the level and access of credit received by farmers and is
categorized into two major headings as accessed credit and no credit access. The table
indicates that a small majority of farmers had access to credit, and these were in
diverse forms and comprised of loans from financial institutions (particularly
community and rural banks) and financial assistance from friends and relations. The
number of farmers who had access to credit represented 64.67% and 35.33% as those
who had no access to credit. Based on the data available for the study, farmers who
received no form of credit based their inability to access loans from financial
institutions as a major factor that militated against their expansion and productivity.
They also cited the high rate of interest charged and collaterals demanded by these
financial institutions as a major constraint in accessing credit. Though farmers’ access
to credit is a necessary factor that contributes positively to agricultural production,
less than seventy percent (70%) of the farmers’ received any form of credit. Thus
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their ability to expand their share and use of land, acquire new farm implements and
purchase agro-chemicals and planting material to increase production is
limited.
Table 5: Farmers’ access to credit
CREDIT ACCESS
FREQUENCY
PERCENTAGE (%)
No credit received
53
35.33
Accessed credit
Total
97
150
64.67
100.00
Source: author’s computations based on Household Database, 2014.
5.3 Summary statistics of the production variables.
Table 6 presents the summaries of the various production inputs used in the analysis
of the production function. These summaries include the general measures of central
tendency such as mean, standard deviations, minimum and maximum values of the
production variables.
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Table 6: Summary statistics of production variables
Variables
Mean
Std Dev
Min
Max
Output (kgs/acre)
585.5667
631.4747
100
5000
Farm size (acres)
3.891333
2.810358
1.2
20
Labour (man/days)
5.453333
3.661127
2
22
Fertilizer (kgs)
4.533333
3.104806
2
17
Planting material (kgs)
23.12
21.10502
3
150
Capital (GH¢)
526.6
628.7004
50
5500
Source: Author’s computation using Stata 13.0
The quantity of output that is produced from any agricultural activity generally
depends on the quantity and quality of the various inputs used in production. The
results of the table on summaries statistics of the output and input variables indicates
that, farmers’ use of land for pineapple production had a mean of 3.89 acres with a
standard deviation of 2.81. The use of land by pineapple farmers’ ranged between 1.2
and 20 acres for lowest and highest acreage use respectively. The relatively smaller
use of land by these farmers’ is exhibited in their lower production output. From the
summary statistics, the average pineapple produced were 585.56 kilograms with a
standard deviation of 631.47.With the low usage of land, the minimum and maximum
output of pineapple produced by the farmers were also found to be 100 and 5000
kilograms respectively.
5.4 Estimation of production frontier function using Ordinary Least Square
In the estimation of the relative efficiency of pineapple farmers’, the log-linear Cobb-
Douglas production function is assumed as the appropriate functional form for the
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study. The appropriateness of the translog function specification was also tested but
rejected in favour of the Cobb-Douglas specification. The result from the translog
specification does not yield desirable estimates and most of the coefficients are found
not to be statistically significant and thus are not reported in the study. Based on the
results from both functional forms, results from the Cobb-Douglas specification
provided the best estimates. As a first step in estimating the production parameters,
the results from the OLS method were used. This was carried out to ascertain how the
production variables used in the estimation fitted the specified model.
The ANOVA table (Appendix 5) shows that the input parameters are jointly
significant in explaining the variations in the model. This is explained by the high R2
and adjusted R2
values 57.2% and 55.7% respectively. The high R2 value implies that
about 57.2% of the variation in the model is explained by the input variables. The F
statistic of joint linear restriction between the input parameters showed that there exist
a strong relationship between the input and output variables and was found to be
significant at the 1% level. The OLS estimation approach is used as a preliminary test
of the input parameters for the frontier analysis. The results of the OLS estimation are
presented in table 7.
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Table 7: Ordinary Least Squares Estimation (OLS) of the Cobb-Douglas
production function
Variables
Parameter
Coefficient
t-ratio
Constant
0
4.617208
(.3642757)
12.68
Ln farm size
1
.9266578
(.0893328)
10.37
Ln Labour
2
.1232953
(.079462)
1.55
Ln fertilizer
3
.1266024
(.0820537)
1.54
Ln planting material
4
.0105547
(.0667458)
0.875
Ln capital
5
-.0112004
(.3642757)
-0.20
R2 0.5722
F-statistic
38.52
Source: Author’s computation using Stata 13.0
5.5 Stochastic frontier production function estimation using Maximum
Likelihood
The stochastic frontier production function is used as a means of meeting the first
objective of the study. In frontier studies, the estimated parameters of the stochastic
frontier function indicate the best practice performance that is technically efficient in
the application of the variable inputs used in the production process. Table 9 and 10
shows the summary statistics and the Maximum Likelihood Estimates (MLE) for the
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stochastic frontier production function of the input variables. The results were
obtained using the Stata statistical package version 13. Bravo-Ureta and Rieger
(1991) have stated that the MLE approach is far more an appropriate and efficient
method at estimating frontier functions than the conventional OLS and COLS
approach. The analysis of efficiency measurement is not necessarily concerned with
the production variables, but rather the determining factors that cause inefficiencies of
production.
Table 8: Summary statistics of the production variables
Variables
Mean
Std Dev
Min
Max
In Output 6.020342 .7934214 4.60517 8.517193
In farm size 1.168346 .5902459 .1823216 2.995732
In labour 1.525984 .5679417 .6931472 3.091043
In fertilizer 1.325946 .5846889 .6931472 2.833213
In planting material 2.891249 .7063128 1.098612 5.010635
In capital 5.897537 .8066911 3.912023 8.612503
Source: Authors’ computation using Stata 13.0
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Table 9: Maximum Likelihood estimation of the Cobb-Douglas production
function.
Variables
Parameters
Coefficient
Standard Error
z-statistic
Constant
0
5.004141***
.3849455
13.00
Ln farm size
1
.93445724***
.0856176
10.91
Ln labour
2
.1180118*
.0774201
1.52
Ln fertilizer
3
.13500055**
.08075
1.67
Ln planting material
4
.0157188
.065
0.24
Ln capital
5
-.0232332
.055625
-0.42
Source: Author’s computation using Stata 13.0
The use of the Ordinary Least Square (OLS) estimation in table 7 was to serve as a
pre-test for the production variables in the estimation of the production function using
the maximum likelihood estimation approach. The coefficients in the production
functions indicate the elasticity of the various input variables to output. The results
from the estimation of the production function shows that of the production
parameters used, farm size, labour, fertilizer use and planting materials had the
expected positive signs and were found to be significant with the exception of capital
use which had a negative coefficient. These estimated coefficients indicated that,
these variables had positive effect on affecting farmers’ productivity.
The coefficient of farmers’ use of land (farm size) had the highest elasticity of 0.934
and was found to be the most significant factor of production. It was also found to be
significant at the 1% level. The high and positive coefficient of farm size indicated
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that a percentage increase in farmers’ use of land would result in 9.34% increase in
output. The results of farmers’ use of farmlands is consistent with the findings of
Abdulai and Huffman (1998) Goni et al (2007), and Alhassan (2012) who found
positive relationship between farmers use of land and farm output. Imoudu (1992),
Onyenweaku et al (1996) and Ohajianya (2006) have also suggested the significant
role that farm size plays in productivity and profitability. The results of the study are
hence in consonance with other related studies on efficiency. This result thus
indicated that the use of land in agricultural production is of importance if farmers are
to make significant gains from their activities. Studies related to agricultural
efficiency have strongly posited the importance of the efficient use of land resource
towards productivity.
Another input variable that was of significant importance relates to farmers’ use of
chemical fertilizer. The efficient use and application of fertilizers in agriculture has
being argued to improve output and enhance productivity. Fertilizer usage is to
augment for poor soil fertility and increase output. The use of fertilizer hence
becomes a significant factor for pineapple production. The estimated coefficient for
fertilizer use in pineapple production was found to be positive and significant. Though
farmers’ use of chemical fertilizer had a relatively smaller elasticity of 0.135
compared to the elastic of farm size, it was found to be the second most significant
input that affected farmers’ performance and productivity. The positive elasticity of
fertilizer indicates a positive relation between the application of fertilizer and output.
This relation is expressed that an increase in farmers’ use of fertilizer by 1% will
result in increasing output by 1.35%. The finding of fertilizer having a positive impact
on output conforms to the results reported by Weier (1999), Idiong (2007) and Kyei et
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al (2011) reported the correlation between fertilizer use and agricultural output. The
findings however contradicts the findings of Abdulai and Huffman (2000) who
reported a negative relation between farmers’ use of fertilizer and the output of rice
farmers in Northern Ghana. This notwithstanding does not imply that fertilizer
application will necessarily affect output. The production output levels will only be
affected if the resource is efficiently and appropriately applied in the right proportions
and quantity.
Aside farm size and fertilizer which were found to significantly impact on production,
labour employed was also found to be the third most significant factor for production.
From the results, the elasticity of land as a factor of production was estimated to be
0.11, and had the expected a priori sign. However, the coefficient of labour as a factor
of production was not statistically significant as a production input. Alhassan (2012)
also found similar results in his study of rice farmers in the upper east region of
Ghana and stated that the sheer insignificance of the variable does not imply it is not
an important production variable. Its elasticity of 0.11 suggests that a unit increase in
labour results in 1.1% in output. The elasticity of planting material had the expected
positive sign though it was the smallest of all the estimated coefficients. It had an
elasticity of 0.015 and was found to be significant at the 10% level. This result was
not surprising since most of the farmers cultivated their crop on small-holder bases.
Farmers’ ability to purchase farming inputs largely depends on their ability to use
their capital resources efficiently. Capital use by farmers as a production variable was
found to have a negative effect on output. Its elasticity was estimated to be -0.023 and
was also statistically insignificant in affecting production output. Capital use was the
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only input factor that had a negative effect and deviated from the expected a priori
sign. The negative effect of capital on output can partly be attributed to the difficulty
in raising the needed capital to expand their farms and purchase new implements.
Conventionally capital usage is expected to increase farm output, however the limited
financial capabilities of small-holders makes it impossible for such goals to be
achieved. Abbam (2009) and Essilfie (2011) have also found similar effects of capital
on the output of pineapple non-exporters and maize farmers respectively in their
studies.
5.6 Determinants of inefficiency in production
The study further analyzes the effects that farmers’ socio-economic characteristics
have on their levels of efficiency. Ali and Chaundry (1990), Kumbhakar (1991) and
Huang and Liu (1994) have all in related studies identified farm specific
characteristics that affects farmers efficiency. The most commonly used socio-
economic characteristics that impacts on farmers efficiency includes farmers
educational levels, age, household size, credit, extension contacts and level of
experience. Since farmers socio-economic characteristics impact on their technical
efficiencies, these derived characteristics were related to firm-specific characteristics
that affects each producer. The study used farmer-specific characteristic to measure
the levels of technical efficiencies.
The socio-economic characteristics used to measure the level of efficiency of
pineapple producers includes age, educational level, access to credit and experience of
farmer. Farm size was included in the measure of inefficiency. The inclusion of farm
size as a factor of inefficiency is derived from the fact that, farmers output levels that
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depart from the frontier point can be brought closer to the frontier by increasing the
use of land. These socio-economic variables were chosen based on their availability in
the dataset used. The summary statistics of the socio-economic variables and the
estimates for the technical inefficiency effects are presented in table 10 and 11. From
table 10, it was found that pineapple farmers within the study area had an average of
3.2 years of formal education with the highest and lowest number of years of
education being 19 and 0 years respectively. The mean number of years of formal
education translates to imply that a majority of the farmers had lower levels of
education.
On farmers’ age, the results indicated that, the sampled farmers had an average age of
39.1 years with the maximum age being 78 years and 23 years as the minimum age. A
dummy variable was used to indicate whether farmers had access to credit or not. The
use of a dummy variable (1= access credit, 0= no access to credit) was to measure
how much credit farmers’ were able to access to expand their production activity.
Another indicator of farmers’ socio-economic variable used was farmers’ experience.
Experience of a farmer was to measure for the number of years that a farmer has been
actively engaged in the farming actively. The maximum number of years of
experience that a farmer had acquired was 25 years and a minimum of 1 year, with
mean years of experience being 6.1 years. The mean number of farming experience
indicates that more farmers have been in the pineapple cultivation within the study
area.
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5.7 Diagnostic statistics
A diagnostic test is carried out of the appropriateness and fitness of the specified
production function. The result in table 10 shows that, the estimate of λ, which
measures the degree of variability between the random shocks and inefficiency is
found to be 0.971 which is close to one. Appendix 3 shows the results of the
diagnostic statistic and their corresponding significance levels. The test of
significance of λ being equal to zero is also rejected at the 1% and 5% significance
levels. The sum of the variance (σ) parameter is also found to be statistically different
from zero. These diagnostic test shows that the specified production function is
appropriate to explain the differences that arises in pineapple production.
The results in table 10 show the firm-specific characteristics that affects farmers’
technical inefficiencies. The farm-specific estimates of technical inefficiency were
derived using Ordinary Least Square (OLS) regression and were related to the
farmers’ socio-economic characteristics. Table 10 presents the results of the
inefficiency model. It is to be noted however that the parameters in the inefficiency
model explains inefficiency and not efficiency. This then implies that estimated
coefficients in inefficiency model that have negative signs have negative relations
with inefficiency and a positive effect on efficiency. The results show that farmer-
specific characteristics are able to explain the variations in the inefficiency model.
This is indicated by the high R2 value of 89%. The joint significance of the parameters
was also accepted at the 1% level as being significant in explaining farm-specific
technical inefficiencies. The farm-specific socio-economic factors that influence
farmers’ levels of efficiency in the production process are outlined below.
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Table 10: Ordinary Least Square Estimates for technical inefficiency effects
Inefficiency
estimates
Parameter
Coefficient
Standard Error
t-ratio
Constant
0
5.938023***
.0633693
93.71
Credit
1
-.1442545***
.0353703
-4.08
Experience
2
-.0115897***
.0043876
-2.64
Age
3
-.0026494*
.0015438
-1.72
Education
4
-.0118935***
.0038123
-3.12
Farm size
5
.1961273***
.0060794
32.26
R2
0.8925
F-statistic
239.23***
Source: Author’s computation using Stata 13
Studies of efficiency (Kalirajan 1981; Kalirajan and Flinn, 1983; Lingard et al. 1983;
Bindlish and Evenson 1993; Adesina and Djato 1995; Abdulai and Huffman 2000)
have explained the importance of using farmers’ socio-economic characteristics such
as credit, education, age and experience as determinants for measuring the levels of
efficiency in agricultural production. These studies have explained that these variables
have negative effects on reducing farmers’ inefficiencies. The result of the
inefficiency model indicates a negative and statistically significant estimate for the
coefficient of credit. The negative coefficient of credit indicates that as farmers’
access to credit is increased, there is a corresponding reduction in their level of
inefficiency.
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This finding of the effect of credit reducing farmers’ inefficiency are similar with the
results of Abdulai and Huffman (1998), Essilfie et al (2011) and Alhassan (2012) who
found that increasing farmers’ access to credit significantly reduces their levels of
inefficiency. The reason for such findings suggests the relevance of credit towards
farm production. It is evident that farmers who have access to credit are better suited
to purchase and apply appropriate farm inputs and implements to boost their
production levels. Managerial competences are largely concerned with farmers’
ability to make sound decisions and judgements regarding their farming activity. This
is normally formed through constant practice and full engagement in a particular
activity. The managerial expertise and competences of farmers’ can thus be related to
their years of farming experience in pineapple production.
The results from the OLS regression indicate that farmers’ years of experience
positively influence their levels of efficiencies. This coefficient of experience has the
expected a priori sign and is found to be significant at the 1% and 5% levels. The
negative and significant coefficient of experience implies that increase in experience
of farmers’ reduces the level of inefficiency. The implication of this result is that
farmers’ who have acquired more farming experience tend to be more efficient than
those who have less. The effect of experience on the efficiency of pineapple farmers’
is never disputed, since it is through experience that sound farm management
practices and competences are gained. The result of the study is in conformity with
that reported by Battese and Coelli (1996) and Rahman (2002) who also showed
similar results on the effects of farmer experience on production efficiency on rice
farmers in India and Bangladesh respectively. The effect of experience on efficiency
and productivity explains that experienced farmers are less inefficient than
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inexperienced farmers. Farmer’s accumulation of knowledge is gained through
farming experience and this enables farmers’ to plan and organise their farming
activities more accurately. Sharma et al., (1999) further reported similar results on
their study of productive (allocative and economic) efficiency of swine farmers’ in
Hawaii. Experience of farmers’ can therefore be likened to managerial efficiency
and knowledge that is acquired through continual farming activity and practice.
The coefficient of age is also found to be negative and significant. The negative
coefficient of age in the model implies that younger farmers tend to be more
technically efficient than older farmers. Farmers’ age generally tends to affect their
level of efficiency negatively in reducing their output and productivity. A simple but
major reason that can be attributed to the decline in efficiency of older farmers results
in their inability to frequent their farms due to their advancement in their age. Since
the age of farmers’ negatively affects their productivity and work-effort, younger
farmers tend to be more efficient than their older counterparts. The significance of age
towards reducing farmers’ inefficiency is in line with the findings of Alhassan (2007),
Abdulai and Abukari (2012) and Kuwornu et al (2013) who found similar results in
their respective studies on the effect of age on farmers’ efficiency.
The findings however contradict the results reported by Idiong (2007) and Essilfie et
al (2011) who found positive relationship between farmers’ efficiency and their ages.
The contribution and effect of education at improving agricultural production has
been reported in studies by Bowman (1976), Kalirajan and Shand (1985), Alhassan
(2007) and Abdulai and Abukari (2012). These studies have all reported the role of
education at reducing inefficiency and improving output. The result of the coefficient
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of education is therefore not surprising. Its coefficient is found to be negative and
significant at the 1% level. The negative and statistically significant coefficient of
education implies its effect at reducing inefficiency. This implies that increasing
farmers’ level of education can significantly reduce their levels of inefficiency. The
results of farmers education in reducing the level of farmers’ inefficiency conforms
with the findings of Battese et al (1996), Coelli and Battese (1996), Seyoum et al
(1998), Idiong et al (2007), Onphahdala (2009) and Kuwornu et al (2013), who have
all found significant relations between farmers education and their levels of
efficiencies.
However, Adesina and Djato (1996) have stated different views on the effect of
education on efficiency. They contend that educated farmers’ may not necessarily be
more efficient than uneducated farmers since uneducated farmers’ may have acquired
more farming experience and knowledge than their educated counterparts and may be
more efficient technically. Kalirajan and Shand (1985) have also shared in the results
of Adesina and Djato (1996) that farmer education acquired through schooling may
not generally be a productive factor and hence education alone nay not to a significant
factor towards achieving efficiency. Increasing farmers level of education however
enhances their ability to understand and adopt modern and improved methods of
farming that are aimed at enhancing their productivity. The implication of increased
education reducing inefficiency among farmers’ stems from the fact that, educated
farmers’ have better access to information and improved farming practices than
uneducated farmers’. Hence farmers with more years of schooling tend to be more
technically efficient in pineapple production.
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The role that education plays in reducing inefficiency may not be direct since
education entails the formation of competences and the transmission of information.
These may be achieved through timely and adequate extension services, non-formal
educational programmes and farmer based organizations (FBO) that provide farmers’
with the necessary skills required in their farming activity. It is through such
pragmatic schemes that education can positively affect small-holder farmers’
production and their overall efficiencies.
The study finally measures the effect that farm size has on reducing farmers’
inefficiency. Though not a socio-economic determinant of inefficiency, it was
included to assess its effect on efficiency. It’s inclusion as an inefficiency variable is
conventional and based on the assumption that farm size causes a shift in the frontier
and further pushes the farmers much closer to the efficient frontier if they are to
depart from it. The result of farm size rather shows a positive relation to inefficiency.
Its coefficient is found to be statistically significant at the 1% and 5% levels but its
effect at reducing farm-level inefficiency is not plausible. In the MLE of the
production function, farm size is found to be the most significant production
parameter. However, as a factor of efficiency, its contribution rather causes an
increase in farmer inefficiency. The implication of farm size not a significant
determinant for efficiency means that, the mere increase in farmers’ share of land
does not necessarily imply a reduction in inefficiency. This thus implies that farmers
who increase their use of land without altering the socio-economic factors that causes
inefficiency will not be able to increase their outputs and productivity.
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5.8 Correlation matrix of technical inefficiency and its determinants
The analysis of the correlation matrix in efficiency analysis is essential if we are to
know if there the determinants of inefficiency exhibit multicollinearity.
Multicollinearity is a major problem for most cross-sectional data. Its presence causes
serious problems with the estimated coefficients. The correlation matrix is then used
as a tool to measure for its effect on the inefficiency variables. Table 11 reports the
results of the correlation matrix.
Table 11: Correlation matrix of the technical inefficiency effects
TI
Credit
Experience
Age
Education
Farm
size
TI 1.000
Credit -0.1705 1.000
Experience -0.2587 0.0454 1.000
Age -0.1835 0.1040 0.5890 1.000
Education -0.1449 0.0523 -0.0555 -0.0680 1.0000
Farm size 0.9241 0.0486 0.1496 0.0740 0.0695 1.000
Source: Author’s computation using Stata 13.0
The test for multicollinearity using the correlation matrix shows that apart from farm
size which had a positive effect on technical inefficiency, all the socio-economic
characteristics showed a negative. This result of the negative correlation between
technical inefficiency and its determinants implies that there is no relation between
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the output of farmers and their factors that causes inefficiency. The absence of
multicollinearity in the socio-economic factors gives credit to the findings in table 11.
5.9 Elasticity of production variables and returns to scale
The determination of the elasticity of production inputs is important if we are to
measure the responsiveness of output to inputs used. The regression coefficients of
the Cobb-Douglas production function measure the production elasticities and their
sum indicates the return-to-scale. The results of the elasticities of the input variables
of the Cobb-Douglas function are shown in Table 12 below.
Table 12: Elasticity estimates and returns to scale of pineapple producers
Variable
Elasticity
Farm size
0.9345
Labour
0.11801
Fertilizer
0.1350
Planting material
0.0157
Capital
-0.0232
Total
1.1799
Source: Author’s computation using Stata 13.0
Returns-to-scale in production measures the variation that occurs in output as
production input are also varied. According to Kibaara (2005), the summation of the
output elasticity of the production function yields the coefficient of scale. Increasing
returns-to scale of production results if; the sum of the output elasticities in the
function is greater than one, however, if the sum of the elasticity is equal to one, then
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there is constant return-to-scale of production, and decreasing returns-to scale if the
sum of elasticity is less than one. The results shown above in Table 12 indicates that
all the production inputs used by the farmers’ are inelastic which implies that a one
percentage increase in all inputs results in a less than one percent increase in output
(Kibaara, 2005).
The summation of the output elasticity which shows the returns-to-scale is 1.1799,
implying increasing returns-to-scale in production. The implication for increasing
return-to-scale in production is that, if all the production inputs are varied in the same
proportion, output will increase by about 1.1%. The results of farmers exhibiting
increasing returns-to-scale in the long run is consistent with Kibaara (2005) who
found similar results for small-holder maize farmers’ in Kenya. Similar results are
also reported by Abdulai and Abukari (2012) in their study of technical efficiency of
bee-keepers in the Northern region of Ghana. The results of farmers exhibiting
increasing return-to-scale in the long-run is a positive sign, in the sense that overtime,
small-holder pineapple farmers’ output may increase if their use of production
resources are efficient.
5.10 Measuring resource-use efficiency of pineapple farmers
The study as part of its objectives was aimed at determining the levels of efficiency of
resource-use by small-holder pineapple producers. In order to ensure maximum profit
and the efficiency of resources used, pineapple producers are to utilize their resources
at the level at which their marginal value product (MVP) equals their marginal factor
cost (MFC) under perfect competition (Kabir Miah et al, 2006; Tambo and Gbemu,
2010). The study adopts the measure of resource efficiency proposed by Stephen et al
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(2004), Fasasi (2006) and Goni et al (2007) and applied by Essilfie et al (2011) and
Kuwornu et al (2013). The efficiency of resource use by farmers’ is given as shown in
Table 13 below.
Table 13: Resource-use efficiency of input variables in the frontier production
function
Resource
Mean
Elasticity
MPP
MFC
MVP
MFC
MVPr
Farm size
3.8913
0.9345
140.6228
200.0
98.4359
0.4922
Labour
5.4533
0.11801
12.6716
20.0
8.8701
0.4435
Fertilizer
4.5333
0.1350
17.4389
50.0
12.2072
0.2441
Source: Author’s computation using Household data
With a given level of technology and the respective prices of inputs and outputs,
resource efficiency is estimated by equating the Marginal Value Product (MVP) to the
productive Marginal Factor Cost of the inputs. A resource is optimally utilised if there
is not a significant difference between the ratio of MVP and MFC (i.e. MVP/MFC
=1). With the exception of planting materials whose input price was unavailable, all
other input prices were available. Thus the estimation of the optimal use of resources
is based on farmers’ use of land, labour and fertilizer. The result from Table 14 shows
that farm size has the highest MPP value and implied increasing the use of land by 1%
will result in an increase in the output of farmers.
The efficiency of farm size as a production input is found to be 0.4922 and less than
1. The MPP of fertilizer and labour were also estimated to be 17.43 and 12.67
respectively. The effect of the use of fertilizer and labour on output implies that an
additional use of these resources will increase output substantially by 17 kilograms
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and 12 kilograms. The analysis of the efficiency of the input resources is based on the
ratio of the marginal value product (MVP) and the marginal facto cost (MFC).
Farmers’ use of these productive resources were all found to be less than one,
implying that farmers’ were underutilizing these inputs as productive factors of
production. This analysis of resource of efficiency is based on the methodology of
Goni et al (2007). The underutilisation of these inputs thus restricts farmers from
achieving their maximum output and confounds profit maximization by farmers’.
The implication of this finding is that farmers’ in their bid to increase production must
increase their use of farm size (land), fertilizer and labour. This therefore suggests that
pineapple producers within the study area can increase their output of pineapples by
employing to use more of labour, fertilizer and land as they are found to significantly
impact on output. This result is in conformity with the results of Goni et al (2007)
who reported that rice farmers would be more efficient by increasing the use of
fertilizer, farm size and labour. The results of the MLE showed that farm size,
fertilizer and labour were the most productive inputs; it thus confirms the effects of
these resources as the most significant to affect farmers’ output in pineapple
production. Kibaara (2005) in the study of the efficiency of Kenyan maize farmers
also found significant relations between fertilizer use, seed and labour. The findings
of that study however found the usage of seed by farmers’ as the most to affect their
output. The findings are however in line with Kibaara (2005) on increasing yield
through the increase of labour, fertilizer and farm size. It is also found to be consistent
with Essilfie et al (2011) and Kuwornu et al (2013) who found similar results in their
respective study of the effect of production inputs of maize farmers’ in the
Mfantsiman district and eastern region of Ghana respectively.
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CHAPTER SIX
SUMMARY, CONCLUSION AND RECOMMENDATIONS
6.1 Introduction
This chapter provides the summary and conclusion for this study. Recommendations
for policy analysis and directions are proposed. Areas for further research that will be
aimed towards increasing pineapple productions in the country are provided. The
chapter concludes with the various limitations of the study.
6.2 Summary and conclusion of the study
Efficiency measurement and analysis has been at the fore of most current research in
agricultural production in Ghana. Agricultural production in Ghana is mainly divided
into two main areas; the traditional and non-traditional crop production. Crop
production in Ghana has largely been dominated by the major cash and staple crops.
The development of the horticultural industry has over the years been rising with
pineapples leading as the main export commodity of the sector. Pineapple production
in Ghana is undoubtedly an important component towards the nation’s growth and
development. This role is heightened by the numbers of employment it generates and
the incomes received from exports. In the light of the enormous contribution that
pineapple production plays in the agricultural sector and the economy at large, the
study was focussed on studying the efficiencies of small-holder pineapple farmers’ in
the Akuapem south Municipality. The study area was chosen based on the fact that it
had one of the largest concentrations of pineapple farmers in the country. The trends,
challenges and prospects of pineapple production towards national economic
development were discussed. The motivation for the study was based on three key
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objectives namely; to examine and estimate the levels of efficiency of resource-use
among small-holder pineapple producers, to investigate if farmers’ socio-economic
characteristics had any effect on their efficiencies and productivity, and to provide
policy recommendations based on the efficiency estimates. To achieve these
objectives, the stochastic frontier approach was the main methodology employed to
estimate the efficiency of farmers’ use of resources. The study begins with the
background of pineapple production in Ghana, the objectives and the statement of the
research problem. An overview of the development of pineapple production and its
prospects and challenges are developed and discussed in chapter two. Since the
stochastic frontier approach (SFA) formed the main methodology employed for the
study, its development and application in empirical research studies are discussed.
The literature review commences with the discussion of the SFA which was the main
methodology. The review of literature centres on the development and use of the
approach in empirical studies. The study further takes a look at the approaches that
have formed the basis for most efficiency measurements. These approaches namely
the deterministic frontier approach of the Data envelopment approach (DEA) and the
non-deterministic in the stochastic frontier approach (SFA) are looked at, and their
application reviewed. An exposition to these various approaches for the measurement
of efficiency is provided with empirical evidences that are related to agricultural
production in Ghana.
Studies on agricultural production have highlighted the importance of efficiency
analysis towards agricultural growth and promotion. Relevant studies on agriculture
efficiency both technical and allocative were highlighted. Studies by authors such as;
Alhassan (2007), Abbam (2009), Onumah and Acquah (2010) and Kuwornu et al
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(2013) have provided Ghana specific evidences of efficiency measurements. These
studies have provided enough theoretical and empirical foundations for efficiency
studies in Ghana. The section for methodology and theoretical frameworks clearly
explains the stochastic frontier framework as a means to achieving the stated
objectives of the study. The choice of this methodology for the study is that, the
stochastic frontier approach is able to account for differences that occur in production.
The maximum likelihood estimations (MLE) and Ordinary Least Squares (OLS) were
both used in estimating farm-level efficiencies of the farmers. The OLS approach is
used as a first step method to find significant relationship between the output and
input variables. The MLE approach was then used to estimate the levels of efficiency
and this efficiency were related to farmers’ socio-economic characteristics. The study
relied on cross-sectional household data (secondary data) of pineapple farmers from
ISSER and results from the estimations were generated using the Stata 13 statistical
package.
The study as part of its objectives was aimed at efficiency estimation of resources
used. The summary statistics on gender of farmers’ showed that pineapple farming in
the study area is a male dominating activity though there existed quite an encouraging
number of female farmers involved. Since the Cobb-Douglas production function was
found as the most appropriate functional form, the analysis and discussions of the
estimated coefficients for efficiency were based this functional form. Farm size,
labour, capital, planting material and fertilizer were found to be the major production
input for pineapple production. The estimated coefficients of the Cobb-Douglas
frontier function showed that, farm size, labour and fertilizer use were the most
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significant factors that affected farmers’ output levels. The significance of these
factors to production implies that pineapple farmers’ can increase their yields by
increasing their use of their most productive factors. The coefficients for planting
material and capital were however not found to impact significantly on farmers’ yield.
Though these factors were not found to be statistically significant, marginally
increasing their use in production is expected to boost the outputs of farmers.
The determinants of inefficiencies among pineapple farmers’ were also analysed.
These determinants were made up of farmers’ socio-economic characteristics. They
included age, credit, experience, farm size and educational levels of farmers’. These
factors were included in the inefficiency model to analyse their effects on affecting
farmers’ efficiency. All the estimates of the inefficiency model had that expected
negative signs and were all found to be statistically significant with the exception of
farm size. The negative and significant socio-economic characteristics showed that
they had a negative influence on reducing inefficiency in production. Farmers’ age
was found to have significant effects on their levels of efficiency. The negative
coefficient of age on inefficiency showed that younger farmers’ tend to be more
efficient than older farmers.
Access to credit was also found to impact on reducing inefficiency. Its negative and
significant coefficient showed that farmers had the capacity to increase output and
reduce inefficiency significantly. The role of credit to agricultural production is
unarguable, since credit provides farmers with the needed capital required to purchase
farm inputs and implements. It was therefore not surprising that it influenced
positively in reducing inefficiency among the farmers’. The impact of education
towards agricultural productivity and output improvement is a well known fact. The
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result of the study hence confirms educations importance in reducing inefficiency.
Thus in order to improve farmers’ efficiency, their levels of education should be
improved. This increase in education does not simply imply that providing farmers
with formal education, but rather any appropriate educational method that is aimed at
improving their understanding of new and improved farming methods. Its effect
confirms with other related studies that have found positive relations between
farmers’ efficiency and improved education.
Finally, the effect of farmers’ experience on reducing inefficiency was found to be
significant. The experience of farmers is generally reflected in their managerial
decision making. Experience entails farmers’ ability to plan and make sound decisions
regarding their farming activity. The significance of experience as an inefficiency
factor shows that farmers with more years of experience had lower levels of
inefficiency relative to their inexperienced counterparts. The study concludes that
though small-holder farmers were generally inefficient in their use of resources, the
coefficient for returns to scale which shows an increasing returns to scale is an
indicator that farmers have a potential at increasing output and profitability over time.
6.3 Recommendations for policy implementation and further studies
Based on the findings of the study, the following recommendations are made for
policy implementation. It is envisaged that these recommendations would provide a
framework for increasing the overall efficiencies of small-holder pineapple farmers
within the study area and other related areas. The following recommendations are
provided based on the results of the study:
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As part of increasing the production of pineapples, the study recommends that
farm inputs should be made readily accessible to farmers and also at
subsidized prices.
The study recommended that farm inputs should be made available to farmers
at highly subsidized rates and makes them available timely, through adequate
supply and efficient distribution.
Government policies can be instituted to provide farmers with credit (loans)
facilities without requiring collateral.
Efforts should be made to improve farmers’ education, since education was
found to affect farmers’ productivity positively. This can be achieved through
increased extension contact, non-formal education and farmer-based
organizations (FBOs) that promote farmer education.
There is the need for farmers’ to increase their use of labour, fertilizer and
land since they were found to impact of their output.
The development and formulation of pro-poor agricultural policies that are
targeted primarily on increasing small-holder pineapple farmers.
Finally, there is the need for government to create an enabling environment
that will encourage the youth to engage in pineapple production as a tool for
creating employment.
This study further paves the way for more studies to be considered on factors that
affect the efficiency and profitability of small-holder pineapple production. These
studies can explore the efficiency of farmers and the effect of climate change and
climate change awareness on production. Further studies can also be targeted at
examining the risk factors that hinders the growth of the pineapple sector in Ghana at
large.
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APPENDICES
APPENDIX 1
ORDINARY LEAST SQUARE RESULTS
Number of observations 150
F( 5, 144) 38.52 R2 0.5722
Prob> F 0.000 Adj R-squared 0.5573
Variables Coef. Std. Err. T P>t [95% Conf. Interval]
Lfarmsize 0.9266578 0.0893328 10.37 0.000 .7500849 1.103231
lLABOUR 0.1232953 0.079462 1.55 0.123 -.0337673 .2803579
lFERTILIZER 0.1266024 0.0820537 1.54 0.125 -.0355829 .2887877
lPLANTINGMATERIAL 0.0105547 0.0667458 0.16 0.875 -.1213735 .1424828
lCAPITAL -0.0112004 0.0568018 -0.2 0.844 -.1234734 1010726
_cons 4.617208 0.3642757 12.68 0.000 3.89719 5.337227
APPENDIX 2
MAXIMUM LIKELIHOOD ESTIMATION OF PRODUCTION FUNCTION Number of obs = 150
Wald chi2(5) = 209.02
Log likelihood = -113.37716 Prob > chi2 = 0.0000
Variables Coef. Std. Err. Z P>z [95% Conf.
Interval]
lFARMSIZE .9344572 .0856176 10.91 0.000 .7666498
1.102265 lLABOUR .1180118 .0774201 1.52 0.127 .0337288
.2697525 lFERTILIZER .1350005 .08075 1.67 0.095 -.0232666
.2932677 lPLANTINGMATERIAL .0157188 .065 0.24 0.809 -.1116788
.1431164 lCAPITAL -.0232332 .055625 -0.42 0.676 -.1322562
.0857899 _cons 5.004141 .3849455 .00 130.000 4.249661
5.75862
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APPENDIX 3
DIAGNOSTIC STATISTIC
Variables Coef. Std. Err. Z P>z [95% Conf. Interval]
/lnsig2v 1.617905 .2408926 6.72 0.000 1.145764 2.090046
/lnsig2u 1.676449 .6723125 2.49 0.013 2.994157 3.587404
sigma_v .4453242 .0536377 .3516837 .223783 .8357964
sigma_u .4324778 .1453801
sigma2 .3853507 .0934474 .2021971 .5685043
Lambda .9711526 .1901714 .5984235 1.343882
Likelihood-ratio test of sigma_u=0: chibar2(01) = 1.14 Prob>=chibar2 = 0.143
APPENDIX 4
VALIDATION OF TEST HYPOTHESIS
Null hypothesis 2 Prob >2 Decision
0: 321 OH 44.17 0.0000 Reject OH
0: 321 OH 4.76 0.0190 Reject OH
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