UNIVERSITY OF GHANA DETERMINANTS OF TECHNICAL …

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

University of Ghana http://ugspace.ug.edu.gh

i

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


ii

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.


iii

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.


iv

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


vii

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


viii

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


ix

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


x

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


xi

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.


xii

SSA Sub-Saharan Africa

UNCTAD United Nations Conference on Trade and Development

UNEP United Nations Environment Programme

USAID United States Agency for International Development


1

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


2

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


3

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


4

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


5

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


6

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


7

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


8

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.


9

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.


10

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


11

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.


12

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.


13

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.


14

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


15

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


16

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.


17

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


18

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


22

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


23

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


24

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.


25

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


26

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


27

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


29

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


30

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.


31

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


32

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


33

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


34

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


35

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


36

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


37

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


38

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.


39

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


40

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


41

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


42

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


43

(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(


44

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)


45

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


46

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


47

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.


48

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


49

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,


50

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.


51

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


52

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.


53

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


54

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.


55

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


56

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


57

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.


58

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


59

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


60

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:


61

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.


62

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.


63

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


64

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


65

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.


66

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


67

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


68

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


69

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


70

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


71

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


72

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.


73

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.


74

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


75

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.


76

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


77

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


78

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 .

.


79

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


80

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


81

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.


82

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’


83

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.


84

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


85

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.


86

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


87

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


88

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.


89

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


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


90

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.


91

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


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


92

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


93

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


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


94

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


95

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


96

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


97

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.


98

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.


99

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.


100

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


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


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


106

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


110

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


111

(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


112

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


113

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:


114

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.


115

REFERENCES

Abdulai, A., & Huffman, W. (2000). Structural adjustment and economic efficiency

of rice farmers in Northern Ghana. Economic and Cultural Change, 48(3),

503-520.

Abdulai, A-M., & Abubakari, M. (2012). Technical efficiency of beekeeping farmers

in Tolon-Kumbungu district of Northern region of Ghana. Journal of

Development and Agricultural Economics. 4(11), 304-310.

Adekunle, A. A., Ellis-Jones, J., Ajibefun, I., Nyikal, R. A., Bangali, S., Fatunbi, O &

Ange, A. (2012). Agricultural innovations in sub-Saharan Africa: Experiences

from multiple-stakeholder approaches. Forum for Agricultural Research in

Africa (FARA).

Afari-Sefa, V. (undated). The micro-level distributional effects of horticultural export

value chains among smallholders in southern Ghana. Paper submitted to the

4th GARNET conference on "Food Security and Sustainable Development:

Challenges for the Governance of International Relations.

Afriat, S. N. (1972). Efficiency estimation of production functions. International

Economic Review 13, 568-598.

Aigner, D. J., & Chu, S. F. (1968). On estimating the industry production function.

American Economic Review 58, 826-839.

Aigner, D. J., Lovell, C. A. K., & Schmidt, P. (1977) Formulation and estimation of

stochastic frontier production function models. Journal of Econometrics 6, 21-

37.

Ajibefun, I., & Abdulkadri, O. A. (1991). An investigation of technical inefficiency of

production of farmers under the national directorate of employment in Ondo

State, Nigeria. Applied Economics Letters, 6(3), 111 – 114.

Akhtaruzzaman, K., Fakir, A., & Huda, A. A. (2010). Farm household technical

efficiency: A study on rice producers in selected areas of Jamalpur District in

Bangladesh. European Journal of Social Sciences. 14(2)

Akinwumi, A. A., & Djato, K. K. (1997). Relative efficiency of women s farm

managers: profit function analysis of rice farms. Agricultural Economics,

14(2), 93 – 102.

Al-Hassan, R. M., Sarpong, D. B., & Mensah-Bonsu, A. (2006). Linking smallholders

to markets. Ghana Strategy Support Program (GSSP). Background Paper No.

GSSP 0001. International Food Policy Research Institute.

Al-hassan, S (2008). Technical efficiency of rice farmers in Northern Ghana. African

Economic Research Consortium (AERC). Research Paper No. 178.


116

Al-hassan, S. (2012). Technical Efficiency in smallholder paddy farms in Ghana: An

analysis based on different farming systems and gender. Journal of Economics

and Sustainable Development, 3(5)

Baker, C. B., & Holcomb, M. (1964). The emerging financial problems in a changing

agriculture. Journal of Farm Economics, 46(5)

Banker, R. D., & Thrall, R. M. (1992). Estimation of returns to scale using data

envelopment analysis. European Journal of Operational Research, 62(1), 35 –

44.

Barrientos, S., Anarfi, J., Lamhauge, N., Castaldo, A., & Anyidoho, N. A. (2009).

Social protection for migrant labour in the Ghanaian pineapple sector.

Development Research Centre on Migration, Globalisation and Poverty.

Working Paper T- 30.

Battese, G. E., & Coelli, T. J. (1988). Prediction of firm-level technical efficiencies

with a generalized frontier production function and panel data. Journal of

Econometrics 38, 387-399.

Battese, G. E., & Corra, G. S. (1977). Estimation of a production frontier model: With

application to the pastoral zone of Eastern Australia. Australian Journal of

Agricultural Economics 21, 169-179.

Bravo-Ureta, B. E., & Pinheiro, A. E. (1993). Efficiency analysis of developing country

agriculture: A review of the frontier function literature. Agriculture and Resource

Economics Review, 22(1), 88-101.

Chamberlin, J. (2007). Defining smallholder agriculture in Ghana: Who are

smallholder, what do they do and how are they linked with markets? GSSP

Background Paper 6, Washington, DC: IFPRI.

Charnes, A., & Cooper, W. W. (1990). Data envelopment analysis. In Bradley H. E.

(ed.), Operational research ’90. Oxford: Pergamon.

Charnes, A., Cooper, W. W. & Rhodes, E. (1978). Measuring the efficiency of

decision making units. European Journal of Operational Research. 2(6), 429

– 444.

Chavas, J. P., & Aliber, M. (1993). An analysis of economic efficiency in agriculture:

A nonparametric approach. Journal of Agricultural Resource Economics,

18(3), 1-16.

Chirwa, E. W. (2007). Sources of technical efficiency among smallholder maize

farmers in South Malawi. African Economic Research Consortium, Nairobi.

Research Paper No. 172

Coelli, T. J. (1995). Recent developments in frontier modelling and efficiency

measurement. Australian Journal of Agricultural Economics 3, 219-245.

Coelli, T. J., Rao, D. S. P., & Battese, G. E. (1998). An introduction to efficiency and

productivity analysis. Norwell, MA: Kluwer Academic Publishers.


117

Coulombe, H., & Wodon, Q. (2007). Poverty, livelihoods and access to basic services

in Ghana. Ghana CEM. Meeting the challenge of Accelerated and shared

growth.

Danielou, M., & Ravry, C. (2005). The Rise of Ghana’s pineapple industry: From

successful takeoff to sustainable expansion. Africa Region working paper.

Series No.93. Washington DC: ESSD Africa.

Dawson, P. J., & Lingard, J. (1989). Measuring firm efficiency over time on

Philippine rice farms. Journal of Agricultural Economics, 40(2), 168 – 177.

Debreu, G. (1951). The Coefficient of resource utilization. Econometrica, 19(3), 273-

292.

Desai, A., & Schinnar, A. P. (1987). Technical issues in measuring scholastic

improvement due to compensatory education programmes. Socio-Economic

Planning Sciences 24(2), 143 – 153.

Ellis, F. (1993). Peasant economics: Farm households and agrarian development, 2nd

Ed. Cambridge University Press: Cambridge.

Essilfie, F.L., Asiamah, M. T., & Nimoh, F. (2011). Estimation of farm level technical

efficiency in small-scale maize production in the Mfantseman Municipality in

the Central Region of Ghana: A stochastic frontier approach. Journal of

Development and Agricultural Economics. 3(14), 645-654.

FAO (2002b). Organic agriculture, environment and food Security. Rome, Italy, 252.

FAO (2013). Analysis of trade impacts on fresh pineapple sector in Ghana. FAO

Commodity and Trade Policy. Research working paper No. 41.

Forsund, F. R., & Hjalmarsson, L. (1979). Frontier production functions and technical

progress. A study of general milk processing in Swedish dairy plants.

Econometrica, 47(2), 883 –900.

Fòrsund, F. R., Lovell, C. A. K., & Schmidt, P. (1980). A survey of frontier

production functions and of their relationship to efficiency measurement.

Journal of Econometrics 13, 5-25.

Ghana Shared Growth and Development Agenda (2010). Medium-term National

Development Policy Framework. Volume I. Government of Ghana.

Goni, M., Mohammed, S., & Baba, B. A. (2007). Analysis of resource-Use efficiency

in rice production in the Lake Area of Borno State, Nigeria. Journal of

Sustainable Development in Agriculture & Environment 3, 31-37

Green, W. H. (2000). Simulated likelihood estimation of the normal-gamma

stochastic frontier function. Stern School of Business. New York University.

Greene, W. H. (1980). Maximum likelihood estimation of econometric frontier

function. Journal of Econometric 13, 27-56.


118

Greene, W. H. (2000) Econometric Analysis, 4th Ed., Prentice Hall, Upper Saddle

River, New Jersey.

Idiong, I. C. (2007). Estimation of farm level technical efficiency in small scale

swamp rice production in Cross River State of Nigeria: A stochastic frontier

approach. World Journal of Agricultural Sciences, 3(5), 653-658.

IFPRI (2005). The future of small farms. Proceedings of a research workshop.

Washington, DC: International Food Policy Research Institute.

ISSER (2003). The state of the Ghanaian economy in 2002. Institute of Statistical

Social and Economic Research. University of Ghana. Legon, Accra.

Jondrow, J., Lovell, C. A. K., Materow, I. S., & Schmidt, P. (1982). On the estimation

of technical inefficiency in the stochastic frontier production function model.

Journal of Econometrics, 19, 233–38.

Kabir Miah M. A., Ashraful Alam., A. K. M., & Rahman, A. H. M. A. (2006).

Impact of agricultural credit on MV Boro rice cultivation in Bangladesh.

Journal of Agriculture and Rural Development. 4(1&2), 161-168.

Kalirajan, K. P., & Shand, R. T. (1985). Types of education and agricultural

productivity: a quantitative analysis of Tamil Nadu rice farming. Journal of

Development Studies, 21(5), 232 – 243.

Kebede, T. A (2001). Farm Household Technical Efficiency: A stochastic frontier

analysis. A study of rice producers in Mardi Watershed in the western

development region of Nepal. Unpublished MSc Thesis. Agricultural University of

Norway.

Kibaara, B. W. (2005). Technical efficiency in Kenyan’s maize production: An

application of the stochastic frontier approach. Unpublished Master’s thesis.

Colorado State University Fort Collins, Colorado.

Kleemann, L. (2011). Organic pineapple farming in Ghana - A Good choice for

smallholders? Kiel Institute for the World Economy. Working Paper No. 1671.

Koopmans, T. C. (1951). An analysis of production as an efficient combination of

activities. In T. C. Koopmans, (Ed.) Activity Analysis of Production and

Allocation, New York: John Wiley & Sons.

Kumbhakar, S. C. (1990). Production frontiers, panel data and time-varying technical

inefficiency. Journal of Econometrics 46, 201-211.

Kuwornu, J. K. M., Amoah, E., & Seini, W (2013). Technical efficiency analysis of

maize farmers in the eastern region of Ghana. Journal of Social and

Development Sciences 4(2), 84-99.

Kuwornu, J. K. M., Nafeo, A. A., & Osei-Asare, Y. B (2013). Financial viability,

value addition and constraint analyses of certified pineapple production and

marketing in Ghana. African Journal of Basic and Applied Sciences 5 (1): 12-

24.


119

Kyei, L., Foli, G., & Ankoh, J. (2011). Analysis of factors affecting the technical

efficiency of cocoa farmers in the Offinso district-Ashanti region, Ghana.

American Journal of Social and Management Sciences. 2 (2), 208-216.

Leibenstein, H. (1966). Allocative efficiency vs. X-Efficiency. American Economic

Review, 56(3), 392 – 415.

McMillan, M. (2012). Blue skies: How one firm overcame “binding” constraints.

Ghana Strategy Support Program (GSSP). Transforming Agriculture

conference. IFPRI.

Meeusen, W., & van den Broeck, J. (1977) Efficiency estimation from Cobb-Douglas

production functions with composed error. International Economic Review

18, 435-444.

Ministry Of Food and Agriculture (2011). Agriculture in Ghana. Facts and Figures.

Statistics and Research and Information Directorate (SRID).

Ministry of Food and Agriculture, (2007). Food and Agriculture Development Policy

(FASDEP II). Republic of Ghana, Accra.

Obeng, S. I. (1994). Effect of domestic policies on production and export of non-

traditional agricultural commodities: A case study of fresh pineapples in

Ghana. (Unpublished master's thesis). University of Ghana, Legon, Accra.

Ogundari, K., & Ojo, S. O. (2007). Economic efficiency of small scale food crop

production in Nigeria: A stochastic frontier approach. Journal of Social

Sciences, 14(2), 123-130.

Olagoke, M. A. (1991). Efficiency of resource use in rice production systems in

Anambara State, Nigeria, in Doss C-R and Olson C (eds); Issues in African

Rural Development. Winrock International; 282-303.

Onphanhdala, P. (2009). Farmer education and agricultural efficiency: Evidence from

Lao PDR. Graduate School of International Cooperation Studies, Kobe

University. Working Paper Series.

Onumah, E. E., & Acquah, H. D. (2010). Frontier analysis of aquaculture farms in the

southern sector of Ghana. World Applied Sciences Journal 9(7), 826-835.

Owusu. V., & Owusu, A. M. (2010). Measuring market potential for fresh organic

fruits and vegetables in Ghana. Paper presented at the Joint 3rd African

Association of Agricultural Economists (AAAE)

Quartey, P., Al-Hassan, S., Udry, C., & Sheshie, H (2012). Agricultural financing and

credit constraints: The role of middlemen in marketing and credit outcomes in

Ghana. International Growth Centre. Working paper 12/0160

Richmond, J. (1974) Estimating the efficiency of production. International Economic

Review 15, 515-521.


120

Schmidt, P. (1976). On the statistical estimation of parametric frontier production

functions. The Review of Economics and Statistics 58,238-239.

Schmidt, P., & Lovell, C. A .K. (1980). Estimating stochastic production and cost

frontiers when technical and allocative inefficiency are correlated. Journal of

Econometrics 13, 83-100.

Sengupta, J. K. (1987). Production frontier estimation to measure efficiency: A

Critical evaluation in light of Data Envelopment Analysis. Managerial and

Decision Economics, 8(2), 93-99

Seyoum, E. T., Battese, G. E., & Fleming, E. M. (1998). Technical efficiency and

productivity of maize producers in eastern Ethiopia: A study of farmers within

and outside the Sasakawa-Global 2000 project. Agricultural Economics, 19(2),

341-348.

Shehu, J. F. & Mshelia, S. I. (2007). Productivity and technical efficiency of small

scale rice farmers in Adamawa State, Nigeria. Journal of Agriculture and

Social Sciences, 3(4), 117 – 120.

Smith, P. (1997). Model misspecification in Data Envelopment Analysis. Annals of

Operational Research, 67(2), 141–161.

Stevenson, R. E. (1980). Likelihood functions for generalized stochastic frontier

estimation. Journal of Econometrics 13 (1), 57-66

Suhariyanto, K. (2000). Agricultural productivity in Asian countries. In tomorrow’s

agriculture: incentives, institutions, infrastructure, and innovations:

Proceedings of the 24th International Conference of Agricultural Economists.

Berling, Germany, Asgate, 376 – 382.

Tambo, J. A., & Gbemu, T. (2010). Resource-use efficiency in tomato production in

the Dangme West District, Ghana. Conference on International Research on

Food Security, Natural Resource Management and Rural Development.

Zurich

Tauer, L. W., & Belbase, K. P. (1987). Technical efficiency of New York dairy

farms. Agricultural and Resource Economics Review, 22, 1-9.

Umoh, G. S. (2006). Resource use efficiency in urban farming: An application of

stochastic frontier production function. International Journal of Agricultural

Biology, 8(5), 38 – 44.

UNEP (2002), Africa environment outlook: Past, present and future perspectives,

UNEP, Nairobi, 422.

Weier, S. (1999). The effects of education on farmer productivity in rural Ethiopia

(WPS99-7). Oxford: University of Oxford, Department of Economics, Centre

for the Study of African Economies.

Yao, S., & Liu, Z. (1988). Determinants of grain production and technical efficiency

in China. Journal of Agricultural Economics, 49(2), 171 – 184.


121

Yeboah, G. (2005). Challenges facing potential investors in the pineapple industry in

Ghana. University of Kentucky. Department of Agricultural Economics.

Yeboah, G. (2005). The farmapine model: a cooperative marketing strategy and a

market-based development approach in Sub-Saharan Africa. American

Agricultural Economics Association, 20(1), 81-86.


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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


123

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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