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 University of Ghana http://ugspace.ug.edu.gh 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. University of Ghana http://ugspace.ug.edu.gh 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. University of Ghana http://ugspace.ug.edu.gh 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. University of Ghana http://ugspace.ug.edu.gh v 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 University of Ghana http://ugspace.ug.edu.gh vi 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 University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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. University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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. University of Ghana http://ugspace.ug.edu.gh 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. University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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. University of Ghana http://ugspace.ug.edu.gh 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. University of Ghana http://ugspace.ug.edu.gh 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. University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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. University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 19 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 University of Ghana http://ugspace.ug.edu.gh 20 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. University of Ghana http://ugspace.ug.edu.gh 21 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 University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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. University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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. University of Ghana http://ugspace.ug.edu.gh 28 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 University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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. University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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. University of Ghana http://ugspace.ug.edu.gh 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 i i Xf eXfTE i  where ui 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 University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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 uvii 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( 2v 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(  University of Ghana http://ugspace.ug.edu.gh 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 δv 2 = 0, and collapses to the Zellner, Kmenta and Dréze (1966) stochastic frontier production model when δu 2 = 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) University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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. University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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, University of Ghana http://ugspace.ug.edu.gh 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. University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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. University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 54 denoted by the function ),,.........( 1 nyyY  for a set of real numbers R m. Then a firm’s production possibility is defined as the subset of the production space which is given by nmR  . 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. University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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. University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 60 by the truncation (zero) of the normal distribution with mean itZ and variance δ 2. 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: University of Ghana http://ugspace.ug.edu.gh 61           ii i iii aa auEu     11/ˆ 2 where  2122 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. University of Ghana http://ugspace.ug.edu.gh 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. University of Ghana http://ugspace.ug.edu.gh 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 X 1 /Y X 2 /Y ● ● ● ● M K L K' I University of Ghana http://ugspace.ug.edu.gh 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 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 σu 2 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. University of Ghana http://ugspace.ug.edu.gh 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. University of Ghana http://ugspace.ug.edu.gh 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 uvInXInXInXInY 1 1 1 0 2 1      5 5 1 5 1 0 2 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 University of Ghana http://ugspace.ug.edu.gh 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. University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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 .  . University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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. University of Ghana http://ugspace.ug.edu.gh 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’ University of Ghana http://ugspace.ug.edu.gh 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. University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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. University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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. University of Ghana http://ugspace.ug.edu.gh 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 Source: Author’s computation using Stata 13.0 The quantity of output that is produced from any agricultural activity generally depends on the quantity and quality of the various inputs used in production. The results of the table on summaries statistics of the output and input variables indicates that, farmers’ use of land for pineapple production had a mean of 3.89 acres with a standard deviation of 2.81. The use of land by pineapple farmers’ ranged between 1.2 and 20 acres for lowest and highest acreage use respectively. The relatively smaller use of land by these farmers’ is exhibited in their lower production output. From the summary statistics, the average pineapple produced were 585.56 kilograms with a standard deviation of 631.47.With the low usage of land, the minimum and maximum output of pineapple produced by the farmers were also found to be 100 and 5000 kilograms respectively. 5.4 Estimation of production frontier function using Ordinary Least Square In the estimation of the relative efficiency of pineapple farmers’, the log-linear Cobb- Douglas production function is assumed as the appropriate functional form for the University of Ghana http://ugspace.ug.edu.gh 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. University of Ghana http://ugspace.ug.edu.gh 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 Source: Author’s computation using Stata 13.0 5.5 Stochastic frontier production function estimation using Maximum Likelihood The stochastic frontier production function is used as a means of meeting the first objective of the study. In frontier studies, the estimated parameters of the stochastic frontier function indicate the best practice performance that is technically efficient in the application of the variable inputs used in the production process. Table 9 and 10 shows the summary statistics and the Maximum Likelihood Estimates (MLE) for the University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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 Source: Author’s computation using Stata 13.0 The use of the Ordinary Least Square (OLS) estimation in table 7 was to serve as a pre-test for the production variables in the estimation of the production function using the maximum likelihood estimation approach. The coefficients in the production functions indicate the elasticity of the various input variables to output. The results from the estimation of the production function shows that of the production parameters used, farm size, labour, fertilizer use and planting materials had the expected positive signs and were found to be significant with the exception of capital use which had a negative coefficient. These estimated coefficients indicated that, these variables had positive effect on affecting farmers’ productivity. The coefficient of farmers’ use of land (farm size) had the highest elasticity of 0.934 and was found to be the most significant factor of production. It was also found to be significant at the 1% level. The high and positive coefficient of farm size indicated University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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. University of Ghana http://ugspace.ug.edu.gh 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. University of Ghana http://ugspace.ug.edu.gh 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. University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 101 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 University of Ghana http://ugspace.ug.edu.gh 102 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. University of Ghana http://ugspace.ug.edu.gh 103 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. University of Ghana http://ugspace.ug.edu.gh 104 5.8 Correlation matrix of technical inefficiency and its determinants The analysis of the correlation matrix in efficiency analysis is essential if we are to know if there the determinants of inefficiency exhibit multicollinearity. Multicollinearity is a major problem for most cross-sectional data. Its presence causes serious problems with the estimated coefficients. The correlation matrix is then used as a tool to measure for its effect on the inefficiency variables. Table 11 reports the results of the correlation matrix. Table 11: Correlation matrix of the technical inefficiency effects TI Credit Experience Age Education Farm size TI 1.000 Credit -0.1705 1.000 Experience -0.2587 0.0454 1.000 Age -0.1835 0.1040 0.5890 1.000 Education -0.1449 0.0523 -0.0555 -0.0680 1.0000 Farm size 0.9241 0.0486 0.1496 0.0740 0.0695 1.000 Source: Author’s computation using Stata 13.0 The test for multicollinearity using the correlation matrix shows that apart from farm size which had a positive effect on technical inefficiency, all the socio-economic characteristics showed a negative. This result of the negative correlation between technical inefficiency and its determinants implies that there is no relation between University of Ghana http://ugspace.ug.edu.gh 105 the output of farmers and their factors that causes inefficiency. The absence of multicollinearity in the socio-economic factors gives credit to the findings in table 11. 5.9 Elasticity of production variables and returns to scale The determination of the elasticity of production inputs is important if we are to measure the responsiveness of output to inputs used. The regression coefficients of the Cobb-Douglas production function measure the production elasticities and their sum indicates the return-to-scale. The results of the elasticities of the input variables of the Cobb-Douglas function are shown in Table 12 below. Table 12: Elasticity estimates and returns to scale of pineapple producers Variable Elasticity Farm size 0.9345 Labour 0.11801 Fertilizer 0.1350 Planting material 0.0157 Capital -0.0232 Total 1.1799 Source: Author’s computation using Stata 13.0 Returns-to-scale in production measures the variation that occurs in output as production input are also varied. According to Kibaara (2005), the summation of the output elasticity of the production function yields the coefficient of scale. Increasing returns-to scale of production results if; the sum of the output elasticities in the function is greater than one, however, if the sum of the elasticity is equal to one, then University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 107 (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 University of Ghana http://ugspace.ug.edu.gh 108 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. University of Ghana http://ugspace.ug.edu.gh 109 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 University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh 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: University of Ghana http://ugspace.ug.edu.gh 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. 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University of Ghana http://ugspace.ug.edu.gh 122 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 University of Ghana http://ugspace.ug.edu.gh 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 University of Ghana http://ugspace.ug.edu.gh