University of Ghana http://ugspace.ug.edu.gh UNIVERSITY OF GHANA MULTI-DIRECTIONAL EFFICIENCY ANALYSIS (MEA) OF THE PERFORMANCE OF GHANAIAN INSURANCE FIRMS BY CARLOS OKO NARKU DOWUONA (10029596) THIS THESIS IS SUBMITTED TO THE UNIVERSITY OF GHANA, LEGON IN PARTIAL FULFILLMENT OF THE REQUIREMENT FOR THE AWARD OF MPHIL RISK MANAGEMENT AND INSURANCE DEGREE JUNE, 2014 University of Ghana http://ugspace.ug.edu.gh DECLARATION Candidate’s Declaration I do hereby declare that this work is the result of my own research and that no part of it has been presented by anyone for academic award in this or any other university. All references used in the work have been fully acknowledged. …………………………………… Date …………………………….. Carlos Oko Narku Dowuona (10029596) i University of Ghana http://ugspace.ug.edu.gh CERTIFICATION We hereby certify that this thesis was supervised in accordance with the guidelines and procedures laid down by the University. 1.…………………………………………… …………………………………. DR. KWAKU OHENE-ASARE DATE (SUPERVISOR) 2.…………………………………………… …………………………………… DR. ALBERT GEMEGAH DATE (SUPERVISOR) ii University of Ghana http://ugspace.ug.edu.gh DEDICATION This work is dedicated to God Almighty. iii University of Ghana http://ugspace.ug.edu.gh ACKNOWLEDGEMENTS Special thanks to Dr. A. Gemegah and Dr. Kwaku Ohene-Asare of the Department of Finance and Operations Management respectively, University of Ghana Business School for supervising this work. I would also like to express my sincere thanks and appreciation to all the lectures of the Department of Finance and Risk Management and Insurance of the University of Ghana Business School, for their immense support and contribution for this programme. To my friends and all technical students who have the opportunity to write the City and Guilds of London Institutes Examinations as part of their studies and Francis A. Aboagye, I acknowledge your immense contributions. Finally, I am very grateful to Professor A. Q. Q. Aboagye, Head of Finance Department, all the lecturers and other staff of the Department of Finance, University of Ghana Business School, for their support during the study period. iv University of Ghana http://ugspace.ug.edu.gh TABLE OF CONTENTS Content Page DECLARATION .................................................................................................................... i CERTIFICATION ................................................................................................................. ii DEDICATION .................................................................................................................... iii ACKNOWLEDGEMENTS ................................................................................................. iv TABLE OF CONTENTS ...................................................................................................... v LIST OF TABLES ............................................................................................................ viii LIST OF FIGURES ............................................................................................................... x ABSTRACT ......................................................................................................................... xi CHAPTER ONE .................................................................................................................... 1 INTRODUCTION ................................................................................................................. 1 1.0 Background of the Study ............................................................................................. 1 1.1 Research Problem ........................................................................................................ 5 1.2 Objectives of the Study ................................................................................................ 8 1.3 Research Questions ...................................................................................................... 8 1.4 Significance of the Study ............................................................................................. 9 1.5 Research Limitations ................................................................................................... 9 1.6 Chapter Outline ............................................................................................................ 9 CHAPTER TWO ................................................................................................................. 10 LITERATURE REVIEW .................................................................................................... 10 2.0 Chapter Introduction .................................................................................................. 10 2.1 Efficiency ................................................................................................................... 11 2.2 Empirical Literature ................................................................................................... 12 v University of Ghana http://ugspace.ug.edu.gh CHAPTER THREE ............................................................................................................. 20 RESEARCH METHODOLOGY ........................................................................................ 20 3.0 Chapter Introduction .................................................................................................. 20 3.1 Study Population and Data Source ............................................................................ 20 3.2 Selection of Input and Output Variables .................................................................... 23 3.3 Methodological Framework ....................................................................................... 24 3.4 Mathematical Formulation ......................................................................................... 27 3.5 Input and Output Orientations ................................................................................... 29 3.7 Multi-directional Efficiency Analysis (MEA) ........................................................... 35 3.8 Formalizing Multi-directional Efficiency Analysis ................................................... 36 3.9 Chapter Conclusion .................................................................................................... 42 CHAPTER FOUR ............................................................................................................... 42 DATA ANALYSIS AND DISCUSSION ........................................................................... 42 4.0 Chapter Introduction .................................................................................................. 42 4.1 Data Description ........................................................................................................ 43 4.2 Independent Sample t-Test ........................................................................................ 44 4.3 Descriptive Statistics .................................................................................................. 45 4.4 Starplots ..................................................................................................................... 48 4.5 Efficiency Analysis .................................................................................................... 49 4.6 Efficiency levels and patterns of Ghanaian Insurance Firms..................................... 49 4.7 The Mann-Whitney U Test ........................................................................................ 51 4.8 Chapter Conclusion .................................................................................................... 60 vi University of Ghana http://ugspace.ug.edu.gh CHAPTER FIVE ................................................................................................................. 61 SUMMARY, CONCLUSION AND RECOMMENDATION ............................................ 61 5.1 Chapter Introduction .................................................................................................. 61 5.2 Summary of findings ................................................................................................. 61 5.3 Contributions, Limitations and possible extensions of the study .............................. 62 5.4 Conclusion and Recommendation ............................................................................. 63 REFERENCES .................................................................................................................... 65 APPENDICES ..................................................................................................................... 71 vii University of Ghana http://ugspace.ug.edu.gh LIST OF TABLES Table 2.1Some studies on efficiency in the Insurance Industry…………………… 17 Table 3.1 Distribution of Life Insurance Companies used in the Study…………… 21 Table 3.2 Distribution of Non-life Insurance Companies used in the Study………. 22 Table 3.3 Envelopment and Multiplier Models……………………………………. 28 Table 3.4 Data for an Input (x) and Output (y)…………………………………….. 31 Table 3.5 Supply Chain Operation within a Week………………………………… 32 Table 4.1 Definitions of Inputs and Outputs……………………………………….. 42 Table 4.2 Independent Sample t-Test……………………………………………… 43 Table 4.3 Descriptive Statistics of Inputs and Outputs for the Pooled meta-data (unit: thousands of Ghana Cedis)……………………………………..….. 44 Table 4.4a Descriptive Statistics of Inputs and Outputs by Type of Company (units; thousands of Ghana Cedis)…………………………………………. 45 Table 4.4b Descriptive Statistics of Inputs and Outputs by Type of Insurance Company…………………………………………………………………………… 45 Table 4.5 Correlation Matrix and p-values for pooled meta-data set……………… 46 Table 4.6 Test of Significance Differences in the average efficiency scores……… 50 Table 4.7a Summary of Relative MEA & DEA Efficiency Scores for Pooled meta-data…………………………………………………………………… 51 Table 4.7b List of Insurance Firms which were MEA efficient for the pooled meta-data…………………………………………………………………... 51 Table 4.8a Summary of MEA & DEA Technical Efficiency Scores for Life Insurance Companies across the whole study period………………...……. 55 Table 4.8b List of Life Insurance Firms which were MEA efficient over the study period………………………………………………………………… 56 viii University of Ghana http://ugspace.ug.edu.gh Table 4.9a Summary of MEA & DEA Technical Efficiency Score for Non-life Insurance Companies across the whole study period…………….. 57 Table 4.9b List of Non-Life Insurance Firms which were MEA efficient over the study period…………………………………………………………… 58 ix University of Ghana http://ugspace.ug.edu.gh LIST OF FIGURES Figure 3.1 Projection to frontier for the input-orientated CCR model……………. 29 Figure 3.2 Projection to frontier for the output-orientated CCR model…………… 30 Figure 3.3 Efficient frontier for the five DMUs of Table 3.4……………………… 31 Figure 3.4 Illustrating DEA efficient frontier……………………………………… 33 Figure 3.5 Diagram showing the Ideal Reference Point (0) and Benchmark (B) for inefficient DMU4……………………………………………………… 41 Figure 4.1 Average aggregated annual MEA and DEA efficiency scores for the two subgroups across the whole study period…………………………….. 49 Figure 4.2 Average annual MEA and DEA efficiency scores for Life Companies and Non-Life Companies for the whole study period………………………… 54 x University of Ghana http://ugspace.ug.edu.gh ABSTRACT The general objective of this study was to estimate the technical efficiency of the Ghanaian insurance firms and also to investigate the levels and patterns of these efficiencies over the study period. Annual reports were obtained from National Insurance Commission (NIC), the Ghanaian insurance regulator on a sample of insurance companies from 2007 to 2012. Basically, the study was quantitative in nature where an optimization technique was used. Specifically multi-directional efficiency analysis (MEA) also called potential improvement of data envelopment analysis (DEA). The study discovered that in general, the Ghanaian insurance firms perform poorly on the inputs resources of gross premium, labour, equity capital and fixed assets. It concluded that for non-life insurance firms, Activa International and Enterprise Insurance perform very well during the study period, while Met Life Insurance and Capital Express Assurance did same in the life insurance sector over the study period. IGI Life Insurance Company on the average did very well as observed but data on this company was not available from 2010 onwards. The study observed that there were clear differences in efficiency patterns between life and non-life insurance firms during the years 2009, 2010 and 2012. The Mann-Whitney U statistic concluded that there is no significance difference in both DEA and MEA efficiency scores between the life firms and non-life firms in the years 2007, 2008, and 2011. We recommend that as most financial services firms in the developed countries are increasingly using benchmarking techniques to identify areas of their operations that need continues improvement, the Ghanaian insurance industry should do same. xi University of Ghana http://ugspace.ug.edu.gh CHAPTER ONE INTRODUCTION 1.0 Background of the Study The performance of business organizations does not only increase their market shares but contribute to growth of business sectors leading to overall economic growth. Performance evaluation is one of the most important issues among insurance firms and there are many studies focusing on measuring the relative efficiencies of insurance firms(Sabet & Fadavi, 2013). The quest for a reliable insurance industry has currently become a major concern in a fast developing economy like Ghana, considering the recent fire outbreaks in some parts of our country especially the market places. Indeed, no part of the world or human endeavor is free from problems of uncertainties. In many parts of the world, very reliable insurance services have already been established and new insurance products and innovation have become a routine (OECD, 2008). The same cannot be said of Ghana, although many of the victims who lost their goods and properties are aware of the socio-economic importance and benefits of insurance programmes. Available information indicates that these fire outbreaks destroyed properties worth millions of Ghana cedis but most of the victims do not have any form of insurance cover for their loss. During the occurrences of these fire outbreaks, it came out clearly that majority of the market women have no confidence in the insurance industry (Ghanaweb, 2014). Interest in the general topic of efficiency and productivity growth has grown in recent years. There are in fact “efficiency” studies in many countries and about many market or non- market production or service activity (Daraio & Simar, 2007). 1 University of Ghana http://ugspace.ug.edu.gh Performance assessment of various sectors of the economy has become very important for governments, politicians, managers, business leaders, research institutions as well as professional bodies. Stakeholders require this information in order to make informed decisions relating to prudent and effective management of financial resources available to equally operate efficiently in the global market(C. C. Sun, 2014). Performance evaluation and assessment are fundamental to management planning and control activities, and accordingly, have received considerable attention by both management practitioners and academic researchers(Asmild, Paradi, Reese, & Tam, 2007 and Zhu 2009), indicated that performance evaluation and monitoring are a widely used method to identify and adopt best practices as a means to improve performance and increase productivity change, and are particularly valuable when no objective or engineered standard is available to define efficient and effective performance (Fried et al., 2008). Insurance service provision in Ghana has for the past decades been routinely criticized for failing to meet client claim requirements, even though clients believed they have met the condition for claims. Often, the institutions are large and inefficient, and unable to deliver reliable services to the public. In spite of their massive physical and ubiquitous presence, insurance companies in Ghana have not been able to meet the needs of most if not all of their clients (NIC Annual Report, 2011). During the past decade, dramatic changes have taken place in insurance markets worldwide, mainly, driven by financial sector deregulation, liberalization and privatization in Europe, the US and Japan (Cummins & Dionne, 2008;Bawa & Ruchita, 2011). In this study we focus on investigating the patterns and levels of efficiency of the Ghanaian insurance industry based on multi-directional efficiency analysis (MEA) techniques. 2 University of Ghana http://ugspace.ug.edu.gh Many Ghanaians seem unaware of the need for an insurance cover in their day-to-day activities. A deliberate attempt must be made to re-package the insurance concept to the Ghanaian populace in order to increase their confidence in it, especially among individuals. Current efforts must be doubled if the Ghanaian public is to voluntarily sign on to insurance policies and the Industry is to achieve the expected growth. A critical study of the annual reports of National Insurance Commission (NIC) from 2005 to 2011 reveals a lot of complaints against most of the insurance companies by their clients to the Commission. It could be inferred that if this situation is not controlled, the general public would continue to lose confidence in this industry. Basically, the whole concept or idea of insurance revolves around risk management, and usually most financial institutions including banks, insurance companies among others continue to search for ways and means of minimizing or avoiding these risks. Bearing in mind the recent financial crisis as well as the economic downturn, it is more important than ever that insurers review their risk management techniques and procedures in order to improve efficiency. In many developed countries, risk management is an important area which has attracted the attention of governments, business houses, scientists, researchers, as well as individuals in forecasting the imminent risk in undertaking any project/work and taking suitable precautions to avoid or minimize the adverse impact of risk (Gavalas & Syriopoulos, 2014). This may be observed from the numerous articles that have been written in this regard. The importance of risk management in the financial sector, led to the formation of the Global Association of Risk Professional (GARP) in 1996, and this body said that, “risk-taking is an integral part of business and is a catalyst for growth; hence developing a robust risk culture has many benefits”. 3 University of Ghana http://ugspace.ug.edu.gh Insurance as explained by Melnikov (2004) is a contract (policy) according to which one party (a policy holder) pays an amount of money (premium) to another party (insurer) in return for an obligation to compensate some possible losses of the policy holder. The aim of such a contract is to provide a policy holder with some protection against certain risks. Deaths, sickness, disability, motor vehicle accident, loss of property, among others are some typical examples of such risks (Melinkov, 2004). Ruppert, (2011), indicated that the financial world has always been risky, and financial innovations such as the development of derivatives markets and the packaging of mortgages have now made risk management more important than ever before but also more difficult. He further explained that there are many different types of risks. McNeil et al. (2005), mentioned that as well as banks, the insurance industry has a long- standing relationship with risk. They further mentioned that an additional risk category entering through insurance is underwriting risk, the risk inherent in insurance policies sold. A new emerging type of risk is the regulatory risk that looks at the impact on the company of new legislation. Other types of risks include: Settlement Risk which is commonly faced in international transactions, Tax Risk which is the risk that taxes or the interpretation of tax laws will change unexpectedly, Legal Risk refers to the risk that the legal system will fail to enforce a contract, Accounting Risk is the uncertainty over the proper accounting treatment of a derivative transaction, Model Risk is the risk that in pricing a financial instrument such as derivatives, the firm will use an inappropriate model or a model containing errors, or use incorrect inputs (Chance & Brooks, 2008). There are many techniques available for insurance companies to manage risks. These include: loss financing, risk avoidance and loss prevention and control. It must be 4 University of Ghana http://ugspace.ug.edu.gh emphasized that managing risks is an important factor which insurance companies must attend to if they are to achieve better financial performance as part of their operations. Each type of managerial decision carries some fundamental, universal uncertainties while each one of them is characterized by the peculiar uncertainties specific to domain, type, technology, among others(Meshi, Biele, Korn, & Heekeren, 2012). A useful starting point is to acknowledge that operational risk encompasses risk inherent in business activities across an organization. Risk may be associated with operations of every business organization and the way to manage and control these risks will go a long way to determine the future prospects of the organization (Zhu, 2009). Financial and insurance markets always operate under various types of uncertainties that can affect financial positions of companies and individuals, the 2007-2009 economic meltdown is the major subject of recent times (Harris, Huerta, & Ngo, 2013). In financial and insurance theories these uncertainties are usually referred to as risks. Given certain states of the market, and the economy in general, one can talk about risk exposure. Organizations management are often under great pressure to improve the performance of their business activities. Thus in order for these managers to improve performance, one need to continuously monitor and evaluate the various operations or processes relating to each section or department of their organization(Ding, Zhou, Xiao, Ma, & Liu, 2014). 1.1 Research Problem Banker, Cummins, and Klumpes, (2010), mentioned that financial services firms are increasingly using benchmarking techniques to identify operations that need improvement by comparing their performance with other firms in the industry. An important new class of benchmarking methods has been developed called frontier efficiency methodologies (FEM). 5 University of Ghana http://ugspace.ug.edu.gh These include parametric stochastic frontier analysis (SFA) and non-parametric data envelopment analysis (DEA)(Jiang, Yao, & Feng, 2013). An alternative to DEA is the MEA technique developed by Bogetoft and Haugaard and extended by Asmild which is considered to be much more appropriate, especially when one is focusing on the improvement of inefficient decision making units (DMUs). There are few studies that have applied the MEA techniques, this include(Asmild & Pastor, 2010; (Asmild & Matthews, 2012Asmild & Matthews, 2012; Bi, Wang, & Liang, 2014). However, none of these studies to the best of our knowledge have applied the MEA technique in the insurance industry that is not to say that frontier efficiency studies have not been performed in the insurance sector. In Ghana, and other countries frontier efficiency methodologies studies have been carried out in the insurance industry(David Cummins & Sommer, 1996;Cummins & Xie, 2009;Owusu-Ansah, Dontwi, Seidu, Abudulai, & Sebil, 2010; Ansah-Adu, Andoh, & Abor, 2012;Barros, Nektarios, & Assaf, 2010; Biener & Eling, 2012;Cummins & Zi, 1998;. Cummins et al., 2004: Eling & Luhnen, 2010 and Bertrand & Prigent, 2011),but none consider MEA technique. Frontier methodologies measure firm performance relative to ‘best practice’ frontiers derived from the firms in the industry. Such measures are superior to traditional techniques such as financial ratio analysis because they summarize performance in a single statistic that accounts for differences among firms using a sophisticated multidimensional framework(L. Sun & Chang, 2011). Two primary frontier methodologies have been developed to estimate frontier efficiencies: (1) Parametric or stochastic frontier analysis (SFA), which generally makes assumptions about the functional form of the technical, cost, revenue, or profit function and error term distributions and estimates efficiency using econometric techniques; and (2) non-parametric techniques, most prominently data envelopment analysis (DEA), which do not make assumptions about functional forms and estimate efficiency using linear programming and other nonparametric 6 University of Ghana http://ugspace.ug.edu.gh methods. DEA developed by Charnes et al. (1978) is a linear programming methodology for evaluating the relative technical efficiency for each member of a set of peer decision making units (DMUs) with multiple inputs and multiple outputs. Again, most of these DEA-based efficiency analyses were restricted to the radial expansions of outputs or radial contractions of inputs(Cheng, Zervopoulos, & Qian, 2013). A large number of studies relating to performance evaluations and efficiency analysis in the financial sector and other areas using Data Envelopment Analysis (DEA) have been carried out (Li & Reeves, 1999;Jenkins & Anderson, 2003; Avkiran, 2006;Yang, 2006;Johnes, 2006;Fethi & Pasiouras, 2010;Saranga & Moser, 2010;Edirisinghe & Zhang, 2010;Tsolas, 2011;Shyu & Chiang, 2012;Amado, Santos, & Marques, 2012and Chang, Cheng, Pan, & Wu, 2013).. Eling & Luhnen (2010) mentioned that the insurance sector, in particular, has seen rapid growth in the number of studies applying frontier efficiency methods (FEM). Multi-directional efficiency (MEA) also sometimes referred to as potential improvement of the DEA is a more recent technique which was first introduced by Bogetoft and Hougard in (1999) and subsequently operationalised by Asmild et al (2003). Unlike the DEA approach, the MEA approach, the MEA selects benchmarks such that the input contractions or output expansions are proportional to the potential improvement identified by considering the improvement potential in each input or output variable separately, not just the efficiency levels but also the efficiency patterns of different systems can be detected (Wang et al., 2013). The complexity of insurance products and diversity of providers are sufficient reasons for assessing the efficiency and effectiveness of this sector industry (OECD, 2008). 7 University of Ghana http://ugspace.ug.edu.gh The question under investigation is ‘what is the level and pattern of efficiency among Ghanaian insurance companies? 1.2 Objectives of the Study The objective of this study is to investigate the efficiencies of the insurance industry using MEA. The specific objectives are: 1. To undertake a novel application of the multi-directional efficiency analysis by assessing the efficiency levels of Ghanaian insurance firms. 2. To identify the levels of efficiency differences over timebetween the life and non-life insurance firms. 3. To investigate the patterns of efficiencies between life and non-life insurance firms in Ghana, following Asmild and Matthews (2012) 1.3 Research Questions Basically, the study seeks to answer the following questions; 1. Do Ghanaian insurance firms perform differently when their efficiencies are estimated via MEA than DEA? 2. Are life insurance firms more efficient than non-life ones? 3. Does an efficiency difference exist between life and non-life insurance firms over time? 4. Which variables do Ghanaian insurance firms perform well on? 5. Are non-life firms more efficient than life on labour, premiums, investments, claims and benefits? 8 University of Ghana http://ugspace.ug.edu.gh 1.4 Significance of the Study This study will suggest areas of efficiency improvement relating to the insurance industry. It is further hoped that the findings and the recommendations of the study would contribute to the development of the insurance industry by assisting management and other stake holders to improve upon the efficiency and performance of their operations. Also, the findings of this study will contribute to industry players in identifying areas in their operations that are inefficient and need continues improvement. Finally, the findings of this study could be seen as a contribution to existing works on the literature of efficiency studies in the insurance industry in Ghana. 1.5 Research Limitations Due to lack of appropriate record keeping in our various institutions, researchers usually encounter several challenges in obtaining data for their research work. Since the research will be conducted on various Ghanaian Insurance Companies and most of these companies usually are unwilling to volunteer vital information about their operations, the nature (quality and quantity) of the data collected would be affected. 1.6 Chapter Outline The remainder of this paper is structured as follows. Chapter two contains the framework for the study by reviewing the existing literature about some of the available research undertaken in this area, with particular attention given to performance evaluation and efficiency investigations using Data Envelopment Analysis (DEA) and multi-directional 9 University of Ghana http://ugspace.ug.edu.gh efficiency analysis (MEA). During the review process, attention was given to studies which concentrated on efficiency issues and concepts, as well as the methods used. Chapter three is on the methodology used. This section describes the research design, including the target population, sampling frame, sample size, and method of data collection among others. The chapter explains the input-orientation and the output-orientation models in data envelopment analysis (DEA). Finally, the potential improvement method also known as the multi-directional efficiency analysis (MEA) method is be explained. Chapter four presents the data analysis and discussion section. Each analysis is directed towards answering an objective listed earlier in this chapter. Here, a description of the specific effects examined in each analysis is given. Chapter five focuses on the discussion of summary of finding, contribution of the study and conclusion and recommendation as well as suggesting ways of further future research. CHAPTER TWO LITERATURE REVIEW 2.0 Chapter Introduction This chapter reviews some of the previous work done on efficiencies in the insurance sector. Available literature shows that while there have been a large number of valuable studies done on the efficiency of the insurance industry in developed countries, there are few that focus on developing countries including Africa (Sabet & Fadavi, 2013;Owusu-Ansah, 10 University of Ghana http://ugspace.ug.edu.gh Dontwi, Seidu, Abudulai, & Sebil, 2010; Ansah-Adu, Andoh, & Abor, 2012 and Turkan, Polat, & Gunay, 2012). This study uses the multi-directional efficiency analysis (MEA) techniques of the frontier efficiency methodologies to investigate the efficiency of the Ghanaian insurance sector. However, within the insurance industry in Ghana, to the best of our knowledge there is no study that has applied the MEA techniques to the insurance industry. 2.1 Efficiency Daraio and Simar (2007), mentioned different authorities such as Debreu (1951), Pareto- Koopmans (1951), Fare and Lovell (1978) and Russell (1985, 1988, 1990) among others who have examined and defined efficiency from several dimensions. Various types of efficiencies were mentioned. These includes; technical, allocative, revenue, scale and structural. In the words of Farrell, (1957) overall productive efficiency may be defined as the product of technical and allocative efficiency. Farrell explained that technical efficiency measures the firm’s success in producing maximum output from a given set of inputs (output orientation) or is the ability of a firm to reduce all inputs given set of outputs (input- orientation). The allocative efficiency in economic theory measures a firm’s success in choosing an optimal set of inputs with a given set of input prices (Farrell, 1957). The concept of structural efficiency is an industry level concept which broadly measures the extent to which an industry keeps up with the performance of its own best practice firms (Farrell, 1957).Thus it is a measure at the industry level of the extent to which its firms are of optimum size i.e. the extent to which the industry production level is optimally allocated between the firms in the short run. Revenue efficiency measures the firm’s success in maximizing revenues by 11 University of Ghana http://ugspace.ug.edu.gh comparing the firm’s actual revenues to the revenues of a fully efficient firm with the same quantity of inputs (Fried et al., 2008). 2.2 Empirical Literature Eling and Luhnen, (2010) provide new empirical evidence on frontier efficiency measurement in the international insurance industry, a topic of great interest in the academic literature during the last several years. They conducted a broad efficiency comparison of six thousand four hundred and sixty-two (6462) insurers from thirty-six (36) countries. In their study, different methodologies, countries, organizational forms, and company sizes are compared, considering life and non-life insurers. They found a steady technical and cost efficiency growth in international insurance markets from 2002 to 2006, with large differences across countries. The study showed that Denmark and Japan have the highest average efficiency, whereas the Philippines is the least efficient. Finally, the study reveals that only minor variations are found when comparing different frontier efficiency methodologies (data envelopment analysis, stochastic frontier analysis). The major contribution of their paper is that it provided new empirical evidence on frontier efficiency measurement in the international insurance industry, a topic of great interest in the academic literature during the last several years. However, the problem with these techniques has to do with the choice of estimation technique to use whether parametric or non-parametric since no method is strictly preferable over the other. Pasiouras and Gaganis (2013), provides the first cross-country study on the association between firms' soundness and regulatory policies in the insurance industry. Measuring solvency with an accounting based measure of distance to default, namely the Z-score, they find that the power of the supervisory authorities, and regulations related to both technical provisions and investments have an impact on soundness that is robust to controls for firm- 12 University of Ghana http://ugspace.ug.edu.gh specific and country-specific factors. In contrast, corporate governance and internal control rules do not influence soundness. Similarly, capital requirements do not appear to have a robust impact on soundness. Moshirian (1999), analyzed the sources of growth in international insurance services. The study defined international insurance services in the context of the new definition of trade in financial services. Cross-border trade and foreign direct investment in insurance services are categorized into four distinct groups, based on the movement of providers and receivers of insurance services. The empirical results of a model of the movement of providers in insurance services indicate that insurance premiums and the national income of the host countries contribute to the expansion of multinational insurance companies. Furthermore, bilateral trade, labor costs, economic growth and the cost of capital are also contributing to the expansion of international insurance services. In addition, the empirical results indicate that foreign direct investment (FDI) in banking is a complement to the expansion of international insurance services. Available literature shows that there are only five published papers on the MEA technique, this include (Asmild, Hougaard, Kronborg, & Kvist, 2003; Asmild & Pastor, 2010; Liu & Chen, 2011; Asmild & Matthews, 2012a and Wang, Wei, & Zhang, 2013b). All these papers used the MEA technique in different application areas. But, my motivation for the study, come from the fact that Asmild and Matthews used the MEA method to evaluate efficiency levels and patterns in Chinese banks. Since the insurance sector is considered as part of financial institutions, the MEA technique can equally be applicable in this industry as well. Asmild and Matthews (2012), showed how differences in the efficiency patterns between different subgroups within a data set can be investigated using the more recent MEA 13 University of Ghana http://ugspace.ug.edu.gh methodology. They specifically looked at the cases of Joint Stock Banks and State Owned Banks in China and were able to empirically test hypotheses of whether or not there are differences in the levels and also in the patterns of inefficiencies between the two banks. Their study observed that certain differences are expected, based on differences in objectives and constraints in the two types of banks and find empirical support for most of those expected patterns. Though this study was done for the banking industry, it can be used for the insurance industry as both industries are considered as financial service providers and this paper is the motivation for my work. Wang et al.(2013) analyzed the energy and emission efficiency patterns of Chinese regions utilizing the multi-directional efficiency analysis (MEA) approach. The results of the empirical study indicate that, in general, the MEA efficiency of China experienced an increasing process over the study period 1997–2010; the east area overall is more MEA efficient than the central area and the west area of China during the study period; the significant higher MEA efficiency of the east area to the central area and the west area are due to both the higher energy specific efficiency and the higher emissions specific efficiency of the east area compared to the other two areas; the provinces of Hebei, Shanxi, Inner Mongolia, Shandong, Henan, and Hubei etc. have both high energy saving potentials and high emissions reduction potentials, thus they will play the most important roles in China’s effort on energy conservation and CO2 emissions mitigation. The work of Asmild and Pastor, (2010) is very pertinent in an effort to study multi- directional efficiency analysis (MEA). In their study, they extended two directional distance function models, the Multi-directional Efficiency Analysis (MEA) Model and the Range Directional Model (RDM), in order to account for any type of technical inefficiency, i.e. both directional and non-directional inefficiencies. They first focused on the variable returns 14 University of Ghana http://ugspace.ug.edu.gh to scale (VRS) case, because both VRS-MEA and RDM are translation invariant models, which mean that both models are able to deal with negative data. The main result is the definition of a new comprehensive efficiency measure which is units’ invariant and translation invariant and covers both models. Secondly, they introduced the RDM model under constant returns to scale (CRS) together with a new comprehensive efficiency measure. A taxonomy of some available efficiency studies in the insurance industry has been provided in table 2.1, with some details mentioned. 15 University of Ghana http://ugspace.ug.edu.gh Table 2.1: Some of studies on efficiency in the insurance industry Author(s) Countries No. Sample Lines of Method Input type Output type Main types of Selected findings Insurers period Business efficiencies Barros and Nigeria 10 2001- Life, non- DEA Capital, Profits, net Technical, pure Majority companies Obijiaku 2005 life operative premiums, settled technical, scale are vrs efficient (2007) costs, labour, claims, total outstanding investments claims, investment income Yao et al, China 22 1999- Life, non- DEA labour, capital, Premiums , Technical Average efficiency of (2007) 2004 life payment and investment 0.77 for non-life benefits income and0.70 for life companies Xie,(2008) US 107 1993- Non-life DEA labour, Loss incurred, Cost, revenue Performance on cost, 2004 business real investment revenue is the same services and assets for Initial public material, offering(IPO) and equity. private firms Tone and India 1982- life DEA labour, Present value of Technical, Increase in allocative Sahoo (2005) 2001 business loss incurred, allocative, cost, inefficiencies after services,debt ratio of liquid scale 1994; increase in cost capital, equity assets to efficiency in 2000 liabilities Cummins et Italy 94 1985- Life, non- DEA Labour, fixed Sum of benefits, Technical Stable efficiency over al. (1996) 1993 life capital changes in time (70%-78%) for expense, reserves, invested industry with sharp equity capital assets. losses decline (25% incurred cumulative) 17 University of Ghana http://ugspace.ug.edu.gh Author(s) Countries No. Sample Lines of Method Input type Output Main types of Selected findings Insurers period Business type efficiencies Owusu-Ansah et Ghana 10 2002-2007 Life, non- DEA Debt capital, Premium Technical Overall efficiency al. (2010) life equity capital, claims 68%, technical management invest- efficiency 87% and expenses ent scale efficiency income 78% Ansah-Adu et al. Ghana 30 2006-2008 Life, non- DEA Fixed assets, Profit or Cost Higher average (2012) life total capital, loss, net efficiency scores total premium, for life than non- investment investme life companies nt income Bawa and India 10 2002-03 to Life DEA Equity capital, Net Technical, put Overall average Ruchita (2011) 2009-10 labour, other premium technical, scale technical efficiency expenditure 73%, pure technical 92%, scale 78% Saad and Idris Malaysia 2000-2005 Life DEA Commission, Premium Technical, Main source of (2011) and Brunei management , productivity efficiency change expenses investme change is scale rather than nt pure technical income 18 University of Ghana http://ugspace.ug.edu.gh Due to the dynamic and multidimensional nature of performance, we think that traditional DEA will not provide enough details about inefficient DMUs, but family of network DEA models proposed by Fare and Grosskoft can play an important role in identifying sources of inefficiency in parts of the organization processes (Amado, Santos, & Marques, 2012b). As rightly pointed out by Wang et al. (2013), most of the studies on efficiency mentioned above are all based on the traditional DEA approach in which the DMUs under evaluation are restricted to the radial contractions on all input variables or radial expansions on all output variables. However, this assumption may be somewhat inappropriate in efficiency evaluation, since different input or output variables may adjust with different proportions so as to get more reasonable and specific efficiency measure. Since MEA selects benchmarks such that the input contractions or output expansions are proportional to the potential improvement identified by considering the improvement potential in each input or output variable separately, not just the efficiency status but also the efficiency patterns, it can be assumed that the (MEA) approach will provide better result than the DEA approach. 2.3 Chapter Conclusion In this chapter, we described some of the available literature or cross country and efficiency studies in the insurance industry. We started by having a brief look at the concept, history and types of efficiencies. We then moved on to look at published papers that have used the MEA concept and their applications. We provided taxonomy of some efficiency studies in the insurance industry using frontier techniques. Finally, a general review of the DEA technique was provided. 19 University of Ghana http://ugspace.ug.edu.gh CHAPTER THREE RESEARCH METHODOLOGY 3.0 Chapter Introduction This chapter is devoted to the population, data collection techniques used, design of the study, intervention methods used and finally how the data would be analyzed. To be able to choose and decide on the main methods for the analysis of this data, exploratory data analysis was performed on the collected information. This assisted in observing some basic patterns demonstrated by the variables in the study. Charts such as line graphs, curves etc were constructed to assist in the explanations. Copies of some of these results could be found in this chapter, the next chapter as well as the appendix section of this dissertation. The statistical packages used for this analysis are the R-Language, SPSS and EViews. The R statistical software was used to compute the MEA and the DEA technical efficiency scores because, to the best of my knowledge, currently it is the only software that can be used to perform multi-directional efficiency analysis (MEA), while EViews was used to compute the descriptive statistics and also to draw the average MEA and DEA graphs. 3.1 Study Population and Data Source By the time of this study period, Ghana has forty five (45) insurance companies made up of 26 Non-life and 19 life, 2 reinsurance companies, 54 Broking Companies, 1 each of Loss Adjuster, Reinsurance Broker and Oil and Gas Company and about 4000 insurance agents, according to available records from National Insurance Commission (NIC), the Ghanaian insurance regulator’s website (nicgh.org 2013).However, this study uses data set covering different insurance companies for a six year period 2007-2012. The annual financial statements of these companies were obtained from the NIC database and those which were 20 University of Ghana http://ugspace.ug.edu.gh not available were computed using ratio estimates from the NIC annual report for this analysis. These companies were selected based upon the availability of data and the number of years that these insurance companies have been operating in the industry. Table 3.1: Distribution of Life Insurance Companies used in the Study NO. Company and Year Codes 2007 2008 2009 2010 2011 2012 TOTAL 1 Enterp(A1) 1 1 1 1 1 1 6 2 Donew(A13) - 1 1 1 - - 3 3 Glico(A3) 1 1 1 1 1 1 6 4 Ghana Life(A2) 1 1 1 1 - - 4 5 Express(A16) - - 1 1 1 1 4 6 Golden(A14) 1 1 1 1 - - 4 7 GUA(A15) - 1 1 1 1 1 5 8 IGI(A4) 1 1 1 1 - - 4 9 Metrop(A5) 1 1 1 1 1 1 6 10 Phoenix(A6) 1 1 1 1 1 1 6 11 Provident(A7) 1 1 1 1 1 1 6 12 Quality(A8) 1 1 1 1 1 1 6 13 SIC(A9) 1 1 1 1 1 1 6 14 Star(A10) 1 1 1 1 1 1 6 15 Unique(A11) 1 1 1 1 1 1 6 16 Vanguard(A12) 1 1 1 1 1 1 6 17 Capital(A13) - - 1 - 1 1 3 TOTAL 13 15 17 16 13 13 87 21 University of Ghana http://ugspace.ug.edu.gh Table 3.2: Distribution of Non-Life Insurance Companies used in the Study NO. Company and Year codes 2007 2008 2009 2010 2011 2012 TOTAL 1 Activa(B1) 1 1 1 1 1 1 6 2 Allianz(19) - - - 1 1 1 3 3 Colina(B18) - - - 1 1 1 3 4 Donew(B2) 1 1 1 1 1 1 6 5 Enterp(B3) 1 1 1 1 1 1 6 6 Equity(B16) - 1 1 1 1 1 5 7 GUA(B15) 1 1 1 1 1 1 6 8 Glico(B4) 1 1 1 1 1 1 6 9 IGI(17) 1 1 1 1 - - 4 10 IEI(B21) - 1 1 1 1 1 5 11 IntW(B22) - - 1 1 - - 2 12 Metrop(B5) 1 1 1 1 1 1 6 13 NEM(B20) - - 1 1 1 1 4 14 NSIA(B6) 1 1 1 1 1 1 6 15 Phoenix(B7) 1 1 1 1 1 1 6 16 Prime(B8) 1 1 1 1 1 1 6 17 Provident(B9) 1 1 1 1 1 1 6 18 Quality(B10) 1 1 1 1 1 1 6 19 Regency(B23) - 1 1 1 1 1 5 20 SIC(B11) 1 1 1 1 1 1 6 21 Star(B12) 1 1 1 1 1 1 6 22 Unique(B13) 1 1 1 1 1 1 6 23 Vanguard(B14) 1 1 1 1 1 1 6 TOTAL 16 19 21 23 21 21 121 22 University of Ghana http://ugspace.ug.edu.gh 3.2 Selection of Input and Output Variables One challenge in efficiency application of DEA techniques is in the selection of inputs and outputs. The selection of inputs and outputs should be deemed appropriate. Usually, inputs are defined as resources utilized by the DMUs or transform during the production process, while outputs are the benefits generated as a result of the operation or the transformation by the DMUs (Bawa & Ruchita, 2011). Ramanathan (2003), indicates that there is no specific rule in determining the procedure for selection of inputs and outputs for efficiency analysis. However, Banker et al. (2010) and Brockett et al. (2005), mentioned two main approaches for the selection of inputs and outputs variables for efficiency analysis, these are value-added approach and the “flow” or financial intermediation approach. Brockett et al. (2005), identify three insurance outputs – solvency, claims paying ability, and return on investment, proxied respectively by a scalar measure of the insurer’s solvency rating, the liquid assets-to-liabilities ratio, and the ratio of investment income to assets. The value-added and flow methodologies also differ in their inputs. The value-added approach uses labor, financial capital, and business services as inputs, whereas Brockett et al. (2005) utilize total expenses, the level of financial capital, and the change in equity capital as inputs. Cook and Zhu (2007), posit that in conventional data envelopment analysis it is assumed that the input versus output status of each of the chosen performance measures is known. In some situations, however, certain performance measures can play either input or output roles and they refer to these performance measures as flexible measures. Their paper presented a modification of the standard constant returns to scale (CRS) DEA model to accommodate such flexible measures. Both an individual DMU model and an aggregate model are suggested as methodologies for deriving the most appropriate designations for flexible 23 University of Ghana http://ugspace.ug.edu.gh measures. Their study illustrated the application of these models in two practical problem settings. Thus, in general, several researches have shown that there are mixed results in the use of either the value-added approach or the “flow or financial intermediation approach as well as other technique that may be available. However, some guidelines may be used as suggested by Ramanthan (2003). The input and output selections for any efficiency measure differ depending on the aims of the study. In conclusion, the inputs and outputs variables used in this study were considered based on the role they play to the success of the method used for the study. The study use four inputs and two outputs. The inputs are gross premium (gprem), labour, equity capital (equity) and fixed assets (fixass), while the output comprises of investment income (invinc) and claims incurred (clmincu). 3.3 Methodological Framework Several authors (Bawa & Ruchita, 2011: Shyu & Chiang, 2012:Collier, Johnson, & Ruggiero, 2011) have shown that, the principles of frontier analysis date back to Farrell (1957), but the method did not receive wide attention until the paper by Charnes, Cooper and Rhodes (CCR) (1978), who first coined the term Data Envelopment Analysis (DEA). Since then, a large number of papers have appeared which have extended and applied the DEA methodology (Li & Reeves, 1999; Johnes, 2006 and Fethi & Pasiouras, 2010). The idea behind DEA is to construct an efficient frontier from the available data set using the “best-practice” firms. Then the efficiency of the other firms called DMUs are measured relative to the constructed frontier either in the direction of inputs-orientation or in the direction of output-orientation (Fried et al., 2008). Firms that are on the efficient frontier are deemed efficient and given a score of one (1), but those fully dominated and inside the frontier are given a score less than 1 and rendered inefficient. 24 University of Ghana http://ugspace.ug.edu.gh Performance measurement can be used to direct management efforts to the areas that most need improvement; to identify attractive targets for mergers and acquisitions, and for many other purposes (Rahnamay Roodposhti, Hosseinzadeh Lotfi, & Vaez-Ghasemi, 2012).Performance assessment also can be used within the firm to compare the performance of hospitals, banks, and energy and telecommunications industries. In the literature(Lampe & Hilgers, 2014), there are basically two main approaches in efficient frontier analysis: the parametric or econometric approach and the nonparametric or mathematical programming approach. Free Disposal Hull (FDH) and DEA are the commonest nonparametric frontier techniques. FDH can be seen as a more general nonparametric estimator of frontiers than DEA, or as a non-convex version of DEA(Borger, Kerstens, Moesen, & Vanneste, 1994). Bardhan, Bowlin, Iowa, & Cooper (1996), indicated that FDH approach avoid the danger of identifying a dominated DMU as efficient when non-zero slack is present. The preference of the nonparametric approach over the parametric approach which is based on the functional specification of the frontier, is due to the small amount of assumptions required and mainly to the fact that we do not have to specify the functional form of the relation inputs-outputs and we do not need to specify a distributional form for the inefficiency term (Daraio & Simar, 2007). DEA has been found to be particularly suitable in solving the following three basic performance questions that most organization is faced with (Zhu, 2009). 1. How well are we doing relative to others doing the same things as we do? 2. What do we need to improve? 3. Who are the best performers for benchmarking? 25 University of Ghana http://ugspace.ug.edu.gh This study will use multi-directional efficiency analysis (MEA) or potential improvements (PI), which is an improvement of the traditional DEA technique to investigate the efficiency levels and patterns of the Ghanaian insurance firms. Bogetoft and Otto (2011) indicated that MEA was first introduced by Bogetoft and Hougaard (1999) and subsequently operationalised by Asmild et al. (2003). DEA is a linear programming-based technique for measuring the performance efficiency of organizational units which are termed Decision-Making Units (DMUs) (Emrouznejad & De Witte, 2010). DMU refer to the entity responsible for converting inputs into outputs and whose performances are to be evaluated. In managerial applications, DMUs may include banks, department stores and supermarkets, and extend to car makers, hospitals, and schools, public libraries and so forth. For the purpose of securing relative comparisons, a group of DMUs is used to evaluate each other with each DMU having a certain degree of managerial freedom in decision making (Cooper et al., 2011). CCR proposed the CCR model that had an input orientation and assumed constant returns- to-scale (crs). Banker, Charnes and Cooper (1984) extended the CCR model to variable returns to- scale (vrs). This model is known in the literature as the BCC model. There are four other basic DEA models, used less frequently in the literature: the additive model of Charnes et al. (1985), the multiplicative model of Charnes et al. (1982), the Cone-Ratio DEA model of Charnes et al. (1990) and the Assurance- Region DEA model of Thompson et al. (1986, 1990). The DEA-CCR and DEA-BCC models do well at identifying the inefficient units, but are weak in discriminating among the efficient units (Seiford &Zhu, 1999). But they often rate too many units as efficient (Borges et al., 2008). 26 University of Ghana http://ugspace.ug.edu.gh 3.4 Mathematical Formulation Let xij (i=1,2,…,m) be m different inputs and yrj (r=1,2,…,s) be s different outputs for DMUJ, j=1,2,…,n. We can evaluate the efficiency of DMUo by using either the envelopment model or the multiplier model. Table 3.3 below provides information on each of these models. In these models, λ, µ and v are weights and θ,φ, z and q are the efficiency scores to be estimated (Toloo, 2009). 27 University of Ghana http://ugspace.ug.edu.gh Table 3.3: Envelopment and Multiplier Models Input- Oriented Envelopment Model Multiplier Model min s max z r yro r1 subject to subject to n s m xij j xio i 1,2,...,m; r yrj vi xij  0 j1 r1 i1 n m  yrj j yro r 1,2,...,s; vi xio 1 j1 i1  j  0 j 1,2,...,n r ,vi  0 Output-Oriented Envelopment Model Multiplier Model max m min q vi xio i1 subject to subject to n m s xij j xio i 1,2,...,m; vi xij r yrj  0 j1 i1 r1 n s  yrj j yro r 1,2,...,s; r yro 1 j1 r1   0 j 1,2,...,n j r ,vi  0 28 University of Ghana http://ugspace.ug.edu.gh 3.5 Input and Output Orientations Usually, a DEA model may be considered as an input-orientation or an output orientation(Lovell & Pastor, 1999), explained that the input oriented framework, based on the input requirement set and its efficient boundary, aims at reducing the input amounts by as much as possible while keeping at least the present output levels. Daraio and Simar (2007), also refer to this “input saving” approach to stress the fact that the outputs level remains unchanged and input quantities are reduced proportionately till the frontier is reached. This is a framework generally adopted when the decision maker can control the inputs but has not the control of the outputs. To illustrate the discussion, let us consider the example presented below in figure 3.1 consisting of five DMUs, labeled DMU1, DMU2, …,DMU5, each consuming a single input to produce a single output (Cooper, et at.,2011). Figure 3.1: Projection to frontier for the input-oriented CCR model 29 University of Ghana http://ugspace.ug.edu.gh Figure 3.2: Projection to frontier for the output-oriented CCR model. The numbers in parentheses in figure 3.1 and 3.2 are interpreted as coordinate values which correspond to the input and output of a DMU where j 1,2,...,5. In each case, the value on j the left-hand side of the parentheses is the input and the value on the right is the output for the DMU alongside which these values are listed (Cooper, et at.,2011). j The efficient frontier and DEA projections are provided in figures 3.1 and 3.2 for the input- oriented and output-oriented CCR models respectively. In both cases, the efficient frontier obtained from the CCR model is DMU2. As can be seen from the points designated by the arrow head in figures 3.1 and 3.2, an inefficient DMU may be projected to different points on the frontier under the two orientations (Cooper et al., 2011). In an input orientation, one improves efficiency through reduction of inputs, whereas an output orientation requires maximization of outputs given inputs. However, it is necessary to distinguish between a boundary point and an efficient boundary point. Moreover, the 30 University of Ghana http://ugspace.ug.edu.gh efficiency of a boundary point can be dependent upon the model orientation (Cooper et al., 2011). An example for five DMUs is provided in Table 3.4 for illustration. Table 3.4: Data for an Input (x) and Output (y) DMUs Input (x) Output (y) DMU1 2 1 DMU2 3 4 DMU3 6 6 DMU4 9 7 DMU5 5 3 Figure 3.3: Efficient Frontier for the five DMUs of Table 3.4. As noticed from figure 3.3, DMU5 is inefficient as it is not located on the frontier. To evaluate the efficiency of DMU5 we can solve the following input-oriented envelopment linear programming (LP) CCR model: 31 University of Ghana http://ugspace.ug.edu.gh min s.t 21 32 63 94 55  5 (input) 11  42 63 74 35  3 (output) 1,2 ,3,4 ,5  0 nonnegativity The data used in the above example contain a single input and a single output. But for graphical illustrations, we use two-dimensional drawing this can be the input-orientation or output-orientation. To illustrate the concept of evaluating the relative efficiency of and inefficient DMU, we consider a simple numerical example as shown in Table 3.5, with five DMUs. Table 3.5: Supply Chain Operations within a Week Inputs Output DMU INPUT (X1) INPUT (X2) (Y) DMU1 3 2 1 DMU2 5 2 1 DMU3 1 4 1 DMU4 6 3 1 DMU5 4 4 1 Figure 3.3 presents the five DMUs and the piecewise linear DEA frontier. DMUs 1, 2, and 3, are on the frontier with DMU4 and DMU not being on the frontier. Considering DMU5 as the target DMU whose efficiency is to be determined, we model the data from Table 3.2 as follows: 32 University of Ghana http://ugspace.ug.edu.gh min s.t. 31 52 13 64  45  6 (input x1) 21  22  43 34  45  3 input x2  1 2 3 4 5 1 output  1,2 ,3,4 ,5  0 nonnegativity This model can be solve for the values of efficiency score ( )and the weights ( j ) Figure 3.4: Illustrating DEA-efficient frontier Using figure 3.4, the efficiency scores for the two inefficient DMUs i.e DMU5 and DMU4 can be calculated as follows: 4 EffDMU 4  EffDMU 4  0.6667  66.67%and 6 2.5 EffDMU 5  EffDMU5  0.625 62.5% 4 33 University of Ghana http://ugspace.ug.edu.gh This means that DMU4, should reduce inputs x1 and x2 to 66.67% of their current levels without changing the output level and similar interpretation for DMU5. 3.6 Some advantages and disadvantages of DEA Outline below are some merits and demerits of DEA as indicated by (Coelli et al., 2005 and Daraio and Simar, 2007). Merits 1. It requires very few assumptions 2. DEA has also been used to provide new insights into activities (and entities) that have previously been evaluated by other methods. 3. Specific changes in the inefficient service units are identified, which management can implement. Demerits 1. One traditional limitation of the nonparametric approach is its deterministic nature and the difficulty in making statistical inference. 2. Measurement error and other noise may influence the shape and position of the frontier. 3. Outliers and extreme values may influence the results. 4. The exclusion of an important input or output can result in biased results. 5. When one has few observations and many inputs and /or outputs many of the firms will appear on the DEA frontier. 6. Treating inputs and/or outputs as homogenous commodities when they are heterogeneous may bias results. 34 University of Ghana http://ugspace.ug.edu.gh 3.7 Multi-directional Efficiency Analysis (MEA) The multi-directional efficiency analysis (MEA) approach is considered to be a potential improvement of the traditional DEA approach(Asmild et al., 2003). MEA was first introduced by Bogetoft and Hougaard (1999) and subsequently operationalised by Asmild et al. (2003). The reason for using MEA here, instead of the more common and well-known DEA methodology of Charnes et al. (1978) is that while DEA uses a radial contraction of all inputs (in the input-oriented version), MEA selects benchmarks such that the input reductions or output expansions are proportional to the potential improvements on efficiency identified by considering the improvement potential in each input or output separately. Thus, this approach is more suitable for separately investigating the efficiency patterns of each DMU (Asmild & Matthews, 2012:Wang et al., 2013). Furthermore, since MEA first considers the improvement potential in each variable separately, it is ideally suited for analyzing situations where the aim of each DMU is to simultaneously reduce some inputs and increase some outputs (Wang et al., 2013a). Traditional DEA models consider either input reductions or output increases and while the hyperbolic efficiency measure of Fare et al. (1985, 1994) enables equiproportional reductions of inputs and expansions of outputs, the resulting non-linearity makes it difficult to solve the models in practice (Asmild & Matthews, 2012:Wang et al.,2013). Asmild and Pastor (2010), indicated that the Multi-directional Efficiency Analysis (MEA) Model of Bogetoft and Hougaard is a linear directional distance function efficiency model in nature, but the directional efficiency measure must be derived ex post and is furthermore based on a benchmark selection that may contain non-directional slack. They also pose that a variable return to scale VRS-MEA is translation invariant model, which means that the model is able to deal with negative data. The Multi-directional Efficiency Analysis (MEA) model considers, for each unit under analysis, an ideal point that determines the direction 35 University of Ghana http://ugspace.ug.edu.gh towards the efficient frontier where the benchmark must be located. MEA selects a specific ideal point for each unit separately and mainly provides a benchmark selection. They also mentioned that in MEA, an efficiency measure is easily derived only after we have certain experiences and knowledge about the inefficient input (a posteriori), but requires the imposition of certain normalization conditions and that MEA can be defined under any returns to scale assumption. 3.8 Formalizing Multi-directional Efficiency Analysis To formalize the MEA model, let N be the set of insurance companies in our data set observed in each of the six year time periods. Any given insurance company jN at time t utilizes m inputs of xij , i=1, 2, 3, 4 (gross premium, labour, equity capital and fixed assets) to produces s outputs of y ,r 1,2 (investment income and claims incurred) using these rj four inputs. First, in order to find the ideal reference point for a specific observation ( x0 , y0 ) , we first solve the following model (1), for each of the input variables. As we are mainly concerned with the reduction potentials for the inputs, whilst keeping the other outputs fixed for each insurance company, here, the input oriented MEA model is utilized. min dio s.t. j xij  dio j  j x(i) j  x(i)o :i 1,...,i 1,i 1,...,m j (1)  j yrj  yro : r 1,..., s j  j  0 : jN 36 University of Ghana http://ugspace.ug.edu.gh In model (1), we consider a set of N DMU’s ( j 1,..., N ) produce s outputs (y :r 1,...,s) using m inputs (x :i 1,...,m) and a production plan (x , y of . We r i o o) DMUo first calculate the value of the potential improvements inefficiency index for DMU the o ideal input reference point x(x ) is found by solving m linear programming problems (one o for each input dimension); Next, we consider the following model (2). max o s.t.  j xij  xio  o (xio  d  io ) : i 1,...,m j  j yrj  yro : r 1,..., s j (2)  j 1 j  j  0 : jN Model (2) is used finally to determine the benchmark selection  relative to the input o specific improvement potential.   The optimal solution of model (2) is ( j ,o ) , and the relative variable specific MEA efficiency for input variable x is defined as follows: io  o (xio d  i )    x (3) io i1,...,m 37 University of Ghana http://ugspace.ug.edu.gh where   is the value of the estimated benchmark from equation (2), x represent the o io specific input to be reduced and d  is the value of the ideal reference point that correspond i with this input. Based on the individual variable specific efficiencies, a single aggregated measure of MEA efficiency for the observation of (xio , y ) could be defined as follows: ro   1  m o (xijo d  io )  jo 1   m x (4)  i1 ijo  with m representing the number of inefficient inputs identified. To illustrate, the methodology, consider the data from Table 3.5. An ideal reference point for the inefficient DMU can be obtained as follows: For input x , the first constraint is used to determine the adjustment potential of the 1 inefficient DMU, in this case DMU4 in order to obtain efficiency and for input x , the second 2 constraint is used to determine this adjustment potential improvement for that same inefficient DMU in the direction of that input variable. These define the coordinates of the ideal reference point for the inefficient DMU. For input : 38 University of Ghana http://ugspace.ug.edu.gh min d 1 s.t. 3 5 1 6  4  d (input x ) 1 2 3 4 5 1 1 2  2  4 3  4  3 (input x ) 1 2 3 4 5 2      1 (output) 1 2 3 4 5      1 (vrs) 1 2 3 4 5  , , , ,  0 1 2 3 4 5 d  2 1  1 3  , , ,  0 1 2 4 5 For input 2 39 University of Ghana http://ugspace.ug.edu.gh min d 2 s.t. 3 5 1  6  4  6 (input x ) 1 2 3 4 5 1 2  2  4 3  4  d (input x ) 1 2 3 4 5 2 2      1 (vrs) 1 2 3 4 5  , , , ,  0 1 2 3 4 5 d  2 2  1 1  , , ,  0 2 3 4 5 Solving for the coordinate of the ideal reference point (d1,d ) , using a Excel Solver we 2 obtain D(2, 2), this is indicated in the figure 3.5 below with the corresponding weight or lambda ( ) values. j Again using (2), and similar procedure, we obtain the value of the benchmark (  ) position for the inefficient DMU4. 40 University of Ghana http://ugspace.ug.edu.gh max  s.t. 3 5 1 6  4  6  (62) (input x ) 1 2 3 4 5 1 2  2  4 3  4  3  (32) input x  1 2 3 4 5 2      1 (vrs) 1 2 3 4 5  , , , ,  0 1 2 3 4 5 Solving   0.8   0.9,  0.1 1 3  , ,  0 2 4 5 The diagram below shows the location of the two inefficient DMUs (i.e. DMU4 & DMU5) for this frontier. Using this diagram, W & D are the two respective ideal reference points for these inefficient DMUs. This is the first stage of the process and the second stage is moving from these ideal reference points to the frontier which in effect produces the benchmark for these inefficient DMUs. 41 University of Ghana http://ugspace.ug.edu.gh Figure 3.5: Diagram Showing the Ideal Reference Point (D) and benchmark (B) for inefficient DMU4 Figure 3.4 shows the ideal reference point (D) and benchmark (B) for DMU4 which is inefficient. E in the diagram refers to Farrell efficient score for DMU4. 3.9 Chapter Conclusion In this chapter, we looked at the research design, data source, target population, sample size and data gathering procedure. Issues of input and output selection were mentioned, as well as input and output orientations. The mathematical formulation of DEA and MEA models were explained with examples including graphical illustrations. CHAPTER FOUR DATA ANALYSIS AND DISCUSSION 4.0 Chapter Introduction This chapter deals with the data analysis section of the study and it is divided into two main sections, with the first section looking at various statistics of the data. While under the second section, the efficiency levels and patterns of the companies used in the study were computed with the main focus been on the results obtained by analysis of the MEA scores, but DEA scores will be used for comparison to evaluate the performances of these insurance companies. 42 University of Ghana http://ugspace.ug.edu.gh 4.1 Data Description As mentioned in the previous chapter, we use data reported in the annual financial statements of the various insurance firms and others were estimated using ratio values reported in the annual reports of NIC, this includes both input data and output data. Table 4.1 below provides more details about the variables used as inputs and outputs in the study. Table 4.1: Definitions of Inputs and Outputs Variable Description Input 1 Gross Premium (gprem) Input 2 Labour (labour) Input 3 Equity Capital (equity) Input 4 Fixed Assets (fixass) Output 1 Investment Income (invinc) Output 2 Claims Incurred (clmincu) 43 University of Ghana http://ugspace.ug.edu.gh As the multi-directional analysis (MEA) technique aims at minimization of inputs, in the analysis, we used an input-orientation framework as our interest lies on the allocation of resources given the level of output obtained by the various insurance companies. The insurance companies included in this study represent about 90% of the market, thus being abundantly representative of the Ghanaian insurance market. This also ensures that the DEA convention that the minimum number of DMUs is greater than three times the number of inputs plus output was observed. 4.2 Independent Sample t-Test In order to check for time effect on each of the six variables used for the study, an independent sample t-test was conducted for each variable on a yearly basis between life and non-life insurance companies over the study period. Table 4.2 shows the result of the independent sample t-test. The test result show that there were no significance difference on each of these variables between life and non-life firms, except investment income in the years 2010, 2011, and 2012. Table 4.2: Independent Samples t-Test Gprem labour equity fixass invinc Clmincu T -1.464 -1.896 -.160 -.079 -.724 -.041 2007 Sig. (2-tailed) .155 .075 .874 .938 .475 .968 T -0.986 -1.120 .379 -.162 1.086 .738 2008 Sig. (2-tailed) .332 .271 .707 .872 .286 .466 T -0.877 -1.030 -.856 -.316 1.787 .778 2009 Sig. (2-tailed) .386 .310 .398 .754 .090 .442 T -0.027 0.266 -.355 .513 2.124 1.180 2010 Sig. (2-tailed) .979 .792 .724 .611 .049 .246 T 0.455 -0.247 -.787 .038 2.299 -.256 2011 Sig. (2-tailed) .652 .806 .437 .970 .039 .800 T 0.265 -0.316 -.500 .389 2.367 .594 2012 Sig. (2-tailed) .793 .754 .621 .700 .035 .557 44 University of Ghana http://ugspace.ug.edu.gh 4.3 Descriptive Statistics After collecting the related data on the four inputs and two outputs, data points of two hundred and eight (208) comprising eighty seven (87) for life insurance firms and one hundred and twenty one (121) for non-life insurance firms were obtained for the study period 2007-2012 and prepared for analysis. Table 4.3: Descriptive Statistics of Inputs and Outputs for the Pooled meta-data (units; thousands of Ghana Cedis) gprem Labour Equity Fixass invincu clmincu Mean 13136408 4687089 6721272 5855081 1160616 3203057 Median 6340000 2605608 2596168 1304082 505325.7 1581644 Maximum 110000000 73956252 86436017 94553061 17970770 25993785 Minimum 70636 6958 4506.9 14770 3097 821.45 Std. Dev. 17935925 7689170 12150813 12966202 2021708 4459187 Skewness 2.712397 5.276112 4.178941 3.99357 4.771226 2.448238 Kurtosis 11.56184 39.86152 23.45052 20.82891 33.52919 9.68578 Jarque-Bera 890.3577 12741.05 4230.007 3307.757 8866.778 595.1844 Probability 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 Observations 208 208 208 208 208 208 Table 4.3 presents summary statistics for the input and output variables used in the study for the pooled meta-data set. A number of pertinent observations are clear from this table. First, it may be observed from the table that gross premium recorded the highest values in the mean, median, maximum and minimum values as well as the standard deviation over the study period. An important revelation from the table is about the result of Jarque-Bera text statistic which was used to test for normality in the data set and the results as well as the corresponding probability values confirms that clearly the data is not normally distributed. This agrees equally with the non-parametric nature of the MEA technique. 45 University of Ghana http://ugspace.ug.edu.gh Table 4.4a: Descriptive Statistics of Inputs and Outputs by Type of Company (units; thousands of Ghana Cedis) Gprem Labour equity Life Nonlife Life Nonlife Life Nonlife Mean 12132042.00 13858555.00 3670082.00 5418325.00 5506510.00 7594695.00 Median 4715195.00 7596910.00 2033984.00 3105505.00 1863115.00 3085173.00 Maximum 100000000.00 110000000.00 19812855.00 73956252.00 39718819.00 86436017.00 Minimum 70636.00 341661.00 6958.00 71828.90 4506.90 8948.00 Std. Dev. 18756866.00 17364711.00 4491405.00 9286636.00 8476434.00 14189834.00 Skewness 2.76 2.69 2.04 4.83 2.14 4.09 Kurtosis 11.29 11.90 6.72 30.66 6.81 20.27 Jarque-Bera 359.78 546.01 110.41 4328.10 119.26 1841.31 Probability 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 Observations 87 121 87 121 87 121 Table 4.4b Descriptive Statistics of Inputs and Outputs by Type of Insurance Company Fixass invinc clmincu Life Nonlife Life Nonlife Life Nonlife Mean 6070393.00 5700269.00 1827783.00 680917.00 3522513.00 2973365.00 Median 957967.00 1504241.00 731461.00 380571.60 1721148.00 1478595.00 Maximum 53354977.00 94553061.00 17970770.00 4960500.00 23937973.00 25993785.00 Minimum 14770.00 79248.00 3097.00 12635.96 901.38 821.45 Std. Dev. 11160514.00 14166420.00 2860544.00 794724.50 4936981.00 4087229.00 Skewness 2.60 4.40 3.33 2.70 2.08 2.80 Kurtosis 9.70 22.77 16.73 13.62 7.05 12.78 Jarque-Bera 260.54 2360.17 844.74 715.27 121.98 640.67 Probability 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 Observations 87 121 87 121 87 121 In Tables 4.4a and 4.4b, we present the summary statistics for the combine life data set as well as the combine non-life data set for the whole six years study period. Using the same 46 University of Ghana http://ugspace.ug.edu.gh set of inputs and outputs variables used to evaluate the performance efficiency, it may be observed that in general, non-life insurance firms recorded higher values in most of the computed statistics than that of life insurance firms. The only portion that is not consistent with this trend is about the skewness and kurtosis. A correlation matrix of all inputs and outputs is calculated for verifying the relationship between the inputs and outputs variables. Table 4.5 shows the results of this correlation matrix for the pooled meta-data set. Generally, there are high positive correlations coefficients between these variables. Correlation Matrix Table 4.5: Correlation Matrix and p-values for pooled meta-data set gprem labour equity fixass invinc clmincu gprem 1.0000 ----- labour 0.6345 1.0000 0.0000 ----- equity 0.7810 0.6236 1.0000 0.0000 0.0000 ----- fixass 0.7300 0.5977 0.7901 1.0000 0.0000 0.0000 0.0000 ----- invinc 0.6935 0.3648 0.4116 0.3850 1.0000 0.0000 0.0000 0.0000 0.0000 ----- clmincu 0.8796 0.5717 0.7441 0.7415 0.6818 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 ----- The highest correlation of (0.8796) was recorded between gross premium (gprem) and claim incurred (clmincu), while the lowest correlation of (0.3648) occurs between investment income (invinc) and labour during the study period. As expected all the p-values were 47 University of Ghana http://ugspace.ug.edu.gh statistically significant, which confirms that there is quite high correlation existing among every variable, since the outputs variables depends to a large extent on the inputs variables. Similar such tables for the various combined types of insurance companies (life and non- life) will be found in Appendix 1 of this report. 4.4 Starplots Star plots are a useful way to display multivariate observations with an arbitrary number of variables. If the number of variables, K , is not too large, each of a set of n K -dimensional observations can be displayed graphically as a star plot. The star plot is based on K coordinate axes with the same origin, spaced 360º/ K apart on the plane (Wilks, 2006). Each observation is represented as a star-shaped figure with one ray for each variable. For a given observation, the length of each ray is made proportional to the size of that variable. In the star plot we tend to see the configural properties of the collection of variables represented for each observation, and that this perception is affected by the ordering of variables around the perimeter and by the arrangement of stars on the page. (Friendly, 1991). Appendices 2-13 show a star plot of the inputs and output variables used in the analysis. These six variables are arranged around the perimeter as shown in the variable assignment key included in each plot. A study of each starplot shows that large values of a variable should reflect a "better" performance of that course and appear as long rays. The near – symmetry of the stars suggests strong correlations for the pairs of like variables. 48 University of Ghana http://ugspace.ug.edu.gh 4.5 Efficiency Analysis In this study, we estimated an input-oriented, technical efficient (TE) DEA and MEA index, assuming that the Ghanaian insurance companies aims to minimized inputs, while producing at a given output level. In this context, outputs are endogenous and inputs are exogenous, because of the competitive environment in which the units compete. The variable-return-to-scale (vrs) technology was used throughout the analysis. This was because variable-return-to-scale (vrs) score measure pure technical efficiency only. The summary of relative efficiency of Ghanaian insurance companies is presented in subsequent tables later in this chapter. Detailed efficiency scores for each insurance company under any insurance type can be found in the appendix 3, 4 and 5 sections of this report. It must be mentioned here that unlike the DEA efficiency score, under the MEA method, efficiency score lies between 0 and 1 with companies which are efficient getting an index value (MEA-score) 0, whereas inefficient companies get scores larger than 0 and increasing with inefficiency; see Bogetoft and Hougaard (1999) for further theoretical details. 4.6 Efficiency levels and patterns of Ghanaian Insurance Firms We first consider the pooled data meta-analysis in which all observations from all years are pooled into one data set for efficiency evaluation. Comparing the average MEA and average DEA efficiency scores in figure 4.1 for the life and non-life respectively for each year reveals the picture illustrated in the figure below. 49 University of Ghana http://ugspace.ug.edu.gh Fig. 4.1: Average aggregated annual MEA and DEA efficiency scores for the two subgroups across the whole study period. In Fig.4.1, we observe that there are clear differences between the patterns of efficiencies in both DEA and MEA scores for the years 2009, 2010 and 2012 with life firms been consistently more efficient than that for non-life firms, although the graph shows constant pattern in MEA efficiency scores for non-life firms from 2010 to 2011. According to the average MEA efficiency scores, in general, life companies have higher aggregated MEA and DEA efficiency score than non-life companies. 50 University of Ghana http://ugspace.ug.edu.gh 4.7 The Mann-Whitney U Test In order to answer my objectives two and three, the Mann-Whitney U test was used. The Mann-Whitney test is the non-parametric equivalent of the independent t-test and so is used for testing differences between groups when there are two conditions and different participants have been used in each condition (Field et al., 2003). Table 4.6: Test of significance differences in the average efficiency scores Mann- Wilcoxon Year Model Z Sig. Whitney U W DEA 91.500 227.500 -.554 .580 2007 MEA 100.500 191.500 -.155 .877 DEA 92.000 282.000 -1.759 .079 2008 MEA 103.000 223.000 -1.376 .169 DEA 67.500 298.500 -3.289 .001 2009 MEA 87.000 240.000 -2.704 .007 DEA 84.000 360.000 -2.863 .004 2010 MEA 105.000 241.000 -2.262 .024 DEA 107.000 338.000 -1.047 .295 2011 MEA 98.000 189.000 -1.366 .172 DEA 76.000 307.000 -2.181 .029 2012 MEA 77.000 168.000 -2.145 .032 Groups: Life and Nonlife Insurance Companies Table 4.6 provides the results of Mann-Whitney’s U statistic, the value of Wilcoxon’s statistic and the associated z approximation. The important part of the table is the significance value of the test, which gives the two-tailed probability. Based on these results, we conclude that there is no significance difference in both DEA and MEA efficiency scores between the life firms and non-life firms in the years 2007, 2008, and 2011. But there were 51 University of Ghana http://ugspace.ug.edu.gh significance differences in these efficiency scores for the years 2009, 2010 and 2012 as indicated by the corresponding p-values at 5% in the last column of the table. The above evaluation and comparison might be somewhat inappropriate because all the 208 observations for the six years were pooled and measured against a single frontier. However, the efficiency frontier for different years may shift during the whole study period; thus, the benchmarks on the pooled frontier might be inappropriate and unattainable for all the observations. In order to solve this potential problem, we performed the MEA and the DEA method both in the pooled data set and also in the various subsamples of the data set separately. Appendix 14 provides further details of the average MEA and DEA efficiency patterns for both life and non-life insurance firms. Summary of the relative average MEA and DEA efficiency scores for the pooled life and pooled non-life firms’ analysis are shown in Table 4.7a below. Out of the 208 observations, thirty-three (33) were efficient obtaining an MEA efficiency score of zero (0). This represents approximately sixteen percent (16%) of the pooled meta-data used in the study, with the remaining observations being classified as inefficient. Majority of these inefficient pooled meta-data set obtained an MEA efficiency scores ranging between 0.8 and 0.9, this represent approximately thirty- two percent (31.75%) of the combined data set used in the study. Table 4.7a: Summary of Relative MEA & DEA Efficiency Scores for pooled meta- data MEA DEA Efficiency Frequency Percentage Efficiency Frequency Percentage Range Range D  0 33 15.87 0   0.1 5 2.40 0  D  0.1 1 0.47 0.1  0.2 28 13.50 0.1 D  0.2 0 0.00 0.2   0.3 30 14.40 52 University of Ghana http://ugspace.ug.edu.gh 0.2  D  0.3 0 0.00 0.3  0.4 21 10.10 0.3 D  0.4 4 1.92 0.4   0.5 24 11.50 0.4  D  0.5 8 3.85 0.5  0.6 22 10.60 0.5  D  0.6 15 7.21 0.6   0.7 8 3.80 0.6  D  0.7 24 11.54 0.7   0.8 12 5.80 0.7  D  0.8 33 15.87 0.8  0.9 16 7.70 0.8  D  0.9 66 31.73 0.9  1 7 3.40 0.9  D 1 24 11.54  1 35 16.80 Total 208 100.00 208 100.00 From Table 4.7a, the corresponding DEA relative efficiency scores showed that thirty-five (35) of the observations were classified efficient with an efficiency score of one (1), representing approximately seventeen percent (16.80%). Further details of the relative MEA and DEA efficiency scores for each of the 208 observations in the pooled meta- data can be obtained from Appendix 15. Table 4.7b: List of Insurance Firms which were MEA efficient for the pooled meta- data Code Name of Insurance Company Number of times efficient A1 Enterprise Life Assurance 1 A2 Ghana Life Insurance 2 A3 Glico Life Insurance 2 A4 IGI Life Insurance 2 A5 MetLife Insurance 3 A7 Provident Life Assurance 1 A8 Quality Life Assurance 1 A9 SIC Life Insurance 2 A11 Unique Life Assurance 1 A12 Vanguard Life Assurance 2 A15 Ghana Union Assurance 1 A16 Express Life Assurance 1 A17 Capital Express Assurance 3 B1 Activa International 3 53 University of Ghana http://ugspace.ug.edu.gh B3 Enterprise Insurance 3 B6 NSIA Insurance Ghana 1 B8 Prime Insurance 1 B11 SIC Insurance 1 B14 Vanguard Assurance 1 B18 Colina Insurance 1 TOTAL 33 Table 4.7b provides details of the specific insurance firms that recorded MEA efficiency score of (0), this amounted to twenty companies with Met Life, Capital Express, Activa International and Enterprise Insurance each being classified efficient three (3) times over the study period. Using the pooled meta-data for life and non-life insurance firms, figure 4.2 below was obtained. The figure shows the average aggregated MEA efficiency scores for the pooled data set for each type of insurance category. Looking at the two figures, clearly there exist differences between the life and non-life firms in efficiency patterns in individual years, however, the difference is not significant between 2007, 2008 and 2011, but was significant in 2009, 2010, and 2012. For the period that there were significant differences, MEA efficiency scores recorded better performance for life insurance firms than the corresponding DEA efficiency scores for life firms. From figure 4.2 we observed that life firms on average are more MEA and DEA efficient than the non-life firms between the periods 2008-2009 and 2011-2012, showing an efficiency improvement as observed by the sharp drop in the MEA graph for life insurance firms during this period. These observations formally confirms the results of the Mann- Whitney U tests that there were significance differences in efficiency patterns between life and non-life insurance companies during the period 2009, 2010 and 2012. 54 University of Ghana http://ugspace.ug.edu.gh Fig. 4.2: Average annual MEA and DEA efficiency scores for life companies and Non-life companies for the whole study period (2007-2012). 55 University of Ghana http://ugspace.ug.edu.gh Table 4.8a provides summary of the MEA and DEA efficiency scores for the combine life insurance firms across the whole study period. From the table, it may be observed that out of the 87 observations, only twenty-six (26) were rated as MEA efficient with a score of zero (0), representing approximately thirty percent (29.90%) of the data points used in the study. The remaining observations were classified inefficient, with the highest among this group being recorded between the ranges (0.7 to 0.8). Table 4.8a: Summary of MEA & DEA Technical Efficiency Scores for Life Insurance Companies across the whole study period (2007-2012) MEA DEA Efficiency Frequency Percentage Efficiency Frequency Percentage Range Range D  0 26 29.90 0   0.1 2 2.30 0  D  0.1 1 1.10 0.1  0.2 1 1.10 0.1 D  0.2 0 0.00 0.2   0.3 3 3.40 0.2  D  0.3 0 0.00 0.3  0.4 3 3.40 0.3 D  0.4 5 5.70 0.4   0.5 12 13.80 0.4  D  0.5 4 4.60 0.5  0.6 6 6.90 0.5  D  0.6 12 13.80 0.6   0.7 8 9.20 0.6  D  0.7 11 12.60 0.7   0.8 7 8.00 0.7  D  0.8 15 17.20 0.8  0.9 11 12.60 0.8  D  0.9 10 11.50 0.9  1 7 8.00 0.9  D 1 3 3.40  1 27 31.00 Total 87 100.00 87 100.00 56 University of Ghana http://ugspace.ug.edu.gh From Table 4.8a, we see that twenty-seven (27) of the data points were classified DEA efficient with an efficiency score of one (1), this represent thirty-one percent (31%) of the combined data points for the life insurance companies used in the study period. The remaining data points are reported to be inefficient, with majority of these inefficient data points occurring between 0.4 and 0.5. Further details of the relative MEA and DEA efficiency scores for each of the 87 observations for the combined life companies can be obtained from Appendix 16of this report. Table 4.8b: List of Life Insurance Firms which were MEA efficient over the study period Code Name of Insurance Company Number of times efficient A1 Enterprise Life Assurance 2 A2 Ghana Life Insurance 2 A3 Glico Life Insurance 2 A4 IGI Life Insurance 3 A5 MetLife Insurance 3 A6 Phoenix Life Insurance 1 A7 Provident Life Assurance 2 A8 Quality Life Assurance 2 A9 SIC Life Insurance 2 A11 Unique Life Assurance 1 A12 Vanguard Life Assurance 2 A15 Ghana Union Assurance 1 A16 Express Life Assurance 1 A17 Capital Express Assurance 2 TOTAL 26 57 University of Ghana http://ugspace.ug.edu.gh Table 4.8b indicates the life insurance firms which recorded the twenty-six (26) efficient data points from the MEA efficient score. It may be noticed that out of the number of life insurance companies used in the study, only three firms did not record an efficiency score of 0 over the study period. These firms include Star Assurance, Donewell Insurance and Golden Life Assurance. Considering the fact Star Assurance and Donewell Insurance Company are assumed to be leaders in the industry, this result is very important. In all, fourteen (14) life insurance firms were classified MEA efficient, with IGI Life Insurance and Met Life Insurance each being classified efficient three (3) times over the study period. Table 4.9a: Summary of MEA and DEA Technical Efficiency Scores for Non-Life Insurance Companies across the whole study period (2007-2012) MEA DEA Eff- Range Frequency Percentage Efficiency Range Frequency Percentage D  0 21 17.36 0   0.1 0 0.00 0  D  0.2 0 0.00 0.1  0.2 2 1.70 0.2  D  0.4 1 0.83 0.2   0.3 27 22.30 0.4  D  0.6 6 4.96 0.3  0.4 22 18.20 0.6  D  0.8 47 38.84 0.4   0.5 18 14.90 0.8 D 1 46 38.02 0.5  0.6 11 9.10 0.6   0.7 6 5.00 0.7   0.8 5 4.10 0.8  0.9 5 4.10 0.9  1 4 3.30  1 21 17.40 Total 121 100.00 121 100.00 A number of comments can be made from Tables 4.9a. First it may be seen from the table that twenty-one (21) observations were both MEA and DEA efficient obtaining an efficient 58 University of Ghana http://ugspace.ug.edu.gh score of zero (0) and one (1) respectively. This results represent a little of over seventeen percent in both cases (17.36% and 17.40%). Secondly, the highest inefficient MEA score lies between efficiency ranges of 0.6 to 0.8, which is about thirty-eight percent (38.48%) of the 121 observations used for non-life companies over the study, while the highest inefficient DEA score was recorded between 0.2 and 0.3, representing about twenty-two percent (22.30%) of the combined non-life data points used for the entire study period. Further details on the MEA and DEA efficiency scores for each company can obtained from Appendix 17 of the report. Table 4.9b: List of Non-Life Insurance Firms which were MEA efficient over the study period Code Name of Insurance Company Number of times efficient B1 Activa International 4 B3 Enterprise Insurance 4 B5 Metropolitan Insurance 1 B6 NSIA Insurance Ghana 1 B8 Prime Insurance 1 B11 SIC Insurance 2 B13 Unique Insurance 1 B14 Vanguard Assurance 1 B16 Equity Insurance 1 B17 Industrial & General Insurance 2 B18 Colina Insurance 1 B20 NEM Insurance Ghana 1 B23 Regency Alliance Insurance 1 TOTAL 21 In all, fourteen non-life insurance firms recorded an MEA efficiency score of (0), out of the maximum number of twenty non-life firms over the study period. Table 4.9b provides details of the non-life firms which were classified MEA and DEA efficient, with Activa 59 University of Ghana http://ugspace.ug.edu.gh International and Enterprise Insurance each being classified efficient four (4) times over the study period. 4.8 Chapter Conclusion This chapter has introduced you to most of the analysis that was done for the study. We started by looking at the inputs and outputs used in the study. The remainder of the chapter was divided into statistical and efficiency discussion. The statistical analysis included descriptive statistics, independent sample t-test, starplots and correlation matrix. The chapter conclude by analyzing efficiency scores, levels and patterns for various insurance firms. As part of the efficiency analysis, the Mann-Whitney U test was conducted to check for significance difference in the average efficiency scores for life and non-life insurance. 60 University of Ghana http://ugspace.ug.edu.gh CHAPTER FIVE SUMMARY, CONCLUSION AND RECOMMENDATION 5.1 Chapter Introduction This chapter gives a brief summary of findings, contributions, limitations and possible extensions of this study as well as conclusions and recommendations. 5.2 Summary of findings This study investigates the performance of the insurance industry using multi-directional efficiency analysis (MEA) technique. For comparative purposes, it can be noted that in general Ghanaian insurance firms do not perform differently when their efficiencies scores are estimated via MEA than DEA, this provides an answer to the first objective of the study. The study also observed that on the average, there is no significance difference in the levels and patterns of efficiencies in the performance between life and non-life insurance companies using either the MEA or the DEA, this provide response to the second and third objectives of the study. Using the results of the pooled meta-data, the analysis shows that out of the number of life and non-life insurance firms used in the study over the period, only twenty firms were classified MEA efficient, with Met Life, Enterprise Insurance, Capital Express and Activa International each being classified efficient three (3) times. Results also show that for life and non-life insurance firms, fourteen companies recorded MEA efficient score of zero (0), with Activa International and Enterprise Insurance each having the highest efficiency appearance of four (4) times for non-life firms. However, IGI Life Insurance and Met Life Insurance each obtained an MEA efficient score of zero (0) three (3) times over the study period. 61 University of Ghana http://ugspace.ug.edu.gh The analysis revealed that three leading insurance firms namely, Star Assurance, Donewell Life Insurance and Golden Life Assurance companies did not record any MEA efficiency score over the study period. This is very surprising as apart from Golden Life Assurance Company, Star Assurance and Donewell Life Insurance Company are generally considered to be among the leading firms in the insurance industry. Although it can be observed from the starplots in appendix 2-13 that Star Assurance Company and Donewell Life Insurance Company have reasonably much of the inputs resources used for the analysis, none of these insurance firms was classified MEA or DEA efficient over the study period. This implies that the management of these firms is under utilizing these inputs resources thus resulting in the inefficient classification over the study period. During the study period, it was observed that the efficiency patterns increased steadily from 2007 to 2009 and dropped sharply from 2010 onwards. A general indication is that Ghanaian insurance firms perform poorly on almost all the inputs variables used in the study over the period, this observation provides answers to the concluding objectives of this study. 5.3 Contributions, Limitations and possible extensions of the study At this stage, it is appropriate to consider the contribution of my paper to the overall literature on insurance, as well as its limitations and possible extensions. The major contribution is its application of the Multi-directional Efficiency Analysis (MEA) technique to this industry. This paper has two sets of limitations: firstly, those relate to the data set, and secondly, those arise as a result of the MEA technique. With regards to the data set, the ratio values obtained from the National Insurance Commission (NIC) annual report for 2010 on Claim Ratio, Expense Ratio, Retention Ratio, Gross Premium to Equity Ratio as well as Investment Income as a Percentage of Premium 62 University of Ghana http://ugspace.ug.edu.gh which were used to estimate some of the variables used in the study when the annual financial reports could not be obtained directly were more of approximated values, hence, their use will introduce some marginal errors in these figures. In order for the study to be more generalized, we would need to have an accurate and a larger panel data set obtain directly from all the insurance companies operating in the country. We have also combined life and non-life insurance companies, which can be criticized since they clearly do not face the same restrictions. The limitations of the MEA model: as the technique is also termed potential improvement (PI) of the DEA technique, therefore it neither imposes any functional form on the data nor makes any distributional assumptions for the inefficiency term or a priori distinctions between the relative importance of any combination of inputs and outputs, MEA does not allow for random errors in the data. 5.4 Conclusion and Recommendation In this study, we have provided a state of the art presentation of one of the nonparametric methods in frontier efficiency analysis. The analysis was focused on recent development which allows the minimization of some of the critical resources which are used as inputs to help generate some outputs in the operations of the insurance industry. In addition, this study adds new contributions to the efficiency literature. It presents in a more unified way a potential improvement non-parametric measure of efficiency based on multi-directional efficiency analysis (MEA). We hope that the reading of this thesis will be useful for all readers who wanted to make use of this recently introduced technique to evaluate and explain the performance of DMU in their field of research without the burden of limitation of traditional methods. 63 University of Ghana http://ugspace.ug.edu.gh The insurance firms which were MEA efficient need to sustain these efficient levels by ensuring that they do not over use these inputs resources. At the individual firm level, the results can be used to compare performance with other firms in the industry. These results only give a rough indication as to what inefficient firms can do in order to become efficient. The full potential of MEA as a benchmarking tool should be exploited for the insurance industry using other inputs and outputs variables. More education about insurance services for individuals needs to be introduced in many parts of the country especially most market places, in order to provide the populace with immediate and comprehensive protection against certain types of risks. Since individual needs to cover the growing and emerging personal risks continue to increase in line with economic growth and social development, education and awareness of financial education with special attention to insurance issues must be intensified to assist in reducing and minimizing various risk exposures. For the insurance industry to grow, they should continue to increasingly use benchmarking techniques to assist in identifying areas of their operations that need continuous improvement as currently, this is the trend in the more advance or developed countries. 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(2009).Quantitative Models for Performance Evaluation and Benchmarking Data Envelopment Analysis with Spreadsheets (2nd Edition) New York, Springer Science Business Media LLC. 70 University of Ghana http://ugspace.ug.edu.gh APPENDICES APPENDIX 1 Correlation Matrix and p-values for Life Insurance Companies gprem labour equity fixass invinc clmincu gprem 1.0000 ----- labour 0.7300 1.0000 0.0000 ----- equity 0.7720 0.6342 1.0000 0.0000 0.0000 ----- fixass 0.5930 0.4142 0.5872 1.0000 0.0000 0.0001 0.0000 ----- invinc 0.8956 0.7400 0.7292 0.4769 1.0000 0.0000 0.0000 0.0000 0.0000 ----- clmincu 0.8616 0.6382 0.7812 0.7390 0.8263 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 ----- 71 University of Ghana http://ugspace.ug.edu.gh APPENDIX 1 CONTINUED Correlation Matrix and p-values for Non-life Insurance Companies gprem labour equity fixass invinc clmincu gprem 1.0000 ----- labour 0.6548 1.0000 0.0000 ----- equity 0.8284 0.6197 1.0000 0.0000 0.0000 ----- fixass 0.8299 0.6704 0.8718 1.0000 0.0000 0.0000 0.0000 ----- invinc 0.7082 0.5168 0.5127 0.5613 1.0000 0.0000 0.0000 0.0000 0.0000 ----- clmincu 0.9098 0.6342 0.8035 0.7717 0.6079 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 ----- 72 University of Ghana http://ugspace.ug.edu.gh APPENDIX 2 Starplots showing the size of the inputs and outputs resources for life Companies in the 2007 used in the study. 73 University of Ghana http://ugspace.ug.edu.gh APPENDIX 3 Starplots showing the size of the inputs and outputs resources for life Companies in the 2008 used in the study. 74 University of Ghana http://ugspace.ug.edu.gh APPENDIX 4 Starplots showing the size of the inputs and outputs resources for life Companies in the 2009 used in the study. 75 University of Ghana http://ugspace.ug.edu.gh APPENDIX 5 Starplots showing the size of the inputs and outputs resources for life Companies in the 2010 used in the study. 76 University of Ghana http://ugspace.ug.edu.gh APPENDIX 6 Starplots showing the size of the inputs and outputs resources for life Companies in the 2011 used in the study. 77 University of Ghana http://ugspace.ug.edu.gh APPENDIX 7 Starplots showing the size of the inputs and outputs resources for life Companies in the 2012 used in the study. 78 University of Ghana http://ugspace.ug.edu.gh APPENDIX 8 Starplots showing the size of the inputs and outputs resources for Non-life Companies in the 2007 used in the study. 79 University of Ghana http://ugspace.ug.edu.gh APPENDIX 9 Starplots showing the size of the inputs and outputs resources for Non- life Companies in the 2008 used in the study. 80 University of Ghana http://ugspace.ug.edu.gh APPENDIX 10 Starplots showing the size of the inputs and outputs resources for Non-life Companies in the 2009 used in the study. 81 University of Ghana http://ugspace.ug.edu.gh APPENDIX 11 Starplots showing the size of the inputs and outputs resources forNo n- life Companies in the 2010 used in the study. 82 University of Ghana http://ugspace.ug.edu.gh APPENDIX 12 Starplots showing the size of the inputs and outputs resources for Non-life Companies in the 2011 used in the study. 83 University of Ghana http://ugspace.ug.edu.gh APPENDIX 13 Starplots showing the size of the inputs and outputs resources for Non-life Companies in the 2012 used in the study. 84 University of Ghana http://ugspace.ug.edu.gh APPENDIX 14 Average MEA and DEA efficiency graphs for Life and Non-life firms across the whole observation period (2007-2012) 85 University of Ghana http://ugspace.ug.edu.gh APPENDIX 15 Table 4.22: Relative MEA & DEA Efficiency Scores for Pooled meta-data code eff.eall. eff.mall. Code eff.eall eff.mall. Code eff.eall. eff.mall. A1 0.2748 0.8422 A5 1.0000 0.0000 A17 0.2170 0.8906 A2 1.0000 0.0000 A6 0.4099 0.7680 A17 1.0000 0.0000 A3 0.3929 0.7710 A7 1.0000 0.0000 A16 0.0820 0.9607 A14 0.9259 0.3820 A8 1.0000 0.3679 A15 0.4971 0.6395 A4 1.0000 0.0000 A9 1.0000 0.0000 A3 1.0000 0.0000 A5 0.8093 0.6910 A10 0.8270 0.5583 A5 1.0000 0.0000 A6 0.1803 0.9109 A11 0.8231 0.7484 A6 0.8072 0.6043 A7 0.4246 0.8136 A12 0.6943 0.5047 A7 0.9035 0.4668 A8 0.6862 0.5577 A13 0.5598 0.7809 A8 1.0000 0.0000 A9 0.8250 0.5137 A1 1.0000 0.0000 A9 1.0000 0.0000 A10 0.4840 0.8251 A16 0.2069 0.9313 A10 0.7421 0.4867 A11 1.0000 0.0000 A2 0.7261 0.7162 A11 0.8019 0.8402 A12 0.5675 0.6450 A15 1.0000 0.0000 A12 1.0000 0.0000 A13 0.4847 0.6592 A3 0.7847 0.6672 B1 1.0000 0.0000 A13 0.9412 0.3490 A14 0.4234 0.8171 B2 0.1604 0.8773 A2 0.7798 0.6297 A4 0.9491 0.4985 B3 1.0000 0.0000 A15 0.5735 0.7536 A5 1.0000 0.0000 B15 0.8098 0.5893 A3 0.4797 0.7438 A6 0.4030 0.8188 B4 0.2713 0.8188 A14 0.6415 0.6918 A7 0.5237 0.7776 B17 0.8533 0.5000 A4 1.0000 0.0000 A8 0.8633 0.5137 B5 0.3488 0.8529 A5 1.0000 0.0000 A9 0.4675 0.6157 B6 0.2921 0.8335 A6 0.3326 0.8077 A10 0.3739 0.8720 B7 0.1212 0.9241 A7 0.8857 0.4780 A11 0.4774 0.7556 B8 1.0000 0.0000 A8 0.5870 0.6701 A12 1.0000 0.0000 B9 0.2860 0.8770 A9 0.9325 0.5299 A17 1.0000 0.0000 B10 0.3069 0.7845 A10 0.5162 0.7208 A1 0.4779 0.7782 B11 0.2576 0.8614 A11 0.7371 0.7045 A16 0.0976 0.9352 B12 0.2944 0.8216 A12 0.7883 0.5083 A15 0.3763 0.7051 B13 0.2053 0.8766 A17 1.0000 0.0000 A3 1.0000 0.0000 B14 1.0000 0.0000 A13 0.5399 0.6682 A5 0.8898 0.7646 B1 0.8679 0.6634 A1 0.9596 0.5653 A6 0.6244 0.7379 B2 0.1464 0.9038 A16 1.0000 0.0000 A7 0.4211 0.8083 B3 0.3374 0.7575 A2 1.0000 0.0000 A8 0.8121 0.4616 B16 0.4688 0.7195 A15 0.7863 0.5717 A9 0.5622 0.5977 B15 0.5905 0.6470 A3 0.7382 0.5252 A10 0.5864 0.6189 B4 0.2243 0.8329 A14 0.4032 0.8612 A11 0.4345 0.6784 B17 0.4526 0.6312 A4 0.9092 0.5000 A12 0.7856 0.5097 B21 0.1117 0.9544 86 University of Ghana http://ugspace.ug.edu.gh APPENDIX 15 CONTINUED code eff.eall. eff.mall. Code eff.eall eff.mall. Code eff.eall. eff.mall. B5 0.5395 0.7202 B21 0.2227 0.8717 B16 0.8142 0.5699 B6 0.2104 0.8753 B22 0.1306 0.9121 B15 0.5190 0.6914 B7 0.1967 0.8555 B5 0.4604 0.7820 B4 0.4179 0.8001 B8 0.0942 0.9382 B20 0.1334 0.9375 B21 0.1859 0.8718 B9 0.2847 0.9223 B17 0.4673 0.6925 B5 0.6637 0.6862 B10 0.3338 0.7822 B21 0.2227 0.8717 B20 0.2381 0.8661 B23 0.2232 0.8622 B22 0.1306 0.9121 B6 0.3605 0.8457 B11 0.5827 0.8490 B5 0.4604 0.7820 B7 0.2951 0.8830 B12 0.2636 0.8399 B20 0.1334 0.9375 B8 0.5767 0.8039 B13 0.1914 0.8929 B6 0.3433 0.8777 B9 0.3926 0.8347 B14 0.1860 0.8698 B7 0.2277 0.8600 B10 0.0785 0.9267 B1 0.1311 0.8956 B8 0.3618 0.8992 B23 0.5970 0.7035 B2 0.5890 0.7628 B9 0.2522 0.8977 B11 1.0000 0.0000 B3 0.7069 0.5000 B10 0.1268 0.9217 B12 0.2711 0.8356 B16 0.1175 0.9253 B23 0.1581 0.9209 B13 0.5589 0.7003 B15 0.6728 0.5971 B11 0.3090 0.8468 B14 0.3397 0.8365 B4 0.4138 0.7294 B12 0.2226 0.8600 B21 0.2227 0.8717 B17 0.4234 0.8554 B13 0.1927 0.9056 B22 0.1306 0.9121 B21 0.1531 0.9285 B14 0.2392 0.8516 B5 0.4604 0.7820 B22 0.0632 0.9505 B1 1.0000 0.0000 B20 0.1334 0.9375 B5 0.7234 0.7345 B19 0.2060 0.8337 B19 0.1271 0.9045 B20 0.4759 0.6911 B18 0.5265 0.7666 B18 0.1991 0.8730 B6 0.3335 0.8248 B2 0.2593 0.8606 B2 0.7615 0.7083 B7 0.1827 0.8779 B3 0.8331 0.6861 B3 1.0000 0.0000 B8 0.1827 0.8980 B16 0.6649 0.6410 B4 0.3010 0.8441 B9 0.2737 0.8933 B15 0.5630 0.7685 B17 0.4673 0.6925 B10 0.3622 0.8052 B4 0.3850 0.7861 B14 0.3270 0.8523 B23 0.1643 0.9005 B21 0.3794 0.7756 B1 1.0000 0.0000 B11 0.3378 0.8309 B5 0.5054 0.7430 B12 0.2855 0.8464 B20 0.1711 0.9316 B13 0.1909 0.9040 B6 1.0000 0.0000 B14 0.1980 0.8560 B7 0.2546 0.8546 B1 0.1767 0.8626 B8 0.5209 0.7841 B19 0.2563 0.8101 B9 0.4021 0.8462 B18 1.0000 0.0000 B10 0.1324 0.9016 B2 0.2285 0.8745 B23 0.6350 0.6268 B3 1.0000 0.0000 B11 0.4057 0.8450 B16 0.1176 0.9286 B12 0.2297 0.8613 B15 0.5277 0.6893 B13 0.8758 0.3748 87 University of Ghana http://ugspace.ug.edu.gh APPENDIX 16 Table 4.4: Relative MEA & DEA Efficiency Scores for Combine Life Firms code eff.elife eff.mlife code eff.elife eff.mlife Code eff.elife eff.mlife A1 0.2819 0.8063 A2 1.0000 0.0000 A15 0.3763 0.7435 A2 1.0000 0.0000 A15 0.8047 0.5787 A3 1.0000 0.0000 A3 0.4500 0.7056 A3 0.7410 0.5287 A5 0.8898 0.7674 A14 0.9553 0.3442 A14 0.4139 0.8488 A6 0.6634 0.7230 A4 1.0000 0.0000 A4 0.9144 0.5024 A7 0.6159 0.5439 A5 0.8093 0.7130 A5 1.0000 0.0000 A8 0.8599 0.3903 A6 0.1813 0.8995 A6 0.4099 0.8051 A9 0.5622 0.6166 A7 0.4539 0.7763 A7 1.0000 0.0000 A10 0.5903 0.6217 A8 0.7923 0.5263 A8 1.0000 0.0000 A11 0.4571 0.7188 A9 0.9407 0.4532 A9 1.0000 0.0725 A12 0.8476 0.4389 A10 0.4850 0.7493 A10 0.8309 0.5855 A17 0.2187 0.8939 A11 1.0000 0.0000 A11 0.8351 0.7910 A1 1.0000 0.0000 A12 0.6106 0.6265 A12 0.7275 0.5316 A16 0.0822 0.9591 A13 0.4963 0.6321 A13 0.6043 0.7427 A15 0.5027 0.6901 A13 0.9412 0.3490 A1 1.0000 0.0000 A3 1.0000 0.0000 A2 0.7883 0.5332 A16 0.2069 0.9313 A5 1.0000 0.0000 A15 0.5735 0.7532 A2 0.7529 0.6800 A6 1.0000 0.0000 A3 0.4877 0.7015 A15 1.0000 0.0000 A7 1.0000 0.0000 A14 0.6800 0.5868 A3 0.8584 0.6411 A8 1.0000 0.0000 A4 1.0000 0.0000 A14 0.4506 0.8027 A9 1.0000 0.0000 A5 1.0000 0.0000 A4 1.0000 0.0000 A10 0.7421 0.5002 A6 0.3326 0.8287 A5 1.0000 0.0000 A11 0.8318 0.8530 A7 0.9241 0.3470 A6 0.4207 0.7514 A12 1.0000 0.0000 A8 0.6017 0.6757 A7 0.6036 0.5545 A9 0.9740 0.4769 A8 0.8784 0.4717 A10 0.5237 0.6479 A9 0.4794 0.6197 A11 0.7371 0.7247 A10 0.3740 0.8413 A12 0.8586 0.3782 A11 0.4774 0.8033 A17 1.0000 0.0000 A12 1.0000 0.0000 A13 0.5441 0.6626 A17 1.0000 0.0000 A1 0.9604 0.5812 A1 0.6206 0.7975 A16 1.0000 0.0000 A16 0.0976 0.9352 88 University of Ghana http://ugspace.ug.edu.gh APPENDIX 17 Table 4.55: Relative MEA & DEA Efficiency Scores for Combine Non-life Firms Code eff.enonlife. eff.mnonlife. Code eff.enonlife. eff.mnonlife. Code eff.enonlife. eff.mnonlife. B1 1.0000 0.0000 B4 0.5432 0.6762 B18 0.8311 0.6265 B2 0.2054 0.8173 B17 0.8860 0.3637 B2 0.2828 0.8928 B3 1.0000 0.0000 B21 0.2453 0.8167 B3 0.8643 0.9303 B15 0.9166 0.5325 B22 0.2870 0.7602 B16 0.6911 0.6288 B4 0.4724 0.6797 B5 1.0000 0.0000 B15 0.6112 0.7309 B17 1.0000 0.0000 B20 1.0000 0.0000 B4 0.4490 0.9334 B5 0.5292 0.6864 B6 0.4028 0.7541 B21 0.4123 0.7108 B6 0.3995 0.7366 B7 0.2631 0.8128 B5 0.5462 0.6701 B7 0.3862 0.6983 B8 0.4813 0.6088 B20 0.3459 0.7155 B8 1.0000 0.0000 B9 0.2825 0.8945 B6 1.0000 0.0000 B9 0.2957 0.8922 B10 0.4371 0.7245 B7 0.2737 0.8616 B10 0.4733 0.6918 B23 0.4082 0.7732 B8 0.6543 0.5967 B11 0.4257 0.8420 B11 0.5793 0.8842 B9 0.4021 0.9150 B12 0.3091 0.8633 B12 0.3541 0.8785 B10 0.2193 0.8050 B13 0.3008 0.7311 B13 0.2830 0.7845 B23 0.8064 0.5228 B14 1.0000 0.0000 B14 0.2386 0.8266 B11 0.7806 1.0000 B1 1.0000 0.0000 B1 0.4013 0.8140 B12 0.2580 0.9025 B2 0.1677 0.8567 B19 0.4445 0.6917 B13 1.0000 0.0000 B3 0.3993 0.9389 B18 1.0000 0.0000 B14 0.3783 0.8659 B16 1.0000 0.0000 B2 0.2731 0.8711 B1 1.0000 0.0000 B15 0.7035 0.6129 B3 1.0000 0.0000 B19 0.2786 0.8317 B4 0.3989 0.7462 B16 0.2784 0.7846 B18 0.3541 0.7970 B17 1.0000 0.0000 B15 0.5431 0.7342 B2 0.8958 0.8976 B21 0.5234 0.8090 B4 0.3236 0.9092 B3 1.0000 0.0000 B5 0.7692 0.5000 B17 0.9303 0.4315 B16 0.9155 0.5966 B6 0.2440 0.8260 B21 0.2576 0.7958 B15 0.5635 0.7195 B7 0.3316 0.7144 B22 0.2826 0.7550 B4 0.5991 0.8410 B8 0.4420 0.6359 B5 0.6230 0.6107 B21 0.3044 0.7269 B9 0.3293 0.8379 B20 0.3527 0.7147 B5 0.9336 0.6180 B10 0.3717 0.7468 B6 0.4361 0.8056 B20 0.4116 0.7833 B23 1.0000 0.0000 B7 0.2612 0.8139 B6 0.4280 0.8318 B11 1.0000 0.0000 B8 0.5400 0.6818 B7 0.3655 0.8182 B12 0.2879 0.8880 B9 0.2553 0.8911 B8 0.7191 0.7384 B13 0.2799 0.7619 B10 0.2551 0.7741 B9 0.3926 0.8819 B14 0.2415 0.8233 B23 0.3416 0.7612 B10 0.1272 0.8966 B1 0.4188 0.7998 B11 0.5456 0.9114 B23 0.6441 0.7386 B2 0.7797 0.8228 B12 0.2652 0.9196 B11 1.0000 0.0000 B3 1.0000 0.0000 B13 0.2019 0.8610 B12 0.3533 0.8852 B16 0.3685 0.7245 B14 0.2693 0.8351 B13 0.5954 0.6224 B15 0.6966 0.6188 B1 1.0000 0.0000 B14 0.4511 0.8671 B19 0.3681 0.7583 89