ASSESSING THE MULTI-DIRECTIONAL EFFICIENCY ANALYSIS OF GHANAIAN INSURERS IN THE PRESENCE OF UNDESIRABLE OUTPUT BY DEBORA AFUA ANTWIWAA ADDO (10531128) A THESIS SUBMITED TO THE UNIVERSITY OF GHANA BUSINESS SCHOOL IN PARTIAL FULLFILMENT OF THE REQUIREMENT FOR THE AWARD OF MASTER OF PHILOSOPHY IN RISK MANAGEMENT AND INSURANCE DEGREE DEPARTMENT OF FINANCE JANUARY 2022 University of Ghana http://ugspace.ug.edu.gh DECLARATION I, Debora Afua Antwiwaa Addo, hereby declare that this work is my own, except for the work of others which have been duly cited. This study is the first of its kind submitted to the University of Ghana Business School. To the best of my knowledge, this study has not been presented to any other university for an academic award. ··· ·····~···························· ll°t-01-JOtJ ,2. .J: ............... . . ;-, DEBORA AFUA ANTWIW AA ADDO DATE (Candidate) University of Ghana http://ugspace.ug.edu.gh CERTIFICATION I hereby certify that this thesis was supervised in accordance with the procedures laid down by the University of Ghana. .t~½ £¥-temhJ~11 ... DR. KWAKU OHENE-ASARE DATE (SUPERVISOR) PROF.CHARLES ANDOH DATE (SUPERVISOR) ii University of Ghana http://ugspace.ug.edu.gh iii DEDICATION This work is dedicated to God for the wisdom, ideas and sound mind to undertake this study. I also dedicate this work to my nuclear family members and eldest cousin, Daniel Boayitey Addo, for the encouragement and support they gave me throughout this study period. I also dedicate it to my friends, Abigail Elorm Bedzra and Charles Zormelo for their unrelenting support. University of Ghana http://ugspace.ug.edu.gh iv TABLE OF CONTENT DECLARATION ........................................................................................................................ i CERTIFICATION ..................................................................................................................... ii DEDICATION ......................................................................................................................... iii TABLE OF CONTENT ............................................................................................................ iv ACKNOWLEDGEMENT ....................................................................................................... vii LIST OF TABLES ................................................................................................................. viii LIST OF FIGURES .................................................................................................................. ix LIST OF ACRONYMS AND ABBREVIATIONS .................................................................. x ABSTRACT ........................................................................................................................... xiii CHAPTER ONE ........................................................................................................................ 1 INTRODUCTION ..................................................................................................................... 1 1.1 Background study ............................................................................................................ 1 1.2 Problem statement ............................................................................................................ 3 1.3 Contributions of the study ................................................................................................ 5 1.4 Research objectives .......................................................................................................... 6 1.5 Research questions ........................................................................................................... 6 1.6 Research scope and limitations ........................................................................................ 7 1.7 Organisation of the study ................................................................................................. 7 1.8 Chapter summary ............................................................................................................. 7 CHAPTER TWO ....................................................................................................................... 9 LITERATURE REVIEW .......................................................................................................... 9 2.1 Introduction ...................................................................................................................... 9 2.2 Theoretical review ........................................................................................................... 9 2.2.1 Multi-criteria production theory ............................................................................... 9 2.2.2 Decision theory ....................................................................................................... 10 2.3 Empirical studies ............................................................................................................ 12 2.3.1 Insurance efficiency ................................................................................................ 12 2.3.2 Variable-specific efficiency .................................................................................... 14 2.3.3 Variable-specific efficiency and undesirable output ............................................... 16 2.3.4 Undesirable output in the insurance sector ............................................................. 19 2.4 Conceptual Framework .................................................................................................. 21 2.5 Frontier efficiency .......................................................................................................... 22 2.6 Overview of the Ghanaian insurance sector .................................................................. 24 University of Ghana http://ugspace.ug.edu.gh v 2.7 Industry challenges and reforms .................................................................................... 26 2.8 Chapter summary ........................................................................................................... 28 CHAPTER THREE ................................................................................................................. 29 METHODOLOGY .................................................................................................................. 29 3.1 Introduction .................................................................................................................... 29 3.2 Research design ............................................................................................................. 29 3.3 Data, sampling and sources............................................................................................ 30 3.4 Formulating the multi-directional efficiency analysis ................................................... 31 3.5 Nonparametric returns to scale assumption ................................................................... 36 3.6 Second stage regression analysis ................................................................................... 38 3.6.1 Econometric tests .................................................................................................... 41 3.6.2 Panel data econometric models ............................................................................... 44 3.7 Data and variables selection ........................................................................................... 46 3.7.1 Insurance provided services .................................................................................... 47 3.8 Modelling inputs and outputs ........................................................................................ 49 3.8.1 Outputs .................................................................................................................... 49 3.8.2 Inputs....................................................................................................................... 51 3.8.3 Second stage variables ............................................................................................ 53 3.9 Instruments for data analysis ......................................................................................... 61 3.10 Chapter summary ......................................................................................................... 61 CHAPTER FOUR .................................................................................................................... 63 DATA ANALYSIS AND DISCUSSION OF FINDINGS ...................................................... 63 4.1 Introduction .................................................................................................................... 63 4.2 Analysis of hypothetical data ......................................................................................... 63 4.3 Analysis of study data .................................................................................................... 77 4.3.1 Descriptive statistics of study data .......................................................................... 77 4.3.2 Findings for claims as undesirable output .............................................................. 81 4.3.3 Variable-specific efficiency scores ......................................................................... 87 4.3.4 Life and non-life efficiencies .................................................................................. 95 4.3.5 Insurance efficiency determinants ........................................................................ 106 4.4 Chapter summary ......................................................................................................... 113 CHAPTER FIVE ................................................................................................................... 116 SUMMARY, CONCLUSION AND RECOMMENDATIONS ............................................ 116 5.1 Introduction .................................................................................................................. 116 5.2 Summary of the study .................................................................................................. 116 University of Ghana http://ugspace.ug.edu.gh vi 5.3 Conclusion ................................................................................................................... 118 5.4 Recommendations ........................................................................................................ 119 5.6 Limitations of the study ............................................................................................... 120 5.7 Chapter summary ......................................................................................................... 120 References .............................................................................................................................. 121 APPENDICES ....................................................................................................................... 146 Appendix A ........................................................................................................................ 147 Appendix B ........................................................................................................................ 150 Appendix C ........................................................................................................................ 151 Appendix D ........................................................................................................................ 152 University of Ghana http://ugspace.ug.edu.gh vii ACKNOWLEDGEMENT My utmost appreciation goes to God for making this study a success. I am grateful to my supervisors, Dr. Kwaku Ohene-Asare and Prof. Charles Andoh for their zeal, dedication and commitment through this study. Finally, I appreciate the assistance, support and encouragement I received from Abigail Elorm Bedzra, Alfred Doudou, David Adeabah and my younger sister. The unrelenting support of my course mates, colleagues, family members and friends are duly acknowledged and appreciated. University of Ghana http://ugspace.ug.edu.gh viii LIST OF TABLES Table 3.1. Description of inputs and outputs………………………………………………...52 Table 3.2 Variable definition and expected signs……………………………………………58 Table 4.1: Illustrative data for hypothetical insurers. .............................................................. 64 Table 4.2: Manual computation of DEA input-oriented efficiency scores for all DMUs ....... 65 Table 4.3. MEA and DEA input-oriented efficiency scores of hypothetical insurers. ............ 74 Table 4.4. MEA non-oriented efficiency scores of hypothetical firms with undesirable output. .................................................................................................................................................. 76 Table 4.5: Descriptive statistics of input/output (pooled data and business type, 2008 - 2019) .................................................................................................................................................. 78 Table 4.6: Tests of returns to scale .......................................................................................... 80 Table 4.7: Correlation of input and output variables. .............................................................. 81 Table 4.8: Average claims efficiency scores (and rankings) for claims as a desirable and an undesirable output (2008 - 2019) ............................................................................................. 84 Table 4.9: Average efficiency of insurers for pooled data (2008 – 2019). .............................. 88 Table 4.10: Average variable-specific efficiencies across time (2008 – 2019). ...................... 92 Table 4.11: Average efficiency of life and non-life insurers (2008 – 2019). .......................... 96 Table 4.12:Variable-specific efficiencies of life and non-life insurers. ................................. 100 Table 4.13: Variable-specific efficiencies of life and non-life insurers ................................ 104 Table 4.14: Descriptive statistics of second stage analysis data. ........................................... 107 Table 4.15: Correlation matrix of regressors and MEA efficiency scores ............................ 108 Table 4.16:Total sample regression results ............................................................................ 110 University of Ghana http://ugspace.ug.edu.gh ix LIST OF FIGURES Figure 4.1: Graphical DEA solution for hypothetical data in input orientation. ..................... 65 Figure 4.2: Graphical MEA input-specific solution for hypothetical data. ............................. 67 Figure 4.3: Claim efficiency for insurers across the years ....................................................... 86 Figure 4.4: Average variable-specific and comprehensive efficiencies across insurers (2008 – 2019) ........................................................................................................................................ 91 Figure 4.5: Variable-specific efficiencies (2008 – 2019) ........................................................ 91 Figure 4.6: Average efficiencies scores over the years (2008 – 2019) .................................... 94 Figure 4.7: Average efficiencies of business groups across years (2008 – 2019) ................... 98 Figure 4.8: Distribution of average efficiency by business types (2008 -2019) ...................... 98 Figure 4.9: Variable-specific efficiency of life and non-life insurers .................................... 103 Figure 4.10: Variable-specific efficiencies of life and non-life insurers ............................... 105 University of Ghana http://ugspace.ug.edu.gh x LIST OF ACRONYMS AND ABBREVIATIONS Abbreviation Full name Activa I Activa international AIC Akaike’s Information Criterion BI Boone Indicator BIC Bayesian Information Criterion CD Cross-sectional Dependence CDH L CDH Life CO2 Carbon Dioxide CRS Constant returns to scale DEA Data Envelopment Analysis DMUs Decision making units Donewell IC Donewell Insurance Company Donewell L Donewell Life DVLA Driver and Vehicle Licensing Authority DWH Durbin-Wu-Hausman Enter L Enter Life Enterprise IC Enterprise Insurance Company Ltd Equity IC Equity Insurance Company FE Fixed effect GCC Gulf Cooperation Council GFC Global Financial Crisis Ghana L Ghana Life Ghana UA Ghana Union Assurance Company Limited GhanaUnion L GhanaUnion Life Glico GI Glico General Insurance Company Ltd Glico L Glico Life GMM Generalised method of moments HHI Herfindahl Hirschman Index IAIS International Association of Insurance Supervisors JSBs Joint Stock Banks L & H Life and Health University of Ghana http://ugspace.ug.edu.gh xi LM Lagrange Multiplier LPP Linear programming program LSCBBs Large state-owned commercial banks MCPT Multi-criteria production theory MEA Multi-directional Efficiency Analysis Met L Met Life Metropolitan IC Metropolitan Insurance Company Ltd MID Motor Insurance Database MPI Malmquist productivity index NIC National Insurance Commission NPL Non-performing loans NSIA GC NSIA Ghana Company Ltd OLS Ordinary Least Squares PCBs Private commercial banks Phoenix IC Phoenix Insurance Company Phoenix L Phoenix Life Prime I Prime Insurance Provident IC Provident Insurance Company Provident L Provident Life Quality IC Quality Insurance Company Ghana Ltd Quality L Quality Life RE Random effect ROA Return on asset ROE Return on equity Regency AI Regency Alliance Insurance Ghana Ltd RTS Return to scale SBM Slack-based measure SCC Spatial correlation consistent SCP Structure-conduct-performance SFA Stochastic frontier analysis SIC State Insurance Company SIC IC SIC Insurance Company Ltd SIC L SIC Life University of Ghana http://ugspace.ug.edu.gh xii SMCBs Small-medium commercial banks SOBs State Owned Banks Star AC Star Assurance Company Star L Star Life TFP Total Factor Productivity Unique IC Unique Insurance Company Ltd Vanguard AC Vanguard Assurance Company Vanguard L Vanguard Life VIFs Variance inflation factors VRS Variable return to scale University of Ghana http://ugspace.ug.edu.gh xiii ABSTRACT Insurance contributes to a country’s economic growth and development. However, despite the plethora of insurance efficiency studies in literature, there are very few insurance efficiency studies in Ghana. Besides, insurance penetration is yet to grow significantly in Ghana, even though various reforms have been enacted to increase insurance penetration and insurance efficiency in Ghana. This study seeks to evaluate the aggregated and disaggregated efficiencies of insurers in Ghana over a sample of 30 insurers from 2008 to 2019, using the non-oriented non-radial multi-directional efficiency analysis and to investigate the impact of competition, leverage, size, solvency, profitability, insurer type and underwriting risk on MEA insurance efficiencies using robust econometric models. The study data was obtained from the audited financial reports submitted to the NIC. The results confirmed the distortions in insurance efficiency assessment when undesirable outputs are excluded from insurance efficiency estimation. Among the insurer variables, investment income was identified as the worst performing output variable, reducing the overall performance of insurers. Claims was identified as the best performing variable followed by labour. Among the insurance groups, life insurers were observed to be performing significantly well on its aggregated and disaggregated efficiencies than the non-life insurers. Finally, the previous year’s overall performance of insurers and the level of competition were identified as the determinants of MEA insurance efficiency in Ghana. The inclusion of claims as an undesirable in insurance efficiency assessment enables insurance regulators identify the true efficiency levels of Ghanaian life and non-life insurers. Key words: claims, insurance, multi-directional efficiency analysis, second-stage analysis, undesirable output. University of Ghana http://ugspace.ug.edu.gh 1 CHAPTER ONE INTRODUCTION 1.1 Background study The insurance and banking sectors contribute positively towards economic growth and development (Han, Li, Moshirian & Tian., 2010; Ibrahim & Alagidede, 2017; Levine, Loayza & Beck, 2000; Pradhan Arvin, Nair, Bennett, & Hall., 2018; Ward & Zurbruegg, 2000). The insurance sector is seen as one of the key components of monetary development as it expands speculations, guarantees legitimate assignment of assets, advances cost decrease through liquidity creation and offers financial assistance to organizations (Chakrabarti & Shankar, 2015; Han et al., 2010; Lee, Chiu & Chang, 2013). Given their importance towards economic growth and development, regulators, policy makers, managers and academic researchers have been looking for ways to determine and improve the efficiency and the dynamic productivity of insurers (Biener, Eling & Wirfs, 2016; National Insurance Commission (NIC), 2018). This has spawned a multiplicity of insurance efficiency and dynamic productivity change studies over the years (Biener et al., 2016; Ho & Hsu, 2021; Kaffash, Azizi, Huang & Zhu, 2020; Lim, Lee & Har, 2020; Ohene-Asare, Asare & Turkson., 2019). Despite the different reforms enacted by the National Insurance Commission (NIC) Ghana; the separation of insurers into life and non-life, increase in minimum capital requirement (MCR), labour units and innovative products, insurance penetration is yet to grow significantly (NIC, 2010, 2019). Hence, the need to study the performance of Ghanaian insurers. However, such insurance efficiency and dynamic productivity studies in Ghana are limited (Ansah-Adu, Andoh & Abor, 2012; Danquah et al., 2018; Ohene-Asare et al., 2019; Oppong, Pattanayak & Irfan, 2019). University of Ghana http://ugspace.ug.edu.gh 2 One approach for the efficiency assessment of insurers is Data Envelopment Analysis (DEA). This is a nonparametric linear programming frontier optimization methodology for assessing the relative efficiency of homogenous decision making units (DMUs) that consume multiple distinct inputs to produce multiple outputs (Banker, Charnes & Cooper, 1984; Charnes, Cooper & Rhodes., 1978; Farrell, 1957; Cooper, Seiford & Zhu, 2004) (i.e. CCR and BCC). The method involves the construction of a production or cost or profit frontier from the observed data points using the best- practice organizational entities and measuring the (in) efficiency of a DMU by projecting the observation via the distance in relation to the frontier constructed by the dominating units (Cook & Zhu, 2005; Cooper, Seiford & Zhu, 2011; Cummins, Rubio-Misas & Zi, 2004; Fried, Lovell & Schmidt, 2008; Lozano & Soltani, 2020; Zhu, 2003). The technique then identifies those firms on the frontier as efficient and determines inefficient units, ranks the DMUs, pinpoints potential improvements (i.e. input contractions and output augmentations) and can be used for benchmarking purposes and to assess managerial and regulatory programs or policies etc. (Baležentis & De Witte, 2015; Golany & Yaakov, 1989; Lozano & Soltani, 2020). However, the use of the radial input decreases and output increases to determine a single CCR and BCC aggregated efficiency scores has been criticized as providing partial insights instead of a completely disaggregated (in) efficiency that captures the contribution of individual-specific inputs and outputs (Asmild, Kronborg & Matthews, 2016; Asmild & Matthews, 2012; Baležentis & De Witte, 2015; Kapelko & Lansink, 2017; Tziogkidis, Philippas, Leontitsis & Sickles, 2020). It is argued in this study that, a particular insurer can be doing better in claims than in another input say, labour or another output, say, net premium. Thus, there is the need to be able to select benchmarks such that the non-radial adjustments to the inputs and outputs correspond to the potential improvements identified by considering the individual improvement potential in the variables (Asmild & Matthews, 2012). This is important given the fact that this study first-hand University of Ghana http://ugspace.ug.edu.gh 3 mathematically models claims as an undesirable output. Even though claims were included in some studies as an input (Gaganis, Hasan & Pasiouras, 2013; Rai, 1996; Wu, Yang, Vela & Liang, 2007; Yang, 2006; Yao, Han & Feng, 2007), they are yet to be properly incorporated in the modelling of the behaviour of the insurance firm. This paper first-hand in literature, models claims as an undesirable output using the non-radial non-oriented multi-directional efficiency (MEA) of Bogetoft and Hougaard (1999) and Asmild et al., (2003). Therefore, the purpose of this study is to evaluate the input-specific and output-specific efficiencies of insurers in Ghana over a sample of 30 insurers from 2008 to 2019, and to pinpoint claims and labour contractions and net premiums and investment income potentials across life and non-life insurers. This will be achieved using the non-oriented, non-radial MEA model. Besides, the study will examine the performance difference(s) between life and non-life insurance groups with their variable-specific efficiencies. Finally, the paper will investigate such insurance-specific factors - competition, size, solvency, leverage, lines of business, profitability and underwriting risk- that may influence the comprehensive efficiency estimates using robust econometric regression methods. 1.2 Problem statement Despite the increasing number of studies on insurance efficiency (Biener et al., 2016; Biener & Eling, 2012; Cummins, Rubio-Misas & Vencappa, 2017; Eling & Luhnen, 2010; Kaffash et al., 2020; Wise, 2017), there are still some recognised gabs in recent studies. First and foremost, notwithstanding the key contributions the insurance sector makes to a country’s economy, none of the insurance efficiency studies has examined the disaggregated view of efficiency estimates via the contributions of individual inputs and/or outputs using the innovative MEA. Existing studies have rather assessed cost or technical or profit efficiency or dynamic productivity (Alhassan & University of Ghana http://ugspace.ug.edu.gh 4 Biekpe, 2016; Allen & Thanassoulis, 2004; Barros, Nektarios & Assaf, 2010; Diacon, Starkey & O'Brien, 2002; Eling & Luhnen, 2010; Ohene-Asare et al., 2019; Yao et al., 2007). Some of these studies further identified the exogenous determinants of insurance efficiency (Alhassan et al., 2015; Biener et al., 2016; Ohene-Asare et al., 2019; Owusu-Ansah, Dontwi, Seidu, Abudulai & Sebil., 2010). However, the identification of specific input and output variables that contribute to (in)efficiency is important to formulate and assess policy reforms. Second, the distortions in efficiency scores potentially caused by the exclusion of undesirable outputs in efficiency assessment (Assaf, Matousek & Tsionas, 2013; Atkinson & Dorfman, 2005; Fernández, Koop & Steel, 2002) has resulted in the development of different efficiency techniques for undesirable outputs (Arabi, Munisamy & Emrouznejad, 2015; Chen, Wang & Lai 2017; Dyckhoff & Allen, 2001; Sueyoshi & Goto, 2010; Maghbouli, Amirteimoori & Kordrostami, 2014) as the classical DEA model does not make room for the assessment of undesirable outputs (Färe & Grosskopf, 2004; Seiford & Zhu, 2002). There has been numerous undesirable output efficiency studies in the energy (Apergis et al., 2015; Bi et al., 2014; Mavi & Mavi, 2019; Wang et al., 2015) and the banking sector (Amirteimoori, Kordrostami & Sarparast, 2006; Asmild & Matthews, 2012; Assaf et al., 2013; Lozano, 2016; Seiford & Zhu, 2002). However, a cursory glance at the 132 DEA studies on insurance efficiency examined by Kaffash et al. (2020), the 27 studies by Eling and Luhnen (2010), and the 32 surveyed studies by Cummins and Weiss (2013) reveals that no insurance efficiency study has examined the potential impact of claims as an undesirable output. This could possibly be as a result of the inability of the classical DEA to compute efficiency scores in the presence of undesirable output(s). With the production of undesirable output(s) (Assaf et al., 2013; Sueyoshi & Goto, 2010) being part of insurance services, there is the need for insurance efficiency to be examined by mathematically modelling claims as an undesirable output. University of Ghana http://ugspace.ug.edu.gh 5 Finally, with MEA being a non-parametric efficiency measure, the existing DEA critics - non statistical and deterministic - as a non-parametric efficiency measure (Schmidt, 1986; Simar & Wilson, 2000, 2007) extends to the novel MEA (Asmild et al., 2019; Asmild & Matthews, 2012; Tziogkidis et al., 2020), non-radial non-parametric efficiency measure. Even though various researchers have suggested alternative approaches to these critics (Banker, 1996; Simar & Wilson, 1998, 2000), several robust econometric regression methods have been adopted in some DEA studies (Ansah-Adu et al., 2012; Barros & Wanke, 2014; Biener et al., 2016; Giantsios & Noulas, 2020; Ohene-Asare et al., 2019). However, to the best of the author’s knowledge, only few studies have examined the impact of exogenous covariates on the integrated efficiencies using robust econometric regression models. This calls for the impact of exogenous covariates to be examined on the MEA integrated efficiency of insurers. 1.3 Contributions of the study From the gaps identified in the problem statements, the study will make contributions to academic literature, policy formulation and insurance practice. First, the measure of insurance efficiency in the absence of claims as an undesirable output distorts efficiency scores hence its inclusion as an undesirable output will help insurance regulators identify true efficiency levels of Ghanaian life and non-life insurers. In addition, the variable- specific efficiency scores of the life and non-life insurers will enable regulators enact appropriate policies so as to how to increase individual insurance efficiency and country insurance efficiency. On practice contribution, the study will provide insurance managers with the variable-specific efficiencies of some life and non-life insurers in Ghana. Managers can easily identify specific (in) efficient outputs and inputs to aid variable-specific efficiency analysis. University of Ghana http://ugspace.ug.edu.gh 6 Finally, the academic contributions come in three folds. This study is the premier insurance efficiency study that mathematically models claims as an undesirable output using the non-radial non-oriented MEA model. Second, it makes an empirical contribution as it uses the non-radial MEA to assess insurance efficiency. Finally, the study identifies the impact of exogenous covariates on integrated insurance efficiencies. 1.4 Research objectives The main objective of the study is to assess the variable-specific efficiency scores of Ghanaian insurers over the period 2008 to 2019, modelling claims as an undesirable output. The specific objectives are to: i. Model claims as an undesirable output with the MEA model, and to compare the efficiency estimates between claims as a desirable and as an undesirable output. ii. Assess the input/output-specific efficiency scores of insurers in a disaggregated view. iii. Assess the comprehensive and variable-specific efficiency differences between life and non-life insurers. iv. Investigate those exogenous covariates that affect MEA insurance efficiencies. 1.5 Research questions The study seeks to answer the following questions: i. Are there differences between the aggregated and claims-specific efficiency scores of insurers when claims are either used as a desirable or an undesirable output? ii. What are the input and output-specific efficiency scores of Ghanaian insurers? University of Ghana http://ugspace.ug.edu.gh 7 iii. Do life insurers outperform non-life insurers in terms of comprehensive and variable- specific efficiencies? iv. Which insurance-specific factors affect MEA insurance efficiencies? 1.6 Research scope and limitations This study is focused on life and non-life insurers operating in Ghana. The analysis of this study is based on 13 life and 17 non-life insurers that had been in operation from 2008 to 2019. This study is limited to insurers whose audited financial reports had been presented to the NIC and had been in operation from 2008 to 2019. Hence, not all Ghanaian life and non-life insurers are used for the study. 1.7 Organisation of the study The study is divided into five chapters. The first chapter discussed the background of the study, the problem statement, the research objectives and questions, as well as the research scope and some limitations that were encountered during the study. The second chapter reviews and discusses existing articles (conceptually and empirically) in the scope of the study whereas the third chapter discusses into detail the method employed in the study. The fourth chapter is used to present the results of the data analyses. The fifth chapter summarises, concludes and makes recommendations for policy, practice and future academic research. 1.8 Chapter summary In general, this study seeks to evaluate the input/output-specific efficiencies of Ghanaian insurers over a sample of 30 insurers from 2008 to 2019, and to pinpoint variable potentials across life and University of Ghana http://ugspace.ug.edu.gh 8 non-life insurers in Ghana. The study seeks to help insurance regulators and academic researchers identify the true efficiency levels of Ghanaian insurers in the presence of undesirable outputs (claims). University of Ghana http://ugspace.ug.edu.gh 9 CHAPTER TWO LITERATURE REVIEW 2.1 Introduction This chapter reviews theoretical and empirical literature on insurance efficiency, undesirable outputs and presents an overview of the Ghanaian insurance sector. The overview of the Ghanaian insurance sector discusses the sector’s history, recent reforms and the present composition of the sector. The empirical review discusses recent literature on insurance efficiency, undesirable output in the insurance sector and variable-specific efficiency assessment whereas the theoretical review section discusses existing theories that support undesirable output in the production process and variable- specific efficiency analysis. 2.2 Theoretical review The main theories that support the study are the multi-criteria production theory (MCPT) for the production of undesirable outputs and decision theory for variable-specific efficiency assessment. 2.2.1 Multi-criteria production theory The MCPT is an extension of the conventional production theories of individual valued added functions. The individual valued added function is defined on relevant input and output variables such that the function transform the input and output variables into different values which are either created or destroyed in the production process (Dyckhoff, 2018). The expansion of the conventional production theories was based on the undeniable contrast between distinct objectives; the input and output variables of a production process objective and the implications of the University of Ghana http://ugspace.ug.edu.gh 10 variables for decision maker's (or an external evaluator's) objective. Whereas the conventional production theories consider these objective to be the same, the MCPT model clearly distinguishes the notion(s) of inputs and outputs. Following Frisch (1965) inputs were defined as things (good and services) which enter the production process, (and sometimes lose their initial identity), and outputs as things (goods and services) which emerge from a transformation process. Dyckhoff (2018) added that the transformation process of inputs into outputs extends to the production of undesirable outputs like waste or emissions. In the economics sense, production is explained as a process which transforms things with the motive of generating more benefits (positive value created and negative values destroyed) than costs (consume positives and generate negatives). As a results, Dyckhoff (2018) suggests the use of different scales (their own (distinct) natural scale) for the valuation of its variables. This concept of production underpins the addition and formulation of undesirable outputs in efficiency assessment. Employing the non-radial and non-oriented MEA, claims is mathematically modelled as undesirable outputs in the insurance production process. 2.2.2 Decision theory Decision theory is a theory that guides decisions making (Hansson, 2005). The theory studies the logic and mathematical properties of decision making when the decision maker/agent is uncertain (Fox, 2000). The theory is concerned with goal-oriented behaviour in the presence of options (Hansson, 2005). It is classified into two main classes; the normative decision theory and the descriptive decision theory. The classification of the theory distinguishes how decisions ought to be taken (normative decision theory) from however decisions are taken (descriptive decision theory) (Hansson, 2005). University of Ghana http://ugspace.ug.edu.gh 11 This theory can be traced back the eighteenth century (Mendoza & Gutleierrex-Pena, 2017). However, in the middle of the 20th century, the theory has developed rapidly through contributions from various academic disciplines (statistics, psychology, mathematics, economics, biology, data science) into an academic field of its own (Mendoza & Gutleierrex-Pena, 2017; Hansson, 1990). Overtime, the theory has received contributions from some newly fields such as jurisprudence, artificial intelligence, optimization, social decision theory and game theory (Hansson, 1991). The goal of all decision makers (firms, individuals, groups, etc) is to obtain desirable result(s) at the end of the decision-making process. In line with Mendoza and Gutleierrex-Pena (2017), the decision problem of decision makers is defined as an instance where the agent/decision maker is presented with a set of options, 𝐴 = { 𝑎1, 𝑎2, … , 𝑎𝑘} with their associated consequence, 𝐶 = { 𝑐1, 𝑐2, … , 𝑐𝑘} to choose from. Decision makers with prior information with the outcome/consequence of an action will be faced with a decision problem with certainty. However, agents are usually presented with decision problems without uncertainty which is mathematically modelled as: 1. 𝐴 = { 𝑎1, 𝑎2, … , 𝑎𝑘} 2. 𝐸 = { 𝐸11, 𝐸12, … , 𝐸1𝑚1; 𝐸22, 𝐸21, … , 𝐸2𝑚2 ; … ; 𝐸𝑘1;, 𝐸𝑘1, … , 𝐸2𝑚𝑘 } and 3. 𝐶 = { 𝑐11, 𝑐12, … , 𝑐1𝑚1; 𝑐22, 𝑐21, … , 𝑐2𝑚2 ; … ; 𝑐𝑘1;, 𝑐𝑘1, … , 𝑐2𝑚𝑘 } where A are exhaustive and exclusive set of actions; E denotes a set of uncertain events for every action 𝑎𝑖. The collection of events is assumed to be a partition of certain events. C is a set of consequences, where each corresponds to a pair (𝑎𝑖, 𝐸𝑖𝑗) (Mendoza & Gutleierrex-Pena, 2017). In line with Bogetoft and Hougaard (1999), the analogy of an ideal plan embedded in this theory is used as an underlying theory for the (variable-specific) efficiency assessment of Ghanaian insurers. University of Ghana http://ugspace.ug.edu.gh 12 2.3 Empirical studies This section reviews some existing efficiency studies in the insurance sector that captured claims as an input or output, including variable-specific efficiency studies in the banking, energy, transport and agricultural sectors. The review comprises the method employed in the study, the study period, sample size and the study's findings. 2.3.1 Insurance efficiency The insurance market has been incredibly profitable over the years; however, the market is being fraught with several challenges (Kaffash et al., 2020) including premium undercutting, motor insurance fraud and many others (NIC, 2017). This has raised significant interest over their efficiency measurement. This is because the efficiency of insurance firms has been demonstrated to have implications for business failure (Eling & Jia, 2018). The literature appears to be dominated by two efficiency measurement techniques, namely, data envelopment analysis (DEA) and stochastic frontier analysis (SFA) (Eling & Luhnen, 2010; Wise, 2017). It is noteworthy to mention that available literature seems univocal in asserting that there is very little difference in the efficiency scores computed with DEA and SFA (Eling & Luhnen, 2010). Using DEA and SFA methodologies, Eling and Luhnen (2010) examined the technical and cost efficiency of over 6400 international insurers from 32 countries. They observed that both technical and cost efficiency in the international insurance market experience a steady growth with Denmark and Japan operating the highly efficient insurance markets while the Philippines is the most inefficient insurance market. Interestingly, the authors find evidence that belies the expense preference hypothesis as larger insurers were observed to be more efficient than smaller ones. University of Ghana http://ugspace.ug.edu.gh 13 Al-Amri, Gattoufi, and Al‐Muharrami (2012) examined the technical efficiency of insurance firms in the GCC regional market. Using DEA methodology on 32 insurers over the period 2005 to 2007, they found that the GCC insurance market is moderately efficient. Similarly, the efficiency performance of the Indian health insurance industry has been found to be operating suboptimal in terms of technical efficiency with just 30% efficient health insurers (Siddiqui, 2021). Additionally, it was noted that stand-alone health insurers had superior level of technical efficiency compared to health insurance division under general insurers, supporting the strategic focus hypothesis against the conglomeration hypothesis. Cummins and Weiss (2013) developed the stochastic frontier analysis and the non-parametric frontier analysis to analyse firm performance. The study identified seventy-four (74) insurance efficiency studies over the period, 1983 to 2011. Over half of these studies published in top tier journals thus were reviewed intensively. It was observed that about 60% of the identified studies used DEA for its analysis. Furthermore, the value-added approach was identified to be commonly used approach for measuring outputs. The corporate reporting practices across countries greatly influenced the input choices in the identified studies. Recently, Kaffash et al. (2020) considered the increasing interest in the use of DEA for efficiency assessment and undertook a comprehensive insurance efficiency survey of published insurance efficiency studies that applied DEA from 1993 to July 2018. The survey built upon the comprehensive work of Cummins and Weiss (2013), combining DEA application to its methodologies. Of the 132 DEA applications studies sampled 42% were published between 2010 and 2016, which recorded the highest DEA applications in the insurance sector. The authors focused on the analysis of the input/output variables used, their selection period, orientation, type of insurer, geographical distribution and application of DEA models. The findings suggest that the University of Ghana http://ugspace.ug.edu.gh 14 impact of recent changes in insurance industries - InsurTechs, market transparency and micro- insurance - on efficiency has not been explored. In addition, unlike other financial industries whereby DEA with the presence of undesirable factors have been assessed, the findings point out that no study has yet used DEA under such conditions. Further findings suggest that newly developed DEA approaches like modified directional distance function, satisficing DEA and fuzzy DEA recorded few applications in insurance efficiency. Despite the extant literary on insurance efficiency in DEA, no study has yet assessed the variable- specific efficiency analysis for the insurance market and no insurance study has assessed efficiency with MEA in the presence of its undesirable factors. There is therefore the need for the assessment of the variable-specific efficiency scores of insurers, in addition with the assessment of insurer efficiency in the presence of undesirable output. 2.3.2 Variable-specific efficiency The MEA approach developed and operationalized by Bogetoft and Hougaard (1999) and Asmild et al. (2003) respectively, was further elaborated by Bogetoft and Hougaard (2004), Asmild and Pastor (2010), Asmild et al. (2016) and Baležentis and De Witte (2015), has been applied in different contexts, such as in the works of Holvad, Hougaard, Kronborg, and Kvist (2004), Asmild and Matthews (2012) and Wang, Wei, and Zhang (2013). Notably, it observed that when undesirable outputs are omitted, efficiency scores become distorted. Equally, in view of disaggregate ion of efficiency scores by MEA, several researchers use the novel MEA to assess firm-level variable-specific efficiency scores in the banking sector (Asmild et al., 2016; Asmild & Matthews, 2012; Tziogkidis et al., 2020), transportation sector (Bi, Wang, Yang, & Liang, 2014; Holvad et al., 2004), agricultural sector (Asmild et al., 2016; Manevska-Tasevska, Hansson, University of Ghana http://ugspace.ug.edu.gh 15 Asmild, & Surry, 2018, 2021), and energy and environmental sectors (Wang et al., 2013; Wang, Yu, Li, & Wei, 2015) in order to assess variable-specific efficiency scores of its inputs and/or outputs, in addition with undesirable outputs. Asmild et al. (2019) applied the novel MEA to measure the patterns and differences in inefficiency scores between Islamic and non-Islamic banks focusing on the period that marked the impact of global financial crisis in Bangladesh. The study sampled 30 private commercial banks (PCBs) which comprised 1st, 2nd and 3rd generation conventional banks, as well as Islamic banks over the period 2001-2015. Using labour costs and other costs as inputs and off-balance-sheet earnings and balance-sheet earnings as outputs, the authors assumed a constant return to scale (CRS) under the non-oriented MEA model. The following results were established. First, there is no observed significant differences in the inefficiency patterns between Islamic and non-Islamic banks for the period outside the depth of the Global Financial Crisis (GFC). Additionally, there was significantly higher efficiencies of both inputs including one of the outputs in the time window of the GFC period for the Islamic banks compared to the private conventional banks. Asmild et al. (2016) researching on managerial and program efficiency in family firms used the novel MEA approach to estimate efficiency. Thus, the authors focus on estimation of input-specific efficiencies, which provides further understanding into the underlying efficiency differences that may exist between farm types. The results show that there is a clear difference between the efficiency scores on the different inputs as well as between the farm types of crop, livestock and mixed farms, respectively. Crop farms have the highest program efficiency, but the lowest managerial efficiency, and that the mixed farms have the lowest program efficiency. A number of researchers have used MEA to investigate the variable-specific efficiency scores of banks in the Chinese banking sector (Asmild et al., 2019; Asmild & Matthews, 2012; Tziogkidis University of Ghana http://ugspace.ug.edu.gh 16 et al., 2020). Zhu et al. 2020, a recent MEA application to the Chinese banking sector applies the novel Malmquist productivity index (MPI) of MEA to investigate the overall total factor productivity growth as well as the variable specific productivity growth of Chinese banks. The study incorporates the MEA-based MPI into the meta-frontier framework considering the heterogenous environment in the Chinese banking sector. 16 main Chinese banks over the period 2005 - 2015 are sample for the study - 176 observations. The banks are divided into two main groups namely large state-owned commercial banks (LSCBBs) and small-medium commercial banks (SMCBs) and considered to have interest expenses and non-interest earnings as its inputs, interest income and non-interest income as its desirable outputs and non-performing loans as its undesirable outputs. They compared the novel MEA-MPI with the conventional DEA-MPI and found a negative overall Total Factor Productivity (TFP) growth, with non-performing loans (NPL) and non-interest income being the main sources impacting TFP growth in the country’s banking sector. They further observe the gap of productivity change between LSCBs and SMCBs to be narrowing and identify technological change to be the main gap between banks. Over, all they assert that the conventional MPI probably overestimates TFP growth. In general, it is observed that there exists no insurance efficiency study that has assessed the variable-specific efficiency of its inputs/outputs. The variable-specific assessment of firms and industries is necessary to effectively assess the impact of enacted reforms in the industry or firm. 2.3.3 Variable-specific efficiency and undesirable output Over the years, various techniques have been developed to measure efficiency performance in the presence of undesirable outputs (Arabi et al., 2015; Chen et al., 2017; Dyckhoff & Allen, 2001; Sueyoshi & Goto, 2010; Maghbouli et al., 2014) due to the inability of the traditional DEA to University of Ghana http://ugspace.ug.edu.gh 17 compute efficiency scores in the presence of undesirable variables (Färe & Grosskopf, 2004; Seiford & Zhu, 2002). These models include DEA directional distance function (DDF) and slack based DEA (Tone, 2001). However, due to the variable-specific nature of the novel MEA and the freedom to use negative inputs and outputs (Bogetoft & Hougaard, 1999), much attention is being given to the model for the assessment of variable-specific efficiencies in the presence of undesirable outcomes (Asmild & Matthews, 2012, Zhu et al., 2019). Asmild and Matthews (2012) is the first study that used MEA to assess the efficiency performance of Chinese banks while capturing one of its output variables as an undesirable output, non- performing loans. The study delved deeper into one of the popular findings of most Chinese banking sector studies - “State Owned Banks (SOBs) are less technically efficient than Joint Stock Banks (JSBs) and the JSBs have improved their position in the run up to the opening up of the banking sector.” The patterns and levels of efficiencies of these two banks were assessed, sampling 14 banks from 1997 through to 2008. The reforms enacted about two decades ago in the China Banking Regulatory Commission guided the study. Following Thanassoulis, Portela and Despic, (2008), non-performing loans, an undesirable output was used as an input in addition with three other inputs namely labour, fixed assets and bank deposits. The inputs were further classified into two groups; discretionary inputs (labour and non-performing loans) and non-discretionary inputs (fixed assets and deposits) while the study outputs were net interest earnings and non-interest earnings. The findings of the study are in contrast with the popular findings, the JSBs are more efficient than the SOBs. The study confirmed one of its hypotheses on the differences in the efficiency patterns in the two types of banks. Zhu et al. (2019) uses an improved MEA approach to evaluate the energy efficiency while considering the slack problem of production. The study focuses on 30 Chinese provinces and three University of Ghana http://ugspace.ug.edu.gh 18 major economic regions as it assesses the energy variable-specific efficiency in addition with the carbon emissions variable specific efficiencies. Both the improvement paths and improvement potential for energy efficiency of these provinces were assessed in the study and in line with Asmild and Matthews (2012), Zhu et al. (2019) used the SBM model aggregation idea of Tone (2001) but develops a more comprehensive MEA overall efficiency model which captures all the variables in the study. The findings reveal that the country’s provincial energy is olived-shaped with significant spatial imbalance. In addition, it reveals a large potential value for CO2 emission in the Central region with a relatively large energy saving potential for the two other regions, Western and Eastern. Wang et al. (2015) attempted to understand regional environmental efficiency differences in China using the novel MEA approach. They evaluated the environmental efficiency of industrial sectors in major Chinese cities considering the period 2006 - 2010. Thirty (30) capital cities of China’s provinces were sampled using three inputs, one desirable output and five undesirable outputs for in the study. The findings recommended that specific attention be given to different industrial pollutants in the various capital cities. In addition, the study identified the beginning of the alleviation of the inequitable nationwide industrial developments of China’s cities. In another study, Bi et al. (2014) aimed at gaining deeper insight into the regional energy and environmental efficiency of the Chinese transportation sector. The authors adopted the modified MEA model to investigate the levels and patterns of efficiency. Unlike previous studies on China’s transportation sector, C02 emission was chosen as an undesirable output in the study. Thirty (30) provinces in mainland for the period 2006-2010 were sampled. Labour and capital were nonenergy inputs; volume of energy consumed in the transportation sector represented energy input and value-added amount and volume of CO2 emissions denoted outputs. The overall comprehensive University of Ghana http://ugspace.ug.edu.gh 19 MEA efficiency for each region, the variable-specific efficiencies for energy and CO2 emission as well the reduction potential for energy and CO2 emission are all assessed. The results showed that not many regions were efficient during the study period. Greater chances of reducing CO2 emission and energy consumption were also identified. In short, the above discussion gives credence to the wide acceptance of the novel MEA approach in modelling efficiency differences instead of the traditional DEA approach. Specifically, the available empirical evidence demonstrates that additional insights can be gained with the novel MEA approach compared to traditional DEA (Asmild et al., 2016). Interestingly, as far as we have reviewed, there is no variable specific study in the insurance industry. We fill this gap in the literature and model the variable-specific efficiency scores of Ghanaian insurers using claims as an undesirable output in the novel MEA framework. 2.3.4 Undesirable output in the insurance sector The production of undesirable outputs from the agricultural, energy and manufacturing sectors have received much attention from environmental policy makers (Fernández et al., 2002; Khan et al., 2018; You & Yan, 2011). Several studies have been carried out to effectively assess their performance while considering the production of these undesirable outputs (Bi et al., 2014; Dyckhoff & Allen, 2001; Fernández et al., 2002; Khan et al., 2018; You & Yan, 2011; Zhu et al., 2019). Furthermore, comprehensive efficiency models have been developed to effectively assess these firms (Khan et al., 2018; You & Yan, 2011). Unlike the bad outputs of the these sectors which affect the environment (Dyckhoff & Allen, 2001; You & Yan, 2011), those of financial firms – claims and non-performing loans - adversely affect the firm. Studies have been carried out in the banking sector which have considered non-performing loans as an undesirable output (Assaf University of Ghana http://ugspace.ug.edu.gh 20 et al., 2013; Bi et al., 2014). However, no much studies have considered claims as an undesirable output in insurance efficiency assessment (Owusu-Ansah et al., 2010). Some studies who came close to this captured claims as an input (Rai, 1996; Yuengert, 1993) following the efficiency basis; minimize inputs and maximise outputs (Charnes et al., 1978). Yang (2006) introduced a new two-stage DEA model which assessed systematic efficiency for the Canadian Life and Health (L & H) insurance industry. The model incorporated the production and investment performances of insurers. To assess production efficiency, labour expenses, general operating expenses, capital equity and claims incurred were chosen as inputs. For this study, the production approach considered insurers to be providers of products and services while undertaking its sole responsibility, risk reduction through pooling. The results of the study demonstrated that the Canadian L & H insurance industry operated fairly during the period under study,1998. The scale efficiency for this insurance industry was also identified. Wu et al. (2007) is another study on the Canadian Life and Health insurance industry. They developed a problem-oriented DEA model which is able to simultaneously assess the production and investment performance of insurers in the Canadian Life and Health insurance industry while considering the interaction that often occurs between the indicators characterizing the two aspects of performance; production and investment. In line with Yang (2006), the inputs chosen for the assessment of production performance included labour expenses, general operating expenses, capital equity and claims incurred with net actuarial reserves, investment expenses, total investments, and total segregated funds were considered as inputs for the investment performance assessment. Again following Yang (2006), claims was used as an input in the production approach because it is appropriate for assessing insurers’ ability to satisfy the claims of its insureds. The results of the study confirmed Yang (2006) findings, the Canadian life and health insurers operated University of Ghana http://ugspace.ug.edu.gh 21 efficiently during the three-year period under study; 1996 – 1998. However, Wu et al., (2007) identified no scale efficiency in the industry. In an insurance efficiency study that investigated whether capital market considers efficiency of insurers, 399 listed insurance firms from 52 countries were sampled for the period 2002 through to 2008 (Gaganis et al., 2013). The study used stochastic frontier analysis to assess the profit efficiency and controlled for country-specific characteristics. Claims was used as an input variable following Rai (1996) - claims form an integral and importance part of the annual expenses of insurer thus must be captured as an input - and the purpose of the study, stockholders like their firms to minimize expenses while maximizing their returns. The efficiency scores were regressed with the stock returns, a positive and statistically significant relationship was identified between the current and past profit efficiency changes and market adjusted stock returns. The improper definition of variables during efficiency assessment results to distorted and inappropriate conclusions. There is the need for an insurance efficiency study to properly define its variables, making room for undesirable outcomes as these outcomes cannot be omitted from the provision of its services. This study captures claims as an undesirable output. Appendix A presents a tabular taxonomy of previous variable-specific studies. 2.4 Conceptual Framework Figure 2.1 presents the conceptual framework that explains the study pictorially. It follows from the empirical and theoretical reviews the presence of an undesirable output in the provision of insurance services and the relationship between the input and (desired and undesirable) output variables. University of Ghana http://ugspace.ug.edu.gh 22 Source: Author’s own construct, 2021 Figure 2.1 Conceptual framework of the relationship between first stage variables. 2.5 Frontier efficiency The modern efficiency and dynamic productivity of decision-making units (DMUs) began with the collective works of Farrell (1957), Debreu (1951), Koopmans (1951) and Seiford and Thrall (1990). In the production framework, efficiency is defined as the comparison of the observed output with the maximum potential output obtainable from the input, or the observed input with the minimum potential input demanded to produce the output or a blend of the two (Farrell, 1957; Fried et al., 2008; Lovell, 1993). This definition explains technical efficiency which can be input reduction (input-conservation), outputs augmentation (output-expansion) or both (non-orientation) (Fried et al., 2008). In summary, the assessment of efficiency and productivity change demands the initial identification of an efficiency frontier formed with best practice firms. The assessment can be undertaken using parametric (econometric approach) or non-parametric (mathematical programming approach) models (Coelli et al., 2005; Daraio et al., 2020; Fried et al., 2008; Lampe & Hilgers, 2015). Inputs *Physical capital *Labour *Equity capital Insurance service production Outputs Desirable outputs *Net premiums *Investment income Undesirable output *Claims University of Ghana http://ugspace.ug.edu.gh 23 DEA is a non-parametric linear programming frontier optimization method of assessing the relative efficiency of homogenous decision making units (DMUs) that consume multiple distinct inputs to produce multiple outputs (Banker et al., 1984; Charnes et al., 1978; Farrell, 1957; Cooper et al., 2004) (i.e. CCR and BCC). The method involves the construction of a production or cost or profit frontier from the observed data points using the best-practice organisational entities and measuring the (in) efficiency of a DMU by projecting the observation via the distance in relation to the frontier constructed by the dominating units (Cook & Zhu, 2005; Cooper et al., 2011; Emrouznejad & Yang, 2018; Fried et al., 2008; Lozano & Soltani, 2020). Under this non- parametric efficiency assessment technique, DMUs on the frontier are identified as efficient whereas DMUs outside the frontier are classified as inefficient units (Baležentis & De Witte, 2015; Golany & Yaakov, 1989; Lozano & Soltani, 2020). Instead of a completely disaggregated (in) efficiency that captures the contribution of individual-specific inputs and outputs, DEA uses the radial input decreases and output increases to determine single CCR and BCC aggregated efficiency scores (Asmild et al., 2016; Asmild & Matthews, 2012; Baležentis & De Witte, 2015; Tziogkidis et al., 2020). Multi-directional efficiency analysis (MEA) is a DEA modification which separates the issue of benchmark selection from the issue of efficiency measurement (Bogetoft & Hougaard, 1999; Kapelko & Lansink, 2017; Labajova et al., 2016). The model was postulated by Bogetoft and Hougaard (1999) who provided an axiomatic foundation which supports the implicit benchmark selection over the potential improvement selection approach. Asmild et al. (2003) further operationalised the potential improvement approach with DEA and proposed the name, multi- directional efficiency analysis (MEA). The model consists of two stages; ideal reference point identification, which is the first stage and improvement potential point selection for each input/output variable which is the second stage (Asmild et al., 2003; Asmild & Matthews, 2012). University of Ghana http://ugspace.ug.edu.gh 24 Unlike DEA, the selection of input reduction and output expansion benchmarks for MEA are based on the specified improvement potential related to each input and output separately (Asmild et al., 2003; Asmild, Baležentis, Hougaard, 2016). In an MEA input-oriented analysis, the largest reduction potentials for each input are identified and combined with the minimum possible input usage in each dimension to identify the ideal reference point (Asmild et al., 2003; Asmild & Pastor, 2010). The difference between the unit under analysis and the ideal reference point is used to find the directional vector of each unit (Asmild & Pastor, 2010). Bogetoft and Hougaard (1999) and Asmild et al. (2003) have discussed some desirable properties of the MEA model over the traditional DEA. First, unlike DEA which selects both weakly and strongly efficient benchmarks, MEA selects only strongly efficient benchmarks. Second, because of its non-radial improvement approach, MEA explicitly recognises improvement potentials between input and output dimensions. Third, MEA can be extended to estimate efficiency under input orientation, output orientation and non-orientation (input reduction and output augmentation simultaneously). Fourth, MEA can be extended to include discretionary and non-discretionary variables simultaneously. Finally, MEA can be run under both the constant return to scale and variable return to scale (VRS) technology, it is invariant to affine transformation under the VRS technology. 2.6 Overview of the Ghanaian insurance sector The commencement of the Ghanaian insurance is traced to 1924, a colonial era, where the Ghanaian insurance industry was populated with oversea insurers which had their head offices situated in the United Kingdom and elsewhere. As a result, they appointed foreign trading companies to act as chief agents in other countries including the then Gold Coast. However, the policies these insurers designed were limited to only the British nationals residing in the countries University of Ghana http://ugspace.ug.edu.gh 25 with the chief agents. Royal Exchange Assurance Corporation was the first of such insurance companies to operate in the Gold Coast and was represented by Barclays Bank, its chief agent, in 1924. Other foreign companies followed suit after Royal Exchange Assurance Corporation which is now Enterprise Insurance Company and opened offices in the Gold Coast. In 1955, the first local insurance company, Gold Coast Insurance Company, was established in the Gold Coast. It provided life assurance policies to its citizens and other Africans that were residing in the country since the foreign insurers were only insuring the Europeans. After the attainment of the country’s independence in 1957, its name was changed to Ghana Insurance Company. In 1958, another local insurance company was established to mainly underwrite fire and motor insurance businesses in the country, the Ghana General Insurance Company. Four years after its operation, it was merged with two other local insurers including the first local insurance company and the Co-operative Insurance Company, to form the State Insurance Corporation (SIC). SIC was incorporated by an Executive Instrument, EI 17. Some laws were passed after its formation which made it monopolistic over all government businesses. Over time, huge sums of monies were paid to foreign reinsurers for reinsurance, as result, legislation laws were passed in 1972 one of which was used to establish Ghana Reinsurance Organization (GRO). Moving forward, other insurance legislations were passed which compelled the foreign insurers to withdraw out of the Ghanaian insurance market. The NIC is the mandated supervisory body for Ghana’s insurance sector. According to the Insurance Act 2006, (ACT 724), NIC is mandated to ensure effective administration, supervision, regulation and control over the insurance businesses in Ghana (NIC, 2019). It is responsible for the approval of both premium and commission rates, provision of bureau for complaints resolution, enforcement of compliance as well as public education of the Ghanaian citizens. The sector is University of Ghana http://ugspace.ug.edu.gh 26 governed by the Insurance Act 2006, ACT 724 which complies with the International Association of Insurance Supervisors (IAIS) core principles. Before Insurance Act 2006 was enacted, NIC was operating under the Insurance Act 1989, (PNDC Law 227). Insurance companies were operating as composite insurers until a new law demanded that general insurance businesses be separated from life insurance businesses. The present Insurance Act requires that insurers operate life businesses and non-life businesses separately. Thus, currently, the sector comprises 20 life insurers, 29 non-life insurers, 3 reinsurers, 93 broking companies and one reinsurance contact office (NIC, 2019). 2.7 Industry challenges and reforms The Ghanaian insurance industry has experienced rapid premium growth over the years since its inception however, the industry is being faced with overarching challenges which are inhibiting the increase of its penetration and efficiency. The NIC Board which was sworn in on 18th August, 2017 started operation by comprehensively addressing the challenges impeding the industry’s growth, profitability and efficiency. The overarching challenges of the industry include low trust from the insuring public, many small inefficient loss-making players, proliferation of fraudulent motor insurance stickers on commercial vehicles, loss of huge investments held by poorly managed micro finance institutions and banks (NIC, 2017). The Chairman of the existing Board, Mr. Emmanuel Ray Ankrah, reported that the Board has developed a four-year strategic plan with the sole aim of the industry excelling its mandate as stated in the Insurance Act, 2006 (Act 724). The strategic plans seek to address the industry’s supply and demand constraints, which consists of construction and implementation of an Electronic Motor Insurance Database (MID), passage of University of Ghana http://ugspace.ug.edu.gh 27 a new Insurance Bill, insurance cover for projects funded by Donors and Development partners, compulsory fire insurance for public places, revamp of agricultural and marine insurance, effective consumer education, development of annuities market, improvement of claims management and many others. In 2019, the existing NIC board constructed and implemented an Electronic MID to be used to store information on all motor insurance policies, making an interface available to Driver and Vehicle Licensing Authority (DVLA) (NIC, 2018). This initiative is to help reduce the proliferation of fake motor insurance stickers while reducing the number of uninsured motor vehicles on the roads. The implementation and construction of an Electronic MID is one of the key initiatives of the current NIC board, to curb one of the overarching challenges facing the industry (NIC, 2018). Passage of a new Insurance Bill into an Act is another initiative developed by the Board to address the sector’s challenges. The chairman reported that the passage of the Bill into an Act will consequently improves the industry’s weak segments – marine and agricultural insurance, compulsory group life and public liability insurance – and protect its policyholders and stakeholders. He explained that, with Ghana being an import dependent country and agriculture being the country’s biggest employer and highest contributor to GDP, calls for the revamp of the insurance terms on goods imported from the country. Furthermore, the NIC board passed an Insurance Bill which outlined a strategic objective of improving the industry’s supervisory effectiveness (NIC, 2018). Included in this main strategic objective were the review of the Minimum Capital Requirements for insurers to ensure the existence and operation of adequately capitalized insurers, the design and implementation of a Market Conduct Supervisory framework to ensure fair and transparency of policyholders, University of Ghana http://ugspace.ug.edu.gh 28 development of a Risk Based Supervisory framework which will issue Supervisory Risk Ratings to each insurer and the implementation of Risk Based Capital framework which links the risks and nature of business with the player’s capital requirement. The board suggests that the implementation of all these reforms coupled with the cooperation of the stakeholders in the insurance industry will improve the industry’s growth, profitability and efficiency. 2.8 Chapter summary This chapter reviewed related theories that supports the study. First, the multi-criteria production theory supports the use of claims as an undesirable output in the insurance industry. Second, the decision theory supports the variable-specific efficiency analysis of insurers. Empirical studies on insurance efficiency, variable-specific efficiency analysis with and without undesirable outputs and undesirable outputs in the insurance sector were all reviewed in this chapter. University of Ghana http://ugspace.ug.edu.gh 29 CHAPTER THREE METHODOLOGY 3.1 Introduction This chapter discusses the concept of efficiency and explains the methods employed in the study. The novel non-parametric efficiency measure, MEA, postulated by Bogetoft and Hougaard (1999) and subsequently operationalised by Asmild et al. (2003), is used to assess the variable-specific efficiency scores of Ghanaian insurers from 2008 to 2019. Robust econometric regression techniques such as the two-step systems Generalised Method of Moment (GMM) are used to examine the impact of exogenous variables – competition, size, solvency, profitability, leverage and type of insurer – on the MEA efficiency scores. R version 4.0.5 is used to generate the descriptive statistics, assess the variable-specific efficiency scores and compute the regression results for the second stage analysis. 3.2 Research design Research design is a vital research framework that connects the gap between the research questions and the research process (Blanche et al., 2006). It plays a key role in the selection process of the research approach, research method(s) and paradigm(s) (Creswell & Creswell, 2018). Irrespective of the rigour used in a statistical analysis, the conclusion of a research may be useless if the research design is not appropriate for the study (Hancock et al., 2010). This confirms the assertion by Miles and Huberman (1994); the choice of a research design constrains and supports the ultimate conclusions of a study. Among the three well-known research approaches; quantitative, qualitative and mixed method (Creswell & Creswell, 2018), the quantitative approach is used because it University of Ghana http://ugspace.ug.edu.gh 30 allows researchers to objectively examine the relationship between input and output variables of insurers and to assess their contribution to the insurer’s efficiency. Paradigms are broadly seen as worldviews. Guba (1990) posits that “worldviews are a basic set of beliefs that guides action” (p.17), that is, a researcher’s belief greatly influences the action(s) employed in research. However, Morgan (2007), suggests that paradigms are not only limited to the things people think about and believe but extend to the thoughts people have about the nature of research; what worldviews consist of. Among the existing research paradigms, the positivist worldview is employed. This paradigm believes in the existence of reality, such that this reality is driven by immutable laws of nature and mechanisms (Guba, 1990). The positivist worldview is adopted because the assessment of the variable-efficiency scores requires the development of numeric measures for insurers which call for objective views rather than subjective views. 3.3 Data, sampling and sources Ghana’s insurance sector presently consists of 20 life and 29 non-life insurers (NIC, 2019). Following the separation of the composite insurers into life and non-life groups in December, 2006, the study sampled both life and non-life insurers to assess both group and individual comprehensive and variable-specific efficiency differences. Hence, 13 life and 17 non-life insurers that had been in operation from 2008 to 2019 were sample for study. The study data was retrieved from the statement of financial position and comprehensive income of the audited annual reports of the sampled insurers. These reports were collected from the National Insurance Commission (NIC). NIC is the regulatory body whose responsibility is to “ensure effective administration, supervision, regulation and control the business of insurance in Ghana” (NIC, 2019). It is mandatory for all life and non-life insurers operating in Ghana to present their audited annual University of Ghana http://ugspace.ug.edu.gh 31 financial report to the NIC. This makes the NIC the most reliable source of data for this study. Despite the law guiding the submission of audited annual reports, the audited annual reports for some insurers were not obtained from the NIC nor were information on their financials found in the NIC annual reports. Following Cummins and Xie (2013) and Eling and Schaper (2017), figures that were not found were mathematically generated (linearly interpolation) in R, hence a balanced data panel is used for this study. NIC has been the data source for several Ghanaian insurance efficiency studies including Owusu-Ansah et al. (2010), Alhassan et al. (2015), Ohene-Asare et al. (2019), Alhassan and Biekpe (2016) and Danquah et al. (2018). The study period for these studies varies from three years to ten years, however, this study considers a twelve-year study period. 3.4 Formulating the multi-directional efficiency analysis The study considers a production technology that uses a vector of input X to produce vectors of output Y (desirable) and C (undesirable). The production technology is defined as: 𝐿 = {(𝑋, 𝑌, 𝐶) produce (𝑌, 𝐶)} (3.1) The production technology 𝐿 considered undesirable outputs as by-products since they are produced with desirable outputs (Färe & Grosskopf, 2004; Bi et al., 2014). Three assumptions of joint production technology are imposed on the production technology in equation (3.1) for the asymmetric treatment of the desired and undesired outputs (Bi et al., 2014; Färe et al., 2005; Reyna & Fuentes, 2018). The three assumptions are as follows: i. Strong or free disposability of desirable outputs: If (𝑋, 𝑌, 𝐶) ∈ 𝐿 and 𝑌∗ ≤ 𝑌, then (𝑋, 𝑌∗, 𝐶) ∈ 𝑇. This assumption is the same traditional assumption handling the disposability of desirable outputs. The axiom states that any University of Ghana http://ugspace.ug.edu.gh 32 output vector with a smaller desirable output is feasible if the observed desirable and undesirable outputs vectors are possible (feasible). This assumption guides the free disposability of desirable outputs without any cost (Färe et al., 2005; Färe & Grosskopf, 2004). ii. Weak disposability of undesirable outputs (Shephard, 1970) : If {(𝑋, 𝑌, 𝐶) ∈ 𝐿 and 0 ≤ 𝜃 ≤ 1, then (𝑋, 𝜃𝑌, 𝜃𝐶) 𝜖 𝑇}. Weak disposability means that the proportional contraction of desirable and undesirable outputs is possible, hence for any given input, bad outputs can be reduced if and only if good inputs are also reduced in proportion. This axiom suggests that undesirable outputs cannot be freely disposed off, hence the sole reduction of undesirable outputs is impossible, due to their costly disposal which affects desirable outputs (Färe et al., 2005; Färe & Grosskopf, 2004; Reyna & Fuentes, 2018). iii. Desirable and undesirable outputs being null-joint (Shephard, Ronald & Fare, 1944): If {(𝑋, 𝑌, 𝐶) ∈ 𝐿 and 𝐶 = 0, then 𝑌 = 0}. This assumption implies that undesirable outputs are by-products of desirable outputs, hence the production of desirable outputs cannot be separated from the production of undesirable outputs. Relating the assumption to the insurance environment, the coverage of a risk is linked with the occurrence of a covered loss which usually demands claim payment - as desirable outputs are being produced, undesirable outputs will be produced alongside (Färe et al., 2005; Reyna & Fuentes, 2018). From axiom (a) and (b), strong disposability of desirable output vector implies weak disposability of both desirable and undesirable outputs. With the imposition of these assumptions, production technology L is an insurance production technology. A set of insurance firms (𝑗 = 1,… , 𝑛) are University of Ghana http://ugspace.ug.edu.gh 33 considered to produce 𝑠1 desirable outputs (𝑟 = 1, … , 𝑠1) and 𝑠2 undesirable outputs (𝑘 = 1, … , 𝑠2) with 𝑚 inputs (𝑖 = 1, … ,𝑚). Consistent with Bi et al. (2014), the insurance production technology L is modelled for a DEA framework as: 𝐿 = {(𝑋, 𝑌, 𝐶): ∑λj n j=1 xij ≤ xij, i = 1,2, … ,m ,∑λj n j=1 yrj ≤ yrj, r = 1, 2, … , s1 ∑λj n j=1 ckj = ckj, k = 1, 2, … , s1} (3.2) 𝜆𝑗 in equations (3.2) represents the weights of the variables (∑ 𝜆𝑗 = 1, 𝜆𝑗 ≥ 0)𝑛 𝑗=1 . The strong or free disposability of the desired outputs and the weak disposability of the undesirable outputs are imposable as a result of the equality and inequality on the undesirable outputs and desirable outputs respectively. A Multi-directional Efficiency Analysis model is formalised following Asmild and Matthews (2012) and Zhu et al. (2019). (𝑥𝑖0, 𝑦𝑟0, 𝑐𝑘0) is chosen as the production plan for 𝐷𝑀𝑈0. For each input, desirable output and undesirable output variable, an ideal reference point is obtained by solving the three linear programming problems (LPP) 𝑚𝑖𝑛 𝑑𝑖0 subject to { ∑𝜆𝑗𝑥𝑖𝑗 ≤ 𝑑𝑖0 𝑛 𝑗=1 , ∑𝜆𝑗𝑥−𝑖𝑗 ≤ 𝑥−𝑖0, -𝑖 = 1, . . . , 𝑖 − 1, 𝑖 + 1, … ,𝑚 𝑛 𝑗=1 ∑𝜆𝑗𝑦𝑟𝑗 ≥ 𝑦𝑟0, r = 1, . . . , 𝑠1 𝑛 𝑗=1 ∑𝜆𝑗𝑐𝑘𝑗 = 𝑐𝑘0, k = 1, … , 𝑠2 𝑛 𝑗=1 𝜆𝑗 ≥ 0, 𝑗 = 1, . . . , 𝑛 (3.3) University of Ghana http://ugspace.ug.edu.gh 34 𝑚𝑎𝑥 𝛿𝑟0 subject to { ∑𝜆𝑗𝑦𝑟𝑗 ≥ 𝛿𝑟0, 𝑛 𝑗=1 ∑𝜆𝑗𝑦−𝑟𝑗 ≥ 𝑦−𝑟0 𝑛 𝑗=1 , −𝑟 = 1,… , 𝑟 − 1, 𝑟 + 1,… , 𝑠1 ∑𝜆𝑗𝑥𝑖𝑗 ≤ 𝑥𝑖0, 𝑖 = 1, …𝑚 𝑛 𝑗=1 ∑𝜆𝑗𝑐𝑘𝑗 = 𝑐𝑘0, 𝑘 = 1,… 𝑠2 𝑛 𝑗=1 𝜆𝑗 ≥ 0, 𝑗 = 1, . . . , 𝑛 (3.4) and 𝑚𝑖𝑛𝜙𝑘0 subject to: { ∑𝜆𝑗𝑐𝑘𝑗 = 𝜙𝑘0 𝑛 𝑗=1 ∑𝜆𝑗𝑐−𝑘𝑗 = 𝑐−𝑘0, −𝑘 = 1,… , 𝑘 − 1, 𝑘 + 1,… , 𝑠2 𝑛 𝑗=1 ∑𝜆𝑗𝑥𝑖𝑗 ≤ 𝑥𝑖0, 𝑖 = 1,… ,𝑚 𝑛 𝑗=1 ∑𝜆𝑗𝑦𝑟𝑗 ≥ 𝑦𝑟0, 𝑟 = 1, … , 𝑠1 𝑛 𝑗=1 𝜆𝑗 = 0, 𝑗 = 1, . . . , 𝑛 (3.5) respectively, for 𝑖 = 1,… ,𝑚, 𝑟 = 1, … , 𝑠1 and 𝑘 = 1,… 𝑠2. From equations (3.3) – (3.5), 𝑥𝑖𝑗 denotes the input level used by 𝐷𝑀𝑈𝑗; 𝑦𝑖𝑗 denotes the quantity of output produced by 𝐷𝑀𝑈𝑗. 𝑚, 𝑠1and 𝑠2 are the input observations, desirable output observations and undesirable output observations respectively. 𝑑𝑖0 and 𝜙𝑘0 represent the inputs and undesirable outputs to be minimised whereas 𝛿𝑟0 represents the desirable outputs to be maximized. The ideal University of Ghana http://ugspace.ug.edu.gh 35 reference point (𝑑𝑖0 ∗ , 𝑦𝑟0 ∗ , 𝑐𝑘0 ∗ ) for each unit (𝑥𝑖0, 𝑦𝑟0, 𝑐𝑘0) is obtained by solving the linear programming problems above. The MEA efficiency of each variable for the production unit (𝑥𝑖0, 𝑦𝑟0, 𝑐𝑘0) is derived as: 𝑚𝑎𝑥(𝛽𝑖0 + 𝛽𝑟0 + 𝛽𝑘0) subject to { ∑𝜆𝑗𝑥𝑖𝑗 ≤ 𝑛 𝑗=1 𝑥𝑖0 − 𝛽𝑖0(𝑥𝑖0 − 𝑑𝑖0 ∗ ), 𝑖 = 1,… ,𝑚 ∑𝜆𝑗𝑦𝑟𝑗 ≥ 𝑛 𝑗=1 𝑦𝑟0 − 𝛽𝑟0(𝛿𝑖0 ∗ − 𝑦𝑟0), 𝑟 = 1,… , 𝑠1 ∑𝜆𝑗𝑐𝑘𝑗 = 𝑛 𝑗=1 𝑐𝑘0 − 𝛽𝑘0(𝑐𝑘0 − 𝜙𝑖0 ∗ ), 𝑘 = 1, … , 𝑠2 𝜆𝑗 ≥ 0, 𝑗 = 1,… , 𝑛 (3.6) 𝛽𝑟0, 𝛽𝑘0, 𝛽𝑖0 measures the proportion by which the desirable outputs are added while the undesirable outputs and inputs are contracted in the same proportion (Bi et al., 2014; Bogetoft & Hougaard, 1999; Kapelko & Lansink, 2017; Tziogkidis et al., 2020). 𝛽𝑖𝑗, 𝛽𝑟𝑗 and 𝛽𝑘𝑗 always falls within the interval, [0,1] hence a DMU is said to have reached the frontier of the best practice firms if 𝛽𝑖𝑗 = 𝛽𝑟𝑗 = 𝛽𝑘𝑗 = 0 otherwise, the DMU is farther away from the frontier of the best practice firms (Asmild et al., 2003;Bi et al., 2014; Bogetoft & Hougaard, 1999; Kapelko & Lansink, 2017). Using the optimal solution, (𝜆𝑗 ∗, 𝛽𝑖0 ∗ , 𝛽𝑟0 ∗ , 𝛽𝑘0 ∗ ), from equation (3.6), the benchmark selection (or the potential improvement point) for the target unit (𝑥𝑖0, 𝑦𝑟0, 𝑐𝑘0) is determined as (𝑥𝑖0 ∗ , 𝑦𝑟0 ∗ , 𝑐𝑘0 ∗ ). The MEA efficiency values for the production unit and its specific variable efficiency scores are defined below: For each input variable 𝑥𝑖, the MEA efficiency value is given as: 𝜃𝑖 = 𝑥𝑖0−𝛽𝑖0 ∗ (𝑥𝑖0−𝑑𝑖0 ∗ ) 𝑥𝑖0 (3.7) University of Ghana http://ugspace.ug.edu.gh 36 For each desirable output 𝑦𝑟, the MEA efficiency value is given as: 𝜃𝑟 = 𝑦𝑟0 𝑦𝑟0+𝛽𝑟0 ∗ (𝛿𝑟0 ∗ −𝑦𝑟0) (3.8) Finally, for each undesirable output 𝑐𝑘, the MEA efficiency value is given as: 𝜃𝑘 = 𝑐𝑘0−𝛽𝑘0 ∗ (𝑐𝑘0−𝜙𝑘0 ∗ ) 𝑐𝑘0 (3.9) From the variable-specific MEA efficiency values above, the vector of relative variable-specific MEA efficiency for the production unit is given as: ( 𝑥𝑖0 − 𝛽𝑖0 ∗ (𝑥𝑖0 − 𝑑𝑖0 ∗ ) 𝑥𝑖0 , 𝑦𝑟0 𝑦𝑟0 + 𝛽𝑟0 ∗ (𝛿𝑟0 ∗ − 𝑦𝑟0) , 𝑐𝑘0 − 𝛽𝑘0 ∗ (𝑐𝑘0 − 𝜙𝑘0 ∗ ) 𝑐𝑘0 ) (3.10) Using the variable-specific MEA efficiency values defined in equations (3.7) – (3.9) and based on the slack-based measure (SBM) model aggregation idea of Tone (2001), a comprehensive MEA efficiency is established consisting of all the input and output (desirable and undesirable) variables. From Zhu et al. (2019), the overall comprehensive MEA efficiency score is given as: 𝜃0 = 1 − 1 𝑚 ∑ 𝛽𝑖0 ∗ (𝑥𝑖0 − 𝑑𝑖0 ∗ ) 𝑥𝑖0 𝑚 𝑖=1 1 + 1 𝑠1 + 𝑠2 [∑ 𝛽𝑟0 ∗ (𝛿𝑟0 ∗ − 𝑑𝑟0) 𝑦𝑟0 𝑠1 𝑟=1 + ∑ 𝛽𝑘0 ∗ (𝑐𝑘0 − 𝜙𝑘0 ∗ ) 𝑐𝑘0 𝑠2 𝑘=1 ] (3.11) 3.5 Nonparametric returns to scale assumption Unlike other efficiency studies (Asmild et al., 2016; Barros et al., 2010; Lozano & Soltani, 2020) that assumed the return to scale (RTS) of an underlying technology of a study, this study tests to identify the appropriate return to scale of its technology following Ohene-Asare et al. (2017). The choice of the specific return to scale of an underlying technology is of great importance as changes University of Ghana http://ugspace.ug.edu.gh 37 in the choice of return to scale result in different conclusions (Ohene-Asare et al., 2017; Leopold Simar & Wilson, 2002). There exist various test approaches for testing the specific return to scale of an underlying technology (Banker, 1996; Barros et al., 2010; Leopold Simar & Wilson, 2002; Simar & Wilson, 2011). Fare and Grosskopf (1985) developed an approach for testing the local return to scale in an estimated frontier. However, the approach does not provide a formal statistical test of return to scale. Simar and Wilson (2002) further developed the global returns to scale of the bootstrap methodology, designed by Simar and Wilson (1998) considering the deterministic nature of non-parametric measures like DEA. This approach is used to test the return to scale of the underlying technology in the study. The approach is based on the hypotheses that: 𝐻0: 𝜓 is globally CRS versus 𝐻1: 𝜓 is VRS (3.12) Consistent with Simar and Wilson (2002) and Ohene-Asare et al. (2017), the test statistic of the mean of ratios (�̂�1) and ratio of means (�̂�2), is defined as �̂�1 = 𝑛−1∑ [ �̂�𝑗 𝐶𝑅𝑆(𝑥,𝑦) �̂�3 𝑗 𝑉𝑅𝑆(𝑥,𝑦) ]𝑛 𝑗=1 (3.13) �̂�2 = ∑ �̂�𝑗 𝐶𝑅𝑆(𝑥,𝑦)𝑛 𝑗=1 ∑ �̂�𝑗 𝑉𝑅𝑆(𝑥,𝑦)𝑛 𝑗=1 (3.14) where �̂�𝑗 𝐶𝑅𝑆(𝑥, 𝑦) and �̂�𝑗 𝑉𝑅𝑆(𝑥, 𝑦) represent the estimated technical efficiency scores assessed under the CRS and VRS assumptions respectively. When �̂�𝑗 𝐶𝑅𝑆(𝑥, 𝑦) = �̂�𝑗 𝑉𝑅𝑆(𝑥, 𝑦) then �̂�𝑖 = 1, 𝑖 = 1,2 hence 𝐻0 is true for all the DMUs (𝑗 = 1,2, . . . , 𝑛). The test statistic developed by Simar and Wilson (2011), mean of ratios less unity (�̂�3), is used to confirm the test results of the mean of ratios (�̂�1) and ratio of means (�̂�2). �̂�3 = 𝑛−1∑ [ �̂�𝑗 𝐶𝑅𝑆(𝑥,𝑦) �̂�𝑗 𝑉𝑅𝑆(𝑥,𝑦) − 1]𝑛 𝑗=1 ≥ 0 (3.15) University of Ghana http://ugspace.ug.edu.gh 38 Since the distribution for �̂� = (�̂�1, �̂�2, �̂�3) and 𝐻0 are not known, bootstrapping method is used to obtain the critical values and p-values of the tests (Ohene-Asare et al., 2017). 3.6 Second stage regression analysis Over time the efficiency assessment of decision-making units (DMU) has become incomplete without regressing environmental variables to the efficiencies, second-stage analysis. Daraio and Simar (2007) explained that the non-parametric efficiency model, DEA, is sensitive to outliers and sampling variations hence it is not appropriate to solely depend on its efficiency scores to make statistical inferences. In addition, environmental variations around firms cannot be ignored due to the direct impact these variations have on firm performance (Dyson et al., 2001). Hence, the assessment of the robustness of non-parametric efficiency scores cannot be left unattended during efficiency assessment. As a result, several non-parametric efficiency studies consider the two-stage approach; assess efficiency in the first stage and then regress the estimated efficiencies on some environmental variables in the second stage (Simar & Wilson, 2007). Different second-stage regression models have been used in various industries (Asmild & Matthews, 2012; Hanif Akhtar, 2013; Molinos-Senante et al., 2016; Zhang & Lin, 2018) including insurance (Alhassan & Biekpe, 2016; Ansah-Adu et al., 2012; Barros et al., 2010; Barros & Dieke, 2008; Kader et al., 2014). However, two of these regression models; Tobit and ordinary least square (OLS) have been strongly criticised due to their failure to consider the presence of serial correlation in non-parametric, DEA, efficiencies estimates and the absence of proper data generating process (McDonald, 2009; Ramalho et al., 2010; Simar & Wilson, 2007). Simar and Wilson’s truncated-bootstrapped regression model on the other hand is believed to have specified a coherent data generating process and hence provides consistent and valid regression results. University of Ghana http://ugspace.ug.edu.gh 39 Many insurance efficiency studies have adopted this regression model so as to obtain consistent and unbiased second-stage estimates irrespective of the correlation between the first stage efficiency estimates and the exogenous variables (Alhassan & Biekpe, 2015; Barros et al., 2010; Barros & Wanke, 2014; Luhnen, 2009). However, this study uses the pooled OLS, fixed effect, random effect, Beck and Katz (1995) for panel-corrected standard errors, Driscoll and Kraay (1998) spatial correlation consistent (SCC) and the two-step system GMM regression to crosscheck the robustness of the MEA efficiency scores. First, the pooled OLS is a widely used regression estimation technique in panel data. It is simple to perform as it does not require the use of any special technique. It is usually used as the baseline model for most pooled analysis (Stimson, 1985). The model assumes all entities (insurers) to operate in the same way over a period of time (Wooldridge, 2002). However, its demerit lies in its inability to consider the differences within entities and time variations (time effects) (Stimson, 1985). Stimson (1985) posits OLS to be only acceptable for a given research question, nonetheless without using other regression models there is no satisfactory method to tell its appropriateness. Second, the fixed effect model explores the link between the predictor and the outcome variables within an entity. It assumes correlation between the entity specific effect and predictors (Nickel, 1981). The model assumes the time-invariant characteristics to be unique to the entity, and does not expect any correlation to exist with other individual characteristics, dummy variables (Bell & Jones, 2015). Xu (2017) and Plumber, Troeger and Manow (2005) believe its exogenous variables to contain unit-specific dummy variables which allow its intercepts to vary by unit. The model in addition controls for all time-variant differences among entities, as a result, omitted time-invariant characteristics cannot cause its estimated coefficient to be bias. Unlike the pooled OLS estimation technique, the fixed effect estimator addresses the omitted variable bias by controlling for fixed University of Ghana http://ugspace.ug.edu.gh 40 effects, but has the tendency of compounding the problem of measurement error (Hauk & Wacziarg, 2009). Third, unlike the fixed effect model which assumes correlation for the predictor and outcome variables, the random effect model assumes no correlation between unobserved entity-specific, time-invariant and regressors (Torres-Reyna, 2007). That is, it assumes variation across entities to be random, correlated with the predictor or independent variables in the model. Bhargava et al, (2001) suggests that although entity-specific, time-invariant and explanatory variables are uncorrelated, the impact of such unobserved variables must be specified in the regression model. Random effect therefore, uses all available data, produces unbiased parameter estimate and smaller standard error, however its unobserved entity-specific, time-invariant variable produce omitted variable bias. An advantage of this technique over the fixed effect is the presence of time invariant variables. (Gunasekara et al. 2014; Firebaugh, Warner & Massogila, 2013). Fourth, the two-step system GMM is a variant of the system-GMM method. It has been proven to be more efficient than its counterpart; one-step system GMM (Agbloyor et al., 2016). It is usually used to estimate the dynamic frontier with time-invariant technical efficiency (Bhattacharyya, 2012). The method uses a set of moment conditions relating to the first differenced regression equation, and another set of moment conditions for the regression equation (Blundell and Bond, 1998). Unlike the difference GMM which deducts the initial observations from the contemporaneous ones, thus enlarging the gaps in the case of panel data which is unbalanced (Arellano & Bond, 1991), the system-GMM method subtracts only the averages of the observations available from the current and future ones, and hence ends up reducing the gaps in the dataset. According to Arellano and Blover (1995) and Blundell and Bond (1998), the system- GMM method has an advantage of improving the difference-GMM by way of equation supplementation in the first difference with the level equations. University of Ghana http://ugspace.ug.edu.gh 41 These econometric models are used in line with Wooldridge (2009), to deal with data and model specifications such as multicollinearity, heteroskedasticity and serial correlation. 3.6.1 Econometric tests Preceding the selection of the appropriate econometric regression model for the study, the correlation matrix in addition to the variance inflation factors (VIFs) are used to test for multicollinearity in the study data. The Chow test in addition to other econometric tests are undertaken to ensure the selection of a robust model. First, to test for poolability of the study’s panel data, the Chow test is conducted with the null hypothesis, 𝐻0: dataset is poolable versus 𝐻1: dataset is not poolable The test statistic of the Chow test is given as: 𝐹1−𝑤𝑎𝑦 = (𝐸𝑆𝑆𝑅−𝐸𝑆𝑆𝑈) (𝑁−1)⁄ (𝐸𝑆𝑆𝑈) ((𝑇−1)𝑁−𝐾)⁄ (3.16) where 𝐸𝑆𝑆𝑅 denotes the residual sum of squares under the 𝐻0; 𝐸𝑆𝑆𝑈