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Analysis of Takaful vs. Conventional insurance firms’ efficiency: Two-stage DEA of Saudi Arabia’s insurance market

Abstract Despite the remarkable growth in the insurance industry over the past two decades, few studies evaluate the performance of Takaful vs. conventional insurance firms with focus on the standard structure of production as a two-stage process, that is, operations and profitability. Thus, this research examines the performance of Saudi Arabia’s insurance market using a two-stage data envelopment analysis to assess the efficiency of the two production stages and accordingly, define the leader stage. The empirical results obtained using data for 26 conventional and seven Takaful insurance firms for 2014–2017 indicate declining average efficiency scores for both firm types. In other words, Saudi Arabia’s insurance market warrants new consolidation and foreign participation regulations to assist firms in becoming dynamic and strong. This study makes a significant contribution given the dearth of an exclusive analysis on the two-stage efficiency of Saudi Arabia’s Takaful and conventional insurance firms. Further, it offers key implications for decision makers, regulators, and managers associated with the insurance industry in Saudi Arabia and other emerging insurance markets.

ABOUT THE AUTHOR Tarifa Almulhim received a bachelor's degree in mathematics from King Faisal University, Alhassa, Saudi Arabia, in 2005; a master's in science degree in operational research and applied statistics from the University of Salford, Salford, United Kingdom, in 2010; and a PhD in business and management (operational research) from the University of Manchester, Manchester, United Kingdom, in December 2014. She is, at present, the vice dean at the College of Business Administration and an assistant professor of quantitative methods at King Faisal University. She has published four research papers related to operational research, risk and insurance, decision theory, and fuzzy logic systems in international journals. Her current research interests include operational research, operations management, risk and insurance, multiple criteria decision analysis under uncertainties, decision theory, and fuzzy logic systems.

PUBLIC INTEREST STATEMENT
This study aims to evaluate the performance of Saudi Arabia's insurance industry, particularly Takaful and conventional insurance firms, during 2014-2017 using a two-stage data envelopment analysis (DEA) method. The efficiency scores are based on data from 33 insurance firms listed on the Saudi stock exchange (Tadawul), of which seven are Takaful firms and 26 are conventional firms. In addition, this research investigates whether the operations and profitability stage is the optimal or leader stage in insurance firms. The key findings highlight that the performance in terms of average efficiency has monotonically decreased for both Takaful and conventional insurance firms. This study can assist regulators and managers attempting to develop Saudi Arabia's insurance industry and improve its performance.
Keywords: Takaful firms; Saudi Arabian insurance market; two-stage data envelopment analysis; efficiency

Introduction
The development of the insurance industry has been commonly acknowledged as a significant catalyst for sustainable economic growth across the world (Ward & Zurbruegg, 2000). The insurance industry has witnessed substantial and accelerated growth over the past two decades (Arena, 2008). Numerous studies have been devoted to understanding insurance market activities and measuring insurance efficiency in both industrialized and developed countries. While there is extensive research on the insurance markets of developed countries, the coverage of the insurance industry in developing countries, particularly the emerging markets of Asia and more specifically, Saudi Arabia, remains narrow.
This study focuses on Saudi Arabia's insurance industry because it is the largest and oldest insurance market among the Cooperation Council for the Arab States of the Gulf, also known as the Gulf Cooperation Council (GCC), 1 countries (Samargandi, Fidrmuc, & Ghosh, 2014). In addition, Saudi Arabia is the largest economy in the Arab region. As per OPEC, it has the second largest (after Venezuela) proven oil reserves in the world, and it is a member of the Group of Twenty (G-20). The 2017 national institution statistics for GCC countries reports that Saudi Arabia's population accounts for 65% of the GCC's population. Saudi Arabia's insurance industry has been significantly growing over the past few years owing to the application of actuarial pricing in 2013 and the increasing demand through economic development projects consistent with the 2030 vision. According to Albilad Capital (2015) report, Saudi Arabia's insurance industry is the second largest in the Gulf region: it is valued at US $9.5 billion with a 16% growth rate driven by the increase in medical and motor coverage, which contributed to 81% of the insurance market during 2015.
Insurance activities are still relatively new to Saudi Arabia, where the Law on Supervision of Cooperative Insurance Companies was enacted at the end of 2003 and its regulations were implemented in 2004. The Saudi Arabian Monetary Authority (SAMA) is responsible for regulating the Saudi insurance sector, licensing insurance firms, and analysing the market. In addition to SAMA, Saudi Arabia follows a cooperative insurance model called Islamic insurance (Takaful), which is an Islamic or Shari'ah-compliant alternative to conventional insurance. The term Takaful originated from the Arabic word "kafl" denoting assurance or responsibility (Jamil & Akhter, 2016). Currently, there are two forms of insurance operated and licensed in Saudi Arabia, conventional and Takaful insurance.
Like any insurance sector in the world, Saudi Arabia's insurance industry has a standard structure, that is, a production process comprising two stages, operations and profitability. While some studies have evaluated the overall performance of Saudi Arabia's insurance companies, their efficiency in the two-stage production process remains insufficiently explored. These concerns can be summarized into the following questions. How efficient are conventional and Takaful insurance companies in the two production stages of operations and profitability? How do companies' decision makers ascertain which is the dominant stage in their overall performance? To the best of the author's knowledge, no research has investigated the efficiency of Saudi Arabia's Takaful and conventional insurance firms in the two-stage production process and their order of priority on the basis of the lead-follow concept. This study aims to bridge this gap by applying the two-stage data envelopment analysis (DEA) (Despotis, Sotiros, & Koronakos, 2016) to evaluate the efficiency of 26 conventional and seven Takaful insurance firms in the Saudi market in the context of operations and profitability. In addition, it adopts Li, Chen, Cook, Zhang, and Zhu (2018) extended method to determine the relationship between the firms' performance and the two substages during 2014-2017. Further, this study identifies which among the two sub-stages is the leader stage to improve our understanding on determining overall efficiency in the two types of insurance firms. It offers insight into the performance of Takaful operators by comparing their profit-sharing root operations with those of conventional insurance firms. Finally, this research offers recommendations for both researchers and regulators in the insurance sector.
The remainder of this paper is structured as follows. Section 2 provides an overview of theoretical papers on efficiency and the empirical literature on Saudi Arabia's insurance industry. Section 3 describes the data and research methodologies utilized in this study. Section 4 presents the empirical analysis and discusses its major findings. Section 5 concludes the paper with a summary of our key findings.

Literature review
The concept of efficiency evaluation has been predominant in the insurance literature. Data envelopment analysis (DEA), introduced by Charnes, Cooper, and Rhodes (1978), is a non-parametric method to assess the efficiency of decision-making units (DMUs) in a single stage that uses multiple inputs to yield multiple outputs. The DEA technique has been widely used to evaluate the performance and efficiency of the insurance industry. This section reviews pertinent efficiency studies in the context of insurance and particularly, research on Saudi Arabia's insurance market.
A majority of research on the efficiency of conventional insurance industries focuses on the United States and other developed countries. Cummins and Zi (1998) perform a DEA and mathematical programming to examine the efficiency of US insurance companies from 1988 to 1992 and deduce that the DEA is a better approach to evaluate insurance industry efficiency. Diacon, Starkey, and Obrien (2002) assess the pure technical and scale efficiencies of 450 insurance firms across 15 European countries and conclude the average technical efficiency declined during 1996-1999. Eling and Luhnen (2010) use DEA to perform a comprehensive efficiency assessment of the global insurance industry. Kaffash and Marra (2017) examine 620 papers published in journals indexed in the Web of Science database during 1985-2016 and employ DEA approaches with focus on financial services (e.g. insurance).
While large numbers of studies evaluate the efficiency of conventional insurance, few pay attention to the efficiency of Takaful insurance. Saad, Majid, Yusof, Duasa, and Rahman (2006) measure the efficiency of Malaysia's life insurance market using data for Takaful and conventional insurance firms. Their findings indicate that conventional firms perform better than Takaful firms and Takaful companies should grow to their optimal size to improve their efficiency score. Kader, Adams, and Hardwick (2009) conduct a DEA to analyse the cost efficiency of 26 Takaful insurance firms in 10 Islamic countries from 2004 to 2006 and indicate that the size of a firm and its board as well as product specialization positively impact Takaful insurance firms' cost efficiency. Ismail, Alhabshi, and Bacha (2011) examine the efficiency of Takaful and conventional insurance firms in Malaysia from 2004 to 2009 and conclude that the efficiency score of Tankful firms is low. Accordingly, they recommend that Takaful companies should decrease their organizational and management expenses to improve their efficiency scores.
Al-Amri, Gattoufi, and Al-Muharrami (2012) analyse the performance of the insurance sector in GCC countries and present a comparative analysis of its different units between 2005 and 2007. Their results reveal that the efficiency of GCC's insurance industry was moderate and there is scope for improvement. However, Al-Amri et al.'s study is limited to four insurance companies and thus, cannot be considered representative of Saudi Arabia's insurance sector. Akhtar (2018) examines the performance of Saudi Arabia's Takaful and conventional insurance companies during 2010-2015 by conducting a DEA and recommend that Takaful and large conventional insurance firms must follow the industry's best practices to improve their efficiency and productivity levels. However, Akhtar considers the production process as a single stage and ignores the intermediate stage, which poses limitations when identifying the sources of inefficiency. Further, Akhtar's (2018) study ignores the fact that the production process of Saudi Arabia's insurance industry, like any insurance sector in the world, is a standard structure comprising two stages, operations and profitability.
Traditional DEA considers the behaviour of decision-making units to be a black box and disregards the intermediate stages, thus detrimentally impacting high overall efficiency scores (Kao, 2009). To overcome this issue, the insurance literature has proposed several DEA frameworks with network systems including internal processes. Kao and Hwang (2008) argue an intermediate stage combining inputs with outputs must be considered in performance analyses to derive a precise overview of insurance companies' performance. Using data on non-life insurance companies from Taiwan, they propose a novel relational DEA approach to evaluate decomposition efficiency in the two-stage production process by considering output variables in the first stage as input variables in the second stage. Cummins, Weiss, Xie, and Zi (2010) employ a two-stage DEA to examine the efficiency scores of insurance firms providing life health and property liability products during 1993-2006. Huang and Martin (2013) evaluate the efficiency of non-life insurance firms in four of the world's fastest growing industries (Brazil, Russia, India, and China) during 2000-2008 using a multi-stage DEA approach. Their study captures inefficiencies attributable to external environmental circumstances, thus implying that country-specific environmental circumstances have a strong effect on the insurance industry. Despotis et al. (2016) present a novel network DEA method to assess multi-stage efficiencies. Their proposed approach overcomes the lack of generality in existing multi-stage DEA approaches and offers unique and unbiased efficiency scores for the two-stage production process while treating each stage equally (Despotis et al., 2016).
However, the two-stage DEA approach has been criticized for failing to define a leader stage. Liang, Yang, Cook, and Zhu (2008) argue the need to understand the relationship among the two stages and conclude that identifying the inefficient stage in a system is important to increase its efficiency by excluding inputs that are actually pending outputs from the efficient stage. Consequently, the authors develop an approach to determine the leader stage between the two stages; more specifically, they extend Despotis et al.'s (2016) study to develop a network DEA with a Pareto solution to examine for the dominant stage.
A survey of the extant literature highlights that research measuring efficiency in multiple stages and identifying the leader stage have neglected the insurance markets, particularly Saudi Arabian insurance market with its two insurance types (conventional and Takaful). Thus, using Despotis et al.'s (2016) approach to estimate two-stage efficiencies, this study evaluates the efficiency of conventional and Takaful insurance companies in Saudi Arabia. In addition, it applies Li et al.'s (2018) proposed approach to determine the leader among the two stages.

Methodology and data description
3.1. Methodology Despotis et al. (2016) propose their composition approach using a bi-objective program model. They use typical DEA scores to determine the ideal efficiency point for each stage and the biobjective program model to locate a point on the Pareto front by minimizing the maximum weighted deviation from the ideal point in the objective function space (Despotis et al., 2016;Li et al., 2018). Unlike existing DEA methods, Despotis et al.'s (2016) approach offers unique efficiency scores and treats each stage equivalently. Figure 1 illustrates the division of the two-stage configuration system into two subsystems of a series, in which the first stage will be the inputs of the second stage.
Consider the following basic notations (Despotis et al., 2016;Li et al., 2018): is the vector of weights for stage-one inputs in the fractional model;  Figure 1. Series of two-stage processes.
intermediate variables in the linear model; ω ¼ ω 1 ; ω 2 ; . . . ; ω s ð Þ is the weights vector for stage-two outputs in the fractional model; u ¼ u 1 ; u 2 ; . . . ; u s ð Þ is the weights vector for stage-two outputs in the linear model; e o j is the overall efficiency of DMU j , e k j is the efficiency of stage k for DMU j , k ¼ 1; 2; E k j is the independent efficiency score of stage k for DMU j , k ¼ 1; 2; e k;L j is the lower bound of stage k's efficiency for DMU j , k ¼ 1; 2; and e k;U j is the upper bound of stage k's efficiency for DMU j , k ¼ 1; 2.
Consider a basic constant-returns-to-scale-DEA (CRS-DEA) model that evaluates the efficiency of the first and second stages to independently assess DMU j o (Despotis et al., 2016;Kao & Hwang, 2008):, s:t: where ε is a non-Archimedean constant (see Amin & Toloo, 2004). Despotis et al. (2016) propose the following bi-objective program model to evaluate the efficiencies of the two stages:, max wZ jo max uY jo wZ jo s:t: Vector ðE 1 j 0 ; E 2 j 0 Þ establishes the ideal point of the bi-objective program (3) in the objective functions space. The optimal solution for model (3) can be achieved using a two-phase procedure, which is equivalent to utilizing lexicographically L∞ and L1 norms (Despotis et al., 2016).
In the first phase, Despotis et al. (2016) assume no specific evidence prioritizing one of the two stages and then employ the unweighted Tchebycheff norm to their assessments as follows:, minδ; s:t: While model (4) is non-linear, it can be easily solved using a bisection search (Despotis, 1996). Let Þbe an optimal solution to model (4) and In the second phase, Despotis et al. (2016) apply an equivalent to utilize the lexicographically L1 norm for the optimal solutions set of model (4) to determine a Pareto optimal solution for Equation (3) as follows:, s:t: In model (5), δ Ã is the optimal value of the objective function in model (4) and w Ã Z jo is the optimal virtual intermediate measure derived by model (4). The optimal solutionv;ŵ;û ð Þfor model (5), which is the Pareto optimal solution from model (3); unit j o 's efficiency scores in the first and second stages; and the overall system efficiency is, respectively, as follows: Sinceê 0 j 0 ¼ê 1 j 0 :ê 2 j 0 ,ê 2 j 0 ¼ê

Data description
This study analyses data for 33 insurance firms listed on Saudi's stock market, Tadawul (www. tadawul.com.sa), of which seven are Takaful firms and 26 are conventional insurance firms. The data are obtained from annual financial reports published by the insurance firms during 2014-2017. For the list of the companies included in this study, see Appendix I.
Drawing on Kao and Hwang (2008) and Akhtar (2018), this study includes the following set of variables: equity (X1), net claims incurred (X2) and general and administrative expenses (X3) are input variables; net premium earned (Y1) and investment and management fee income (Y2) are final output variables; and direct written premium (Z1) and reinsurance premium (Z2) are intermediate variables. The first stage is defined as the operational (or premium) stage, and the second stage is the profitability/investment stage.

Empirical results and discussion
In Tables 1 and 2, the second and third columns present the stage-one efficiency scores, e 1 j ; j ¼ 1; 2 . . . 33, and its rank; the fourth and fifth columns show the stage-two efficiency scores,ê 2 j ; j ¼ 1; 2 . . . 33; and its rank; and the last two columns list the overall efficiency scores, e 0 j ; j ¼ 1; 2; . . . 33, and its rank.
A comparison of the efficiency ranking derived for the two stages (operational and profitability) and the overall efficiency scores for the production process highlights four companies with the overall efficiency of one in both stages during 2014-2016. The results benchmark two Takaful companies, SABB Takaful (No. 31) and Aljazira Takaful Taawuni Co. (No. 29), for 2014 and 2016. Further, Tables 1 and 2 indicate that Bupa Arabia for Cooperative Insurance (No. 10) reports consistent efficiency in both substages and overall efficiency in 2015. In 2017, The Company for Cooperative Insurance (Tawuniya) (No. 21) is benchmarked in the operational stage (first stage) and has high overall efficiency scores during the entire production process. According to SAMA (2017), Bupa Arabia for Cooperative Insurance and Tawuniya are the largest insurance firms (in assets) in Saudi Arabia and operate in diversified business areas (e.g. vehicle, marine, and health insurance as well as protection and savings).
Among the 33 studied firms, Takaful companies are among the top 10 companies in terms of overall efficiency scores and yet, none of them perform efficiently in both sub-processes (see Tables  1 and 2 Evidently, some firms report significant differences in their performance ranking between the two sub-processes. For example, in 2017, AXA Cooperative Insurance Company (No. 9) and SABB Takaful (No. 31) are among the top 10 firms but perform unsatisfactorily in the second stage compared with the first stage. While the overall efficiency assists decision makers in identifying the sub-stage contributing to inefficiencies, it is important to determine the dominant stage. Table 3 shows that the average efficiency scores for Saudi Arabia's Takaful and conventional insurance companies during 2014-2017 is 0.44, which is less than the score (0.61) estimated by Al-Amri et al. (2012) for GCC firms. Similarly, it is less than the average efficiency score (0.83) presented by Akhtar (2018) for both firm types from 2010 to 2014. Thus, exploring production process efficiency in terms of operations and profitability can offer deeper insight, particularly from a managerial perspective.
Table 3 also shows that Saudi Arabia's insurance market is characterized by vast irregularities during the study period, with average efficiency scores for Takaful and conventional firms ranging between 0.05 and 1.00. Determining production process efficiency on the basis of operational and profitability efficiency scores will highlight the desired level of outputs a firm should supply while engaging efficient inputs during the intermediate stage. Table 1-3 present the results. First, the annual average efficiency of Saudi Arabia's Takaful companies is relatively higher than that of conventional insurance companies during 2014-2016. In other words, Takaful insurance firms perform better than conventional insurance firms in the Saudi market. A possible explanation for this result is that companies tend to choose and transform the optimal combination of inputs and intermediate variables into optimal outputs through several lines of insurance business (e.g. motor and health insurance). Thus, as Jamil and Akhter (2016) and Rahman, Akhter, and Khan (2017) highlight, Takaful insurance firms have the opportunity to attract clients who prefer dealing with insurance companies that operate in harmony with Shari'ah principles. Second, the average efficiency for all the insurance firms declines during 2014-2017. Third, about 21% of the firms (6% Takaful firms and 15% conventional insurance firms) are able to maintain their competitive level at an average efficiency score of 0.60 per year. This can be attributed to the decrease in overall economic growth and low interest rates in the country caused by a sharp decline in oil prices in the global market owing to the global financial crisis. In addition, SAMA's new regulation stipulating the "Saudization" of all insurance companies' administrative and non-administrative functions plays a critical role. The lack of Saudi experts in the actuarial sector could be another reason contributing to the decreasing efficiency scores. Saudi Arabia's insurance market is highly fragmented with small firms competing against each other, which hinders the sustainability of the industry. Finally, lower efficiency may be caused by the low levels of penetration and insurance density in the previous years, which in turn, limit insurance revenue. Such firms find it difficult to follow SAMA's new regulations and requirements such as technical underwriting, reserving, and solvency (Akhtar, 2018).
Tables 4 and 5 summarize the results for the leader stage identification. The second and third columns highlight the upper and lower bounds for the stage-one efficiency of In 2017, the investment stage is the leader stage for all Takaful firms and 18 conventional insurance firms, indicating stage-two dominance. It is noteworthy that Takaful and conventional insurance firms that report investment as the dominant stage perform better in 2017. Thus, the dominant investment stage in 2017 for both Takaful and conventional insurance firms could define the efficiency level and accordingly, the input and reserve requirements for the operational stage. However, this is not the case for the years 2014-2016. Consequently, it is necessary to identify the leader stage for each Takaful and conventional insurance firm to gain information on internal decision-making processes, which is occasionally overlooked by decision makers. This approach will help manager and regulators adjust and improve overall efficiency by optimizing the leader stage.

Conclusions
This study aims to analyse Takaful and conventional insurance firms in Saudi Arabia's insurance industry during 2014-2017. To the best of the author's knowledge, this study is the first to use a two-stage DEA (Despotis et al., 2016) to assess the efficiency of the two sub-stages of production with focus on Takaful and conventional industry. In addition, it applies Li et al.'s (2018) extended method to identify whether the operational or profitability stage is the leader stage.
The study offers the following conclusions for the sample period. First, the average efficiency scores for both Takaful and conventional insurance firms have monotonically decreased. Second, a possible solution to low efficiency levels is enhancing the consolidation and foreign participation regulations for the insurance industry so that firms can become dynamic and remain competitive in Saudi Arabia's crowded market. Third, even though Takaful insurance firms perform better than conventional insurance firms in terms of average efficiency scores, there remains scope for improvement in terms of overall efficiency and productivity. Fourth, managers and regulators should take advantage of Takaful/Shari'ah products designed on the basis of the Islam principles of general cooperation and solidarity. Finally, the empirical analysis to identify the leader stage for both Takaful and conventional insurance firms elucidates that optimizing the leader stage is necessary to enhance the balance between the two stages.
This study can assist regulators and managers attempting to improve and develop the overall performance of Saudi Arabia's insurance industry. Further, the empirical results and their implications will help SAMA design clear regulations for a highly competitive environment. Nevertheless, further comprehensive studies are needed given that the insurance sector will be among the major gainers and is among the focus areas of Saudi Vision 2030. Note: The rows highlighted in grey refer to Takaful firms.