American Journal of Mathematics and Statistics
p-ISSN: 2162-948X e-ISSN: 2162-8475
2015; 5(2): 60-71
doi:10.5923/j.ajms.20150502.03
Mohammed Mustapha Wasseja, Samwel N. Mwenda
Kenya National Bureau of Statistics
Correspondence to: Mohammed Mustapha Wasseja, Kenya National Bureau of Statistics.
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Copyright © 2015 Scientific & Academic Publishing. All Rights Reserved.
The importance of life insurance as part of the financial sector and a player in the economy has significantly increased over the last decades, both as a provider of important financial services to consumers and a major investor in the capital market. However, an examination of a few performance indicators, the industry has been inefficient. Inefficiency affects profits through increased waste on resources and earnings thus adversely affecting sustained growth of the industry. Without sustained growth in the industry, a life insurer may not garner the business volume necessary to ensure collective pooling of insurance risk under the law of large numbers upon which the insurance companies operations relies [1]. Understanding the efficiency of the life insurance sector in Kenya is important because an efficient life insurance industry is critical to propel management of risk, promote long-term savings and serve as a conduit to channel funds from policyholders to investment opportunities. The examination of efficiency of life insurance companies will be pivoted on exogenous factors which include: size of the insurance company, the age of the insurance company since it was incorporated, whether the insurance company has been quoted with the Nairobi Stocks Exchange (NSE) and line of specialization of the insurance company. The efficiency over time has been declining for the period of this study. The average level of efficiency has declined from 0.582 in 2004 to 0.499 in 2009. The results from the Mann- Whitney test indicate that this decline is statistically significant. The life insurance sector’s efficiency has thus deteriorated over the study period. The regression analysis of the external factors on efficiency scores using the bootstrapping procedure sheds some light on the possible drivers of efficiency in the life insurance sector. The size of the insurer and stock exchange listing positively and significantly influence the technical efficiency of life insurance firms. Specialization in life insurance and not offering composite insurance negatively affects the insurer efficiency.
Keywords: Efficiency, Insurance, NSE, Kenya
Cite this paper: Mohammed Mustapha Wasseja, Samwel N. Mwenda, Analysis of the Effiency of Life Assurance Companies in Kenya Using the DEA-Model, American Journal of Mathematics and Statistics, Vol. 5 No. 2, 2015, pp. 60-71. doi: 10.5923/j.ajms.20150502.03.
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![]() | Figure 1. Growth of insurance premium |
![]() | Figure 2. Performance Indicators |
![]() | Figure 3. Illustration of the Concept of Efficiency |
A technician is said to be technically efficient if production occurs on the boundary of producer’s production possibilities; it is technically inefficient if production occurs in the interior of the production possibilities set. The term technical inefficiency is used to embrace all reasons for actual performance falling short of the maximum that can be attained using a given set of inputs. In figure 1, the line BB represents the input price, so that the allocative efficiency (price efficiency) of the firm operating at p is defined as:Allocative Efficiency =
The economic efficiency is defined as a product of technical and allocative efficiency, which is overall cost of producing at Q relative to P.Economic efficiency = 
The concept of efficiency is closely linked with the issue of productivity. The productivity of a firm is generally defined as the ratio of the output that is produces to the inputs that is uses. Rising productivity implies either more output is produced with the same amount of inputs, or that fewer inputs are required to produce the same level of output, hence rising efficiency with the outward shift of a production frontier signalling productivity growth.Efficiency MeasureAn attempt to measure firm efficiency started with the research work of [5]. Based on his model, several procedures have been developed over tine to estimate technical efficiency. The most recent of these models are the stochastic frontier analysis (SFA) developed by [6] and data envelopment analysis (DEA) developed by Charnes et al. (1978). The stochastic frontier model requires the specifications of the form of the efficient frontier by assuming a specific functional form. SFA specifies an efficient frontier form usually trans-log and assumes a composed error model where inefficiencies follow an asymmetric distribution and the random error term follows a symmetric distribution, usually normal. DEA puts less structure on the specification of the efficient frontier and does not decompose the inefficiency and error terms.The same characteristics that make DEA a useful analysis tool can also create problems. It is deterministic and gives point estimates that do not provide information about uncertainty in estimation and depends on the correctness of frontier units. Since DEA is a non-parametric technique, statistical hypothesis testing is difficult. [8] proposed a bootstrap procedure as a solution to perform the desired inference under DEA methodology.General level of efficiency over time[9] analyse efficiency of Nigeria’s insurance companies in a two stage DEA model. DEA is widely used to calculate both technical and scale efficiency. The finding indicates that most companies are not the efficient frontier with regards to technical efficiency and two of the insurance companies are scale inefficient. They suggest that insurance companies operating within bank networks tend to have higher efficiency scores which may be explained by the scope economies related to networks. After establishing the efficiency scores, the Mann-Whitney U-test is used to test some hypothesis related to efficiency scores. The hypotheses are with regards to firm size, integration into bank networks and insurer markets share. [10] evaluated the cost efficiency Of Thailand’s life assurance industry using a stochastic frontier approach. They estimated a cost function which constitutes a vector of the output, input price, the inefficiency variable and the random error term to measure how far the life insurer’s cost is relative to its best practice. Inefficiency was then modelled as a function of firms’ specific variable by regressing it on firm specific variables. These variables are age of firms, firm size and a dummy variable for financial crisis. They found that the industry is on average 60% inefficient. They also investigated the relationship between efficiency and profitability and concluded that inefficiency has substantial effect on profitability of life insurers. [11] examine the effects of increasing competition on the structure of the UK life assurance industry over 1989-1993 by employing a stochastic frontier approach. He reports high levels of economic inefficiency (costs are on average about 30% above the estimated cost frontier) and significant positive economies of scale. He argues that the principal beneficiaries from the European single market are likely to be large companies with lower levels of economic inefficiency. [12] measured efficiency of property insurer in the US by estimating a stochastic cost frontier. The results show that insurers operate in a narrow range around an average efficiency level of around 90% relative to their cost frontier. Large insurers over-produce loss settlement services, while small and medium-size insurer’s under-produce this output. The small insurers are characterized by economies of scale, suggesting the potential for cost reduction from consolidation in the industry.Effects of Regulatory Change[13] measure the relative technical efficiency of the Greek insurance industry by means of DEA to analyse the effects of deregulation on the efficiency. The analysis is based on a two stage procedure to regress the efficiency scores to examine the hypotheses that insurance is determined by different contextual variables. They use the double bootstrap procedure in a truncated regression to analyse the effects of environmental factors on efficiency of the Greek insurance market. The external variables used are ownership structure, size, stock exchange listing, market’s share and capital structure. Market share is found to have positive effects on efficiency. [14] measured cost efficiency in the European insurance sector using stochastic frontier analysis and explored variations in efficiency in relations to firm size and market structure. They estimated a flexible form frontier assuming a flexible frontier functional form for the three main business types observed in the EU: life, non-life and composite insurers to measure the impact of liberalization of the European insurance market. They find strong evidence that x-inefficiency of specialist insurer’s increase with firm size. The degree of x-inefficiency for composite firms in low and varies with size. [15] studied the impact of the WTO accession in 2001 by China on technical efficiency of China’s insurance industry using DEA. They used a panel data set of 22 firms the period of 1999-2004, to evaluate their technical efficiency scores. An econometric model was then applied to identify the key determinants of technical efficiency. The results indicated that firm’s size, ownership structure, mode of business and human capital are important factors affecting firm’s efficiency. [16] analysed whether changes in market structure and regulatory environment had an influence on the production performance of Austrian insurance companies over 1994-1999 by employing a Bayern stochastic frontier. They show that the process of deregulation had positive effects on the production efficiency of the Austrian insurance companies. [17] investigate the impact of the single market project of the EU on the German insurance industry efficiency over 1992-1996 by employing DEA and Malmquist analysis[18]. Total factor productivity was found to have increased by 12.8%. [19] studied the effects of deregulation and consolidation on Spanish insurance industry efficiency over 1989-1998 by using DEA and Malmquist indices. They reported a low average cost efficiency of 22.7% in 1998, which is mainly due to low allocative efficiency, 41.2% in the same year (1998). Moreover, firms in the largest size quartile were found to be more cost effective due to higher pure to higher.
Such that

![]() | Figure 4. |
can be derived by solving the following linear programming equation.
i=1,….,n firmsWhere
is a vector of output,
is a vector of inputs, λ is a 1 ×1 vector of constants. The value of
obtained is the technical efficiency score for the ith firm. A measure of
indicates that the firm is technically efficient and otherwise inefficient. This paper utilizes the multi-stage DEA approach which is recommended to handle the problem of slack variables as it is invariant to units of measurement [20]. Data Source and VariablesThis study uses secondary data from 20 life assurance companies in Kenya obtained from Insurance Regulatory Authority for the period 2004-2009. In a bid to use balanced panel Data in the analysis, first insurance and Pan African life insurance companies were left out since they controlled a combined market share of 14%. The 2 insurance companies were not in existence over the study period considered.The most important advantage for using panel data as opposed to cross section data is that it leads to better efficiency analysis as each firm is observed more than once over a period of time and it contains more observations. This enables us to have a better analysis of the determinants of efficiency.The choice of the inputs and the output is guided by the literature review. Labour, business services and material, debt capital and equity capital are used as inputs. The collection of the data was purposive, and therefore, labour and business services are combined as operating expenses (including commission). This simplification is present in other studies [14], [16], [22] among others.As it is evident from most studies on efficiency of life insurance industry, value added approach is used to determine outputs [22]. A good proxy for measuring the output of life insurers is the value of net incurred benefits plus additions to reserve for life insurance. The output variable, which proxies the intermediation function, is the value of total investments.The BootstrapDEA efficiency scores are sensitive to sample composition incase of finite samples. The efficiency scores are also correlated with each other, as the calculation of efficiency of one form incorporates observation of all other firms in the same data set. This renders standard inference approach invalid. Bootstrapping, as described by [8] has been used to analyse the sensitivity of the results. [8] extended this by proposing the double bootstrapping procedure which solves the dependency problem and provides valid estimates for the parameters in the second stage regression. This second bootstrap procedure is used to analyse the impact of external factors on efficiency. Use of Ordinary Least Square regression to estimate this relationship may lead to incorrect statistical inference because the DEA score are correlated with each other as the calculation of efficiency of one insurer takes into account all other insurers in the data set. The procedure applied in this study follows [8].Determinants of EfficiencyTo examine how external factors affect the level of efficiency, we use a two-step approach described by [8] and used by [13]. The efficiency scores derived above are bootstrapped to obtain bias-corrected DEA efficiency scores which are then regressed on the external factors. This has been formulated as:
Where
represents the bootstrap efficiency score. Following [1] and [10], size is taken as the natural log of the total assets of the respective insurer. Size is included among the explanatory variable to account for the association between size and economies of scale in the life insurance industry. Larger insurers have the advantage of economies of scale and therefore, we expect the size coefficient to be positive. Quoted is a dummy variable which is one for companies quoted in the stock exchange and it aims at capturing the effects of stock market governance and disclosure requirements on efficiency. Firms quoted in the stock market are expected to be more efficient given the additional oversight requirement from the capital market regulations. Some insurers only transact only on life insurance while others are composite insurers. Existing literature is conflicting as to whether specialization on one line of insurance increases insurers efficiency or not. [22] found that, multiple-line insurers are more efficient while [19] concluded that diversifying in different lines of business is not better than a strategic focus on one line of insurance. Focus is a dummy variable which equals to 1 for insurers who specialize only on life insurance and 0 for composite insurers. Age denotes the number of years a firm has been in the life insurance business. Following [10] study results, older insurers are expected to be more efficient given the experience in the business. Older firms are more efficient because of learning-by-doing. The coefficient of this variable is thus expected to be positive.
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![]() | Figure 5. Efficiency over time |
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The coefficient for size was positive and significant at 5% significance level. This means that the size of the life insurance firm positively affects efficiency. Large insurers are more efficient than small life insurance firms. This finding supports [10] and [15]. Since some life insurers in Kenya are relatively small in size, consolidation in this sector can lead to increased efficiency. Firms that are listed on the stock exchange are expected to be more efficient. From our results, the coefficient for Quoted is positive and also significant at 5% level of significance. A quoted firm on the Nairobi Stock Exchange can benefit from the enhanced corporate governance and other transparency requirements by the capital market regulator and also increased shareholder expectation with regard to its performance. This then leads to enhanced level of efficiency of the insurer. The coefficient for Focus is negative and significant. From our results, insurance firms in Kenya that specialize in only life insurance and are thus not composite insurers are less efficient than composite insurers. The results obtained in this study are similar to those obtained by that [22] who did a cross country study of 36 countries and found out that multi-line insurance firms are more efficient than specialized ones. Age is not significant at 5% and 10% level of significance indicating that the age of life insurance firms does not matter to efficiency. These results are similar to the findings of [10] in their study of life insurance sector in Thailand.Controlling for the independent factors that are not significant, the model reduces to:
This multi regressive model does not include the constant and the independent factor age since they are not significant at 5% level of significance and therefore they been left out.