1 Applied Maematical Sciences, Vol. 7, 2013, no. 23, HIKARI Ltd, Relative Efficiency Analysis Industry of Life and General Insurance in Malaysia Using Stochastic Frontier Analysis (SFA) Wan Muhamad Amir W Ahmad, Mohamad Arif Awang Nawi and Nor Azlida Aleng Department of Maematics, Faculty of Science and Technology, Malaysia, Universi Malaysia Terengganu (UMT), Kuala Terengganu, Terengganu, Malaysia Abstract Insurance is a form of risk management in which e insured transfers e cost of potential loss to anoer enty in exchange for monetary compensation known as e premium. The purpose of e current study is to measure e relative efficiency of life and general insurances in Malaysia by using SFA referring to Battese and Coelli model for e year 2007 until 2009, consist of 13 life and 26 general insurance companies. All data were analyzed using e software FRONTIER to obtain e maximum likelihood (ML) and to get e relative efficiency of e life and general insurance company. The finding for life insurance showed at Mayban Life is at rank 1 for e ree years and is insurance company has a relative efficiency score higher an most oer companies. Overall results shown at every year ere are an increasing from 1% to 17% for each year in life insurance industry and shows at e performance of life insurance industry are in a good condion. For general insurance, Oriental Capal Assurance Bhd (OCA) is at rank 1 for e ree years and is insurance company has a relative efficiency score higher an most oer companies. Overall results shown at every year ere are an increasing from 0.02 (2%) to
2 1108 Wan Muhamad Amir W Ahmad et al 0.04 (4%) for each year in general insurance industry and shows at e performances of general insurance industry are in a good condion. The value for e variance gamma ( γ ) parameter in is study is far from one, suggesting at all of e residual variations are not due to e inefficiency effects, but to random shocks. It can erefore, be concluded at e technical inefficiency effects associated wh e production of e total profs by e input of e general insurence are very low. This study can be used as a benchmark in determining e efficiency of insurance companies in Malaysia. Key words: efficiency, stochastic frontier analysis, Battese and Coelli model, life and general insurance INTRODUCTION Life insurance provides financial protection to a person against unforeseen circumstances such as dea. Life insurance is a contract between e acquirer policy wh an insurance company as e insurer, to pay a certain sum, togeer wh bonus, when is policy is due or e insured's dea. The coverage period for life insurance is more an a year. This means at e periodic premium payments monly, quarterly or yearly to be paid by e insured. Examples of ose covered by life insurance are dea during e policy period, earnings at retirement, illness and disabily . General insurance comprises insurance of property against fire and burglary, floods, storms, earquakes and so on. It covers personal insurance as well as insurance against accidents and also covers heal insurance and liabily insurance which guards legal liabilies. Then again covers oer areas such as errors and omissions, insurance for professionals, cred insurance etc. Most general insurance policies are annual and e premium payment is in advance. No risk commences unless you have paid e premium. In some long term policies companies have e facily of collecting premiums periodically . Specific Objectives This study aims to measure e relative efficiency of 13 life and 26 general insurance companies in Malaysia from 2007 to The main objectives identified are as follows: i. Measure e relative efficiency of performance for e life and general insurance industry. ii. Identify e most efficient companies based on relative efficiency scores. iii. Analyze e comparative efficiency of insurance companies in Malaysia.
3 Relative efficiency analysis industry 1109 LITERATURE REVIEW Fetcher et al.  has been using e Stochastic Frontier Analysis (SFA) to analyze e cost and efficiency of life insurance and general insurance in France using data from 1984 to From e study found at e average level of efficiency for life insurance is 30% and general insurance is 50%. Greene and Segal  have examined e relationship between cost inefficiency and prof for e life insurance industry in Uned States. Prof is important for an insurance firm because of capal gains and determines e potential of a firm. Greene and Segal  distinguish e cost of efficiency by using stochastic frontier (SF) where is meod using inefficient means for searching e diversy of firms and output. They also propose at e cost efficiency in e life insurance industry will become stronger when e turnover and inefficiency occurs where e gain is measured by return on equy. Fenn et al.  has uses stochastic frontier analysis to estimate Flexible Fourier cost and prof functions for European insurance companies. They also adopt a maximum likelihood approach to estimation in which e variance of bo one-sided and two-sided error terms is modeled jointly wh e frontiers. This approach causes at simultaneously control for e impact of heteroscedasticy on e estimation of scale economies as well as estimating e effect of firm size and market structure on X-inefficiency. Separate frontiers are estimated for life, nonlife and composes companies and using a set data from e financial reports for e period 1995 to This provides technical and nontechnical accounts at year-end for life, non-life and compose insurance businesses in 14 major European countries. The result show at estimates most European insurers are operating under condions of decreasing costs, and at company size and market share are significant factors determining X-inefficiency wh respect to bo costs and profs. Fenn et al.  also state at e larger firms and ose wh high market shares tend to have more cost inefficiency but less prof inefficiency. Kasman and Turgutlu  investigate e technical efficiency of a sample from Turkish life insurance firms by using DEA (data envelopment analysis), CCDEA (chance-constrained data envelopment analysis) and SFA (stochastic frontier analysis) from 1999 to The main objective is to provide new information on e effect of meodological choice on e estimated efficiency by applying econometric and maematical programming techniques to e same data set of Turkish life insurance firms. The empirical results show at e parametric and non-parametric meods provide similar rankings of firms but ey differ significantly when e mean efficiency scores are considered. From e results suggest at e stochastic structure of e CCDEA approach does not eliminate e fundamental differences between DEA and SFA. Besides at, e ree techniques suggest at ere is a significant inefficiency problem in e Turkish life insurance industry over e sample period.
4 1110 Wan Muhamad Amir W Ahmad et al Shazali and Alias  review e performance of productivy and efficiency e life insurance industry for e communy in Malaysia. This study is an attempt to measure productivy in e life insurance industry based on e meod of Malmquist Non-parametric Index. Just as e manufacturing sector, is sector's future grow depends on s abily to compete efficiently. The abily to provide efficient service is an important source of competive advantage in e era of globalization. The study found at alough e insurance industry productivy is increase but e relative grow of life insurance is still low compared wh e actual grow of e Malaysian economy. Furermore, e efficiency of technology development and contribute to e overall productivy in e industry. SPECIFICATION OF STOCHASTIC FRONTIER MODEL Berger et al.  and Berger and Humphrey  have introduced two techniques to measure efficiency. There are several econometric (parametric approach) and linear programming (nonparametric approach). The parametric approach has e advantage of allowing noise in e measurement of inefficiency. However, e approach needs to specify e functional form for production, cost or prof. Coelli  state at e non-parametric approach is simple and easy to calculate since does not require e specification of e functional. The meod for is study is Stochastic Frontier Analysis (SFA) by using e model of Battese and Coelli . SFA is a way in economic modeling. Aigner et al. , Meeusen and van den Broeck , and Battese and Cora  introduced e parametric approach to estimate stochastic production frontiers. These approaches specified a parametric production function and a two-component error term. One component, reflecting e influence of many unaccountable factors on production as well as measurement error, is considered noise and is usually assumed to be normal. The oer component describes inefficiency and is assumed to have a one-sided distribution, of which e conventional candidates include e half normal , truncated normal , exponential  and gamma . Battese and Coelli  assume a tradional random error ( V ) and a nonnegative error term ( U ) representing e technical inefficiency. Here, V is assumed to be independent and identically distributed, i.i.d N (0, σ 2 v) and captures statistical noise, measurement error, and oer random events (i.e., economic suations, quakes, weaer, strikes and luck) at are beyond e company s control. The non-negative error term ( U ) captures e inefficiency and is assumed to be i.i.d as truncations at zero of e N (µ, σ 2 U). Also, V is assumed to be independent of eu. The model may be formed as follows: Y = X β + ( V U ) i = 1,..., K; t = 1,..., T
5 Relative efficiency analysis industry 1111 where Y is output of e i firm in e t time period; X is a K 1vector of inputs of e i firm in e t time period; β is a K 1 vector of unknown parameters; V and U are assumed to have normal and half-normal distribution, respectively. This meod can compile e efficiency of e insurance company according to s function and not using a specific distribution function. Features found in is meod are suable for measuring e efficiency of insurance companies because will be arranged in e most efficient level. Wh e information obtained from is study can help rehabilate e making of new policies for improvement and furer enhance e grow of e life and general insurance industry in Malaysia. The stochastic frontier model to panel data which can be expressed as: lny = β + β1 ln x1 + β 2 ln x2 + β3 ln x3 + β 4 ln x4 + β5 ln x5 where, Y β + ( V U 0 = total profs of companies of e = vector of unknown parameters to be estimate i company in e x = net investment income of e 1 i company in e x 2 = total liabilies and assets of e i company in e x 3 = management expenses of e i company in e x = annual premium of e 4 i company in e x 5 ) t time period t time period t time period t time period t time period = net claims paid by e company of e i company in e t time period U = non-negative random variables, associated wh technical inefficiency of total profs of companies. V = assumed to be independent and identically distributed (i.i.d) N (0, σ 2 v) and captures statistical noise, measurement error, and oer random. Battese and Coelli  has proposed a stochastic frontier production function is defined for panel data on firms, in which e non-negative technical inefficiency effects are assumed to be a function of firm-specific variables and vary over time. The inefficiency effects are assumed to be independently distributed as truncations of normal distributions wh constant variance, but means which are a linear function of observable firm-speciflc variables. The generalized likelihoodratio test is considered for testing e null hypoeses, at e inefficiency effects are not stochastic or at ey do not depend on e firm-specific variables. Reviews of e lerature of ese studies are as Forsund, Lovell and Schmidt ,
6 1112 Wan Muhamad Amir W Ahmad et al Schmidt , Bauer  and Greene . The maximum-likelihood meod is applied for e estimation of e parameters of e model and e prediction of e technical efficiencies of e firms over time. This meod gives more satisfactory results as more efficient an e meod of ordinary least squares (OLS) . Parameters (γ ) must be in e range between 0 and 1. Parameters for e stochastic production function estimated using e maximum-likelihood estimation meod and e calculation by using e Frontier Version 4.1c . In is study, e parameter γ is important because facilates e analysis of e efficiency of life and general insurance companies to be studied efficiently or not. The test statistic t and t distribution are used. Significance level used was = The hypoesis of e study is as follows: H 0 : γ = 0 (Technical inefficiency of e insurance company investigated) H : γ > 0 (Technical efficiency of e insurance company investigated) 1 RESULTS ANALYSIS This study discusses about e life and general insurance company industry where efficiency score indicates e highest value is e most efficient and reflects e company is able to maximize e input which is very well whout any problems. This time period was chosen because e time had remained in a stable phase after a variety of e economic recovery process in Malaysia. The results showed an increase from year to year as shown in Table 1 and Table 2 for bo insurance company. This posive improvement show at e insurance industry has been in high demand among e people. It was found at all bo insurance companies to perform as indicated when eir efficiency is at 0.8 or 80% and above. The result showed at MAYBAN LIFE company is at rank 1 for e ree years and has a relative efficiency score higher an most oer companies. Efficiency scores for MAYBAN LIFE company starts from 0.97 in 2007 and increased to 0.99 in Score for e second posion is GREAT EASTERN company, MAA company and MCIS ZURICH company. All ree of ese insurance companies get score as much as 0.90 in 2007 and increased to 0.99 (rank 1) in year 2008 and Besides at, Uni Asia Life obtain a score of 0.95 in 2007 (rank 3). In 2008 e UNI ASIA LIFE showed an increase of 0.03 (0.98) and in 2009 e score was 0.99 (rank 1). The last posion is CIMB AVIVA company obtained score 0.74 (rank 9) in 2007, 0.91 (rank 5) in 2008 and 0.97 (rank 3) in Mean of efficiency score of life insurance companies were increasing from year to year presented in Table 1. Every company indicates good performance by e year to manage e company's management expenses as well as possible in order to prof e whole companies. The performance efficiency of e life insurance industry increased by an increase of 0.1 (1%) to 0.17 (17%).
7 Relative efficiency analysis industry 1113 Table 1: Relative Efficiency Score for Life Insurance Companies from Year 2007 to 2009 No. Insurance Companies Efficiency Score Rank ALLIANZ LIFE AXALIFE CIMB AVIVA ETIQA GREAT EASTERN HONG LEONG ING MAA MANULIFE MAYBAN LIFE MCIS ZURICH PRUDENTIAL UNI ASIA LIFE Mean of efficiency score Sources: Model Output Display by Battese and Coelli (1992) The result showed at Oriental Capal Assurance Bhd (OCA) is at rank 1 for e ree years and has a relative efficiency score higher an most oer companies. Efficiency scores for OCA company starts from 0.94 in 2007 and increased to 0.97 in Score for e second posionis BERJAYA and MUI CONTINENTAL. All two of ese insurance companies get score as much as 0.92 in 2007, increased to 0.94 for year 2008 and 0.96 in Besides at, Pacific & Orient (P & O) insurance obtain a score of 0.91 in 2007 (rank 3). In 2008 e P & O insurance company showed an increase of 0.03 (0.94) and in 2009 e score was The last posion is PROGRESSIVE company obtained score 0.86 (rank 8) in 2007, 0.90 (rank 6) in 2008 and 0.93 (rank 5) in Mean of efficiency score of general insurance companies were increasing from year to year presented in Table 2. Every company indicates good performance by e year to manage e company's management expenses as well as possible in order to prof e whole companies. The performance efficiency of e general insurance industry increased by an increase of 0.02 (2%) to 0.04 (4%) per year.
8 1114 Wan Muhamad Amir W Ahmad et al Table 2: Relative Efficiency Score for General Insurance Companies from Year 2007 to 2009 Insurance Companies Efficiency Score Rank ACE AGIC AXA BERJAYA ETIQA GREAT EASTERN HONG LEONG ING JERNIH KURNIA LONPAC MAA MCIS ZURICH MUI CONTINENTAL MULTI-PURPOSE OAC OCA P&O PACIFIC PROGRESSIVE PRUDENTIAL QBE RHB BH INSURANCE TOKIO MARINE UNI.ASIA GENERAL Mean of efficiency score (Sources: Model Output Display by Battese and Coelli, 1992) Table 3 presents e maximum likelihood estimate (MLE) for e parameters of e linear production function and realated statistical tests results obtained from e stochastic frontier analysis. For e life insurance, e value of gamma (γ ) for e meod of maximum likelihood estimate is equal to The result obtained from testing e hypoesis of a life insurance company is calculated t statistic is and is greater an e crical value of t statistics (t calculated = > t5 %, 39 = ). Therefore, e null hypoesis is rejected at significance level This indicates a significant relationship between net
9 Relative efficiency analysis industry 1115 investment income, management expenses, annual premium and net claims paid by company. Can be concluded at e life insurance company in 2007, 2008 and 2009 was at an efficient level. Results of maximum likelihood estimation (MLE) found at e elasticy of e total profs for management expenses is e highest This means at wh an increase 1% in input management expenses will increase by % on e profabily of life insurance companies. For e input of e net investment income, e elasticy of e total prof is This means at 1% increase in net investment income input resulted in an increase of 0.375% on e profabily of insurance companies. The result obtained from testing e hypoesis of a general insurance company is calculated t statistic is and is less an e crical value of t statistics (t calculated = > t1 %, 78 = ). Therefore, e null hypoesis is not rejected at significance level This indicates is not significant relationship between net investment income, management expenses, annual premium, total liabilies and assets and net claims paid by company. The value for e variance gamma ( γ ) parameter in is study is far from one, suggesting at all of e residual variations are not due to e inefficiency effects, but to random shocks. It can erefore, be concluded at e technical inefficiency effects associated wh e production of e total profs by e input of e general insurence are very low. Nevereless, e gamma which is statistically significant suggests at e tradional (OLS) function is not an adequate presentation. Results of maximum likelihood estimation (MLE) found at e elasticy of e total profs for annual premium is e highest This means at wh an increase 1% in input annual premium will increase by % on e profabily of general insurance companies. For e input of e net investment income, e elasticy of e total prof is This means at 1% increase in net investment income input resulted in an increase of % on e profabily of general insurance companies. Table 3: Results of maximum likelihood estimation (MLE) Parameters Coefficient t-ratio Life General Life General Constant β 0 = β 0 = * Net investment income β 1 = β 1 = * ** Total liabilies and assets β 2 = β 2 = Management expenses β 3 = β 3 = * Annual premium β 4 = β 4 = * ** Net claims paid by e company β 5 = β 5 = * Gamma γ = γ = * Significantat level, 0.05*, 0.01**
10 1116 Wan Muhamad Amir W Ahmad et al DISCUSSION AND CONCLUSION This study focuses on stochastic frontier analysis approach (SFA) at involves econometric meods used to analyze e efficiency of life insurance companies in Malaysia. Battese and Coelli model (1992) is measure to investigate e relative efficiency of life insurance companies over e period 2007 to From e study, e relative efficiency for life insurance companies have been increasing from year by year. Companies who posted scores e highest relative efficiency for life insurance is Mayban Life company wh e score 0.97 in 2007 and 0.99 in 2008 and In addion, e efficiency performance of e life insurance industry increased by an increase from 0.1 (1%) to 0.17 (17%) by year. Companies who posted scores e highest relative efficiency for general insurance is Oriental Capal Assurance Bhd (OCA) is at rank 1 for e ree years and has a relative efficiency score higher an most oer companies. Efficiency scores for OCA company starts from 0.94 in 2007 and increased to 0.97 in In addion, e efficiency performance of e general insurance industry increased by an increase of of 0.02 (2%) to 0.04 (4%) by year. The value for e variance gamma ( γ ) parameter in is study is far from one, suggesting at all of e residual variations are not due to e inefficiency effects, but to random shocks. The results of is study also assessed by looking at e efficiency score. According to e rank of efficiency included in is study will help people in selecting and evaluating life insurance companies at have good performance and also will help e management and administration of insurance firms involved in making and improves e weaknesses, such as formulating business strategy or marketing strategy to attract customers who can benef e firm. As conclusion, is stdy can be used as a benchmark in determining e efficiency of insurance companies in Malaysia, according to e appropriate model. REFERENCES  Aigner, D. Lovell, C. A. K & Schmidt P. Formulation and estimation of stochastic frontier production function models. Journal of Econometric 6 (1977), ArticleWorld. General Insurance. May Available at.  Battese, G. E., & Coelli, T. J. Frontier production functions, technical efficiency and panel data: Wh application to paddy farmers in India. Journal of Productivy Analysis 3 (1992),
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